AGRICULTURAL POLICY: A LINEAR PROGRAMMING
APPLICATION TO GUATEMALA

BY
HILDA YUMISEVA

A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF

THE UNIVERSITY OF FLORIDA

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE

DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA
1981

ACKNOWLEDGEMENTS

I wish to express my grateful appreciation to my graduate commit-
tee, Drs. Max R. Langham, Chris 0. Andrew, W. W. McPherson, and David
Denslow, for their assistance and guidance throughout my period of
graduate study and research. Special thanks are due to my chairman,
Dr. Max R. Langham, for his constructive suggestions and enormous
patience in going through the revisions of this manuscript, and to my
co-chairman, Dr. Chris 0. Andrew, for the encouragement he provided.

1 am indebted to Messrs. Carlos Pomareda and Peter Hazell from the
World Bank for sharing their knowledge in the earlier stages of this
research while I worked at the Secretariat of Central American Economic
Integration (SIECA) in Guatemala City. While I wish to acknowledge my
great indebtedness to those who helped me, I alone am responsible for
whatever errors might remain.

TABLE OF CONTENTS

Page
ACKNOWLEDGEMENTS

LIST OF TABLES

LIST OF FIGURES

' • vxxx

LIST OF ABBREVIATIONS

EQUIVALENCIES AND SYMBOLS , ±

ABSTRACT

xxi

CHAPTERS

I INTRODUCTION

1

II OVERVIEW OF THE GUATEMALAN ECONOMY 5

III THEORETICAL BACKGROUND 17

Mathematical Programming Model . 17

Risk Considerations 29

Areas for Further Improvement 40

Multi-level Programming , 40

Incorporating Income 44

Empirical Applications: Supply Response 47

IV THE LP MODEL OF GUATEMALA 55

Specification of the Production and

Transformation Block 55

Production Groups 56

Production Technologies 60

Transformation Activities 60

TABLE OF CONTENTS (Continued)

Page

Specification of Inputs , . . . . 62

Labor , 53

Other Inputs . « »...,.,,,.. 66

Input Prices , t 68

The Specification of Demand and Product Prices 70

The Risk Matrix , , _ 73

V MODEL VALIDATION AND RESULTS 79

VI EMPIRICAL TESTING 86

Estimation of Supply Elasticities . 86

Supply Response to Changes in the Price of

Maize 97

Supply Response to Changes in the Price of

Cotton , 102

Effects of Expanding the Cotton Area 108

Effect of Risk on Supply Response ..... 116

Comparative Advantage 120

VII SUMMARY AND CONCLUSIONS 125

Summary 127

Conclusions , 128

Areas for Further Research 154

APPENDICES

A STATISTICAL TABLES ... 134

B EQUATIONS OF THE MODEL ..... 154

BIBLIOGRAPHY , f 169

BIOGRAPHICAL SKETCH , 177

LIST OF TABLES

Table

Page

1 Estimated Land Tenure Pattern in Guatemala,

1970 13

2 LP Tableau for a Single Product 26

3 Capitalize: Intermediate Inputs as Percent of
Variable Costs, Technological Possibilities in

MAYA 61

4 Economically Active Population in Guatemala by-
Category and in Agriculture, by Group 65

5 Labor Restrictions in MAYA 67

6 MAYA Input Prices 69

7 Given Income Elasticities and Calculated Price
Elasticities Using Frisch's Method 74

8 Domestic, Import, and Export Prices in MAYA 77

9 Price Response to Different Values <j> 83

10 Quantity Response to Different Values of <j> 85

11 Supply and Price Response to Variations in the

Price of Maize as Estimated with MAYA 88

12 Supply and Price Response to Variations in the

Export Price of Cotton as Estimated with MAYA 91

13 Arc Elasticities of Supply of Selected Products

as Computed from Estimates Obtained with MAYA 93

14 Arc Elasticities for Maize and Beans as
Computed from Estimates Obtained with MAYA, by

Group 96

15 Production, Yield, and Employment Response to
Variations in the Price of Maize as Estimated

with MAYA, by Group 98

Table

18

LIST OF TABLES (Continued)

Page

16 Arc Elasticities of Supply of Cotton as

Estimated with MAYA, by Group 105

17 Area, Production, and Domestic Price Response
to Variations in the Export Price of Cotton as

Estimated with MAYA, by Group , 107

Labor Supply Response to an 8% Increase in

Cotton Area as Estimated with MAYA, by Group m

19 Area and Production Response to an 8% Increase
in Cotton Area as Estimated with MAYA, by

Group 2_±3

20 Welfare Indicators in the Base Period and
After an 8% Increase in Cotton Area as

Estimated with MAYA 115

21 Profitability of Selected Products in

International Trade as Estimated with MAYA 122

22 Ranking of Products According to Exchange
Cost Calculations Using Estimates Obtained

with MAYA 124

APPENDIX A

I Gross Domestic Product and Trade in Guatemala

by Selected Sectors, 1965-1978 .,..,..,,,,,, 134

II Gross Fixed Capital Formation in Guatemala by

Sector, 1969-1978 , , , , , , 135

III Gross Domestic Product of Guatemala by

Expenditure Category at Current and Constant

Prices, 1967-1979 . . . , 136

IV Guatemalan Agricultural Statistics by Selected

Crops, 1965-1978 , 137

V Basic Grains Guaranteed Prices, Purchases as
Percent of Total Production, and Sales as
Payment of Total Consumption by the National
Agricultural Marketing Institute (INDECA) of
Guatemala, 1971-1978 140

LIST OF TABLES (Continued)

Takle Page

VI Variables Included in MAYA 141

VII Transformation Coefficients and Transformation

Differentials Used in MAYA 144

VIII Labor Restrictions in MAYA per Month, by Group 145

IX Demand Functions in MAYA 146

X Average Prices Received by Farmers in

Guatemala, by Group, 1966-1977 147

XI Cropped Area Response to Different <J> Values as

Estimated with MAYA, by Group 149

XII Production Response to Different <f> Values as

Estimated with MAYA, by Group 150

XIII Area and Technology Response to Different Maize

Prices as Estimated with MAYA, by Group 151

XIV Yields, Input Use, and Risk per Hectare for

Selected Activities in MAYA, by Group 152

APPENDIX B

XV Symbols Used to Define Variables in MAYA 156

vii

LIST OF FIGURES

Figure

Page

1 Political Map of Guatemala 6

2 Area under the Demand Equation (W) and Total

Revenue Function (R) 23

3 Rotation of the Demand Function and Its Effect

on the W Function 27

4 Linearized Programming Problem with Risk 41

5 Overview of the MAYA Model 58

6 Labor Market in MAYA 64

7 Supply Response to Variations in the Price of

Maize as Estimated with MAYA 89

8 Maize Supply Response by Group as Estimated

with MAYA 90

9 Hypothetical Graph Showing Response Associated
with the Increasing Slope of the Demand

Function # 94

10 Total Area Response of Maize, Beans, and
Associated Maize and Beans to Variations in
Price of Maize Using Estimates Obtained with

MAYA 100

11 Maize Yield Response to Variations in Its Own
Price, by Group Using Estimates Obtained with

MAYA 101

12 Supply Response Functions for Cotton as

Estimated with MAYA 104

13 Monthly Distribution of Labor Use in Group 3 with
Base Solution and with an 8% increase in Cotton

Area as Estimated with MAYA 112

14 Supply Response Functions with and without Risk

Using Estimates Obtained with MAYA 117

LIST OF ABBREVIATIONS

AID

ANACAFE

BANDEGUA

BANDESA

CACM
CHAC
CNA

DGE

DIGESA

ECID

FAO
FERTICA

GDP
IBRD

IDB
ICTA

US Agency for International Development

National Coffee Association

(Asociacion Nacional del Cafe)

Guatemalan Banana Exporting Company
(Bananera de Guatemala)

National Agricultural Development Bank
(Banco Nacional de Desarrollo Agricola)

Central American Common Market

Mexican Agricultural Model

National Cotton Council

(Consejo Nacional del Algodon)

Directorate General of Statistics
(Direccion General de Estadistica)

General Directorate for Agricultural Services
(Direccion General de Servicios Agricolas)

Center for Central American Integration and
Development Studies

(Estudios Centroamericanos de Integracion y
Desarrollo)

Food and Agricultural Organization

Central American Fertilizer Company
(Fertilizantes Centroamericanos)

Gross Domestic Product

International Bank for Reconstruction and
Development

Inter-American Development Bank

Institute of Agricultural Science and Technology
(Instituto de Ciencia y Technologia Agricola)

LIST OF ABBREVIATIONS (Continued)

IMF
INDECA

INTA

MAYA
MOCA

SIECA
SGCNPE

International Monetary Fund

National Agricultural Marketing Institute
(Instituto Nacional de Comercializacion
Agricola)

National Institute for Agrarian Transformation
(Instituto Nacional de Transf ormacion Agraria)

Guatemalan Agricultural Model

Central American Agricultural Model
(Modelo Centroamericano)

Secretariat of Central American Economic
Integration

(Secretaria de Integracion Economica
Centroamericana)

National Economic Planning Council

(Secretaria^General del Consejo Nacional de
Planif icacion Economica)

EQUIVALENCIES AND SYMBOLS

1 quetzal (Q) = 1 US dollar
1 ton = 1 metric ton

ha hectare
kg kilogram
G Farm group

Close to zero

Not available

Abstract of Dissertation Presented to the Graduate Council

of the University of Florida in Partial Fulfillment of the Requirements

for the Degree of Doctor of Philosophy

AGRICULTURAL POLICY: A LINEAR PROGRAMMING
APPLICATION TO GUATEMALA

By

Hilda Yumiseva

December, 1981

Chairman: Max R. Langham

Co-chairman: Chris 0. Andrew

Major Department: Food and Resource Economics

This study develops a mathematical programming model of the
Guatemalan agricultural sector (MAYA) for the 1976-1977 period and uses
it to simulate policy. The main objectives were (a) to determine the
optimal pattern of production and show the bias involved when risk-
averse behavior is ignored, and (b) to estimate the effects of different
policies.

MAYA consists of three subsectors based on farm size and technology,
producing 13 annual crops — which could be produced under several tech-
niques and represent 90% of the value of Guatemala's total agricultural
production. These subsectors were linked by an objective function and
by intersectoral transfers of products and inputs. Crops were either
sold directly or transformed. Eighteen final products could be sold in
the domestic market or exported.

The basic optimizing market equilibrium formulation of the model
assumes that producers are profit maximizers and that consumers'
behavior is described by demand functions. This formulation was
modified by introducing risk-averse behavior.

To demonstrate the uses of MAYA several experiments were conducted.
Supply responses to variations in the prices of maize and cotton were
analyzed for selected crops, and technological change was discussed in
detail. Another experiment tested the effects of expanding the area
planted with cotton in order to increase farmers' incomes and employment.
Finally, MAYA was used to obtain schedules of comparative advantage in
international trade. The conclusions drawn from these experiments were
(a) as product prices increased, farmers tended to adopt higher yielding,
more input-intensive techniques which were also riskier; (b) less
advanced farmers behaved no differently from the more advanced ones;
(c) a policy to increase incomes and promote employment through in-
creased cotton production would only be effective in the short run, as
in the long run prices rose cancelling the initial effects; and (d)
Guatemalan agriculture is rather competitive in international markets.

The study demonstrated that mathematical programming models can be
effective tools for planners in underdeveloped agriculture. Their
usefulness could be improved if they were considered within the multi-
level framework — maximizing a set of goals subject to a behavioral
problem — and if income were explicitly incorporated in their formulation.

CHAPTER I
INTRODUCTION

Agricultural policies in Guatemala have been carried out in a
haphazard manner intended to achieve a host of different and often
divergent purposes. As is typically the case with less developed
countries (LDCs) , the agricultural sector is expected to supply food at
low prices, increase income levels of the rural population, raise
government revenues, provide employment, and generate foreigh exchange.
However, the lack of coordination among and within the agencies in
charge of executing agricultural policies has prevented the successful
implementation of such policies. Policies have primarily been directed
toward staple crops, but targets have not been reached. The government
is concerned that Guatemala suffers from domestic food shortages, and
that agricultural income is, in large part, generated by export crops
subject to international price fluctuations. The failure of the
Guatemalan authorities to improve the conditions of the sector makes it
increasingly necessary to formulate a set of consistent policies.

The traditional approach to agricultural planning in Guatemala has
been to arbitrarily set production targets and to estimate the potential
income and employment effects through partial and rather superficial
analysis. This approach has not permitted an evaluation of the overall
behavior of the sector because it disregards substitution effects among

products and among inputs (including land and labor).1 While individual
commodity targets may satisfy the production and foreign exchange objec-
tives, they would only simultaneously satisfy an employment or income
objective by coincidence. Consequently, benefits and costs of imple-
menting different policies have been improperly evaluated. Effective
resource allocation, on the other hand, requires consideration of the
substitution effects; that is, a model must allow for certain prices to
rise and for others to decline in response to different policies. The
sector does not face point demands; it faces demand schedules (Bassoco
and Norton, 1975) . The position on the schedule should be found through
the solution of a resource allocation problem. A model for the whole
agricultural sector, thus, is a prerequisite for complete policy
planning.

Large scale price exogenous linear programming models have been ^
used extensively by agricultural economists to simulate the impact of
farmer plans upon the agricultural sector. These models have taken
market prices or quantities as given.2 When interrelationships between
prices and quantities are considered, the problem can be treated as one
of spatial and/or intertemporal equilibrium. Samuelson (1952) showed
that the problem of spatially separated markets could be solved through
the maximization of the net social payoff which rendered competitive
equilibrium. Takayama and Judge (1964a, b) proposed a quadratic pro-
gramming formulation to solve Samuelson* s maximand. Using separable
programming, Duloy and Norton (1973, 1975) linearized the quadratic

See, for example, Mellor (1975) and Bassoco and Norton (1975)

2
See, for example, Heady and Srivastava (1975).

objective function which permitted the use of the simplex alogrithm to
solve the problem, whereby the size and scope of problems to be consid-
ered were expanded.

The primary objective of this research was to build a linear pro-
gramming model according to the Duloy and Norton specification for
simulating the impact of different policies on key variables in the u"
agricultural sector. Specifically, an attempt was made to estimate
direct and cross-price elasticities for a number of crops, to analyze
the income and employment effects of expanding cotton production, and
to establish comparative advantage in production based on comparative
advantage in international trade. The results are limited in that they
were generated in the context of the assumptions and model specifica-
tions underlying the linear model. The closer these assumptions and
model specifications approach the decision environment of agricultural
producers, the more valid the results are likely to be. An effort
towar^_achieving greater realism was to introduce risk considerations
into the model.

Commodity demand functions are included within the structure of

3
the Guatemalan model (MAYA) , hence prices are determined by the inter-
action of supply and demand. Since relative product and factor prices
are the dominant policy instruments in agriculture, this feature of
the model permits a wide range of policy experiments. MAYA considers
three major groups of farmers who produce 13 crops. Each group is
characterized by a technological level. These crops are transformed
into 18 final products which are sold domestically or exported.

3
MAYA is a name given to the original inhabitants of Guatemala.

To overcome data limitations, MAYA relies heavily on the use of cross-
sectional farm level production cost data.

The dissertation is organized as follows: Chapter II gives a brief
description of the Guatemalan economy in which the agricultural sector
is emphasized. In Chapter III the theoretical background of the model
and the inclusion of risk are discussed. The data base of MAYA is
explained in Chapter IV. Validation of the model is covered in Chapter
V. In Chapter VI various simulation results are presented. The
summary, conclusions, and suggestions for further improvement of the
model are presented in Chapter VII.

CHAPTER II
OVERVIEW OF THE GUATEMALAN ECONOMY

Guatemala is the largest Central American country with an area of
110,000 square kilometers and a population of 7.2 million in mid-1980.
Three quarters of the population live in rural areas. Guatemala has a
wide range of climatic conditions, from the tropical northern and
coastal areas to the volcanic highlands (Figure 1) . Agriculture is
diversified and its potential is large especially in the northern part
of the country. During the last 15 years Guatemala has been able to
diversify its exports (although its major exports are still traditional
crops) and achieve rapid industrial growth and a substantially higher
level of per capita income. Even so, Guatemala is still primarily an
agricultural country.

The economy has been growing rapidly at an annual average of 6.3%
in the last 15 years and generally above the Latin American average.1
The share of agriculture, the most important sector, in GDP has remained
at around 28% (Appendix A, Table I) . Industry accounts for about 15%
(the largest share relative to the other Central American countries) in
large part because the country has been a main beneficiary of the
Central American Common Market (CACM) .

The overall growth of the Guatemalan economy has been highly
dependent on the fluctuations of export prices, particularly the price

During the period 1965-1976, the annual growth of GDP in Latin
America was 4.7% and that of Guatemala, 6.1% (IDB/IBRD/AID, 1977).

rs Correspond to

Name

s of Department

Alta Verapaz

12

Peten

Baja Verapaz

13

Quetzaltenango

Chimaltenanago

ll>

El Quiche

Chiquimula

15

Retalhuleu

El Progreso

16

Sacatapequez

Escuintla

17

San Marcos

Guatemala

18

Santa Rosa

Huehuetenango

19

Solola

Izabal

20

Suchitepequez

Jalapa

21

Totonicapan

Jutlapa

22

Zacapa

Figure 1. Political Map of Guatemala

of coffee. The country has, however, been able to avoid serious balance
of payments problems as import growth rates have followed closely those
of exports and because the government has curtailed demand through
credit restraints.

Over the past 15 years, investment has fluctuated between 12 and
15% of GDP (IBRD, 1978). During the 1960s and early 1970s about 25% of
total fixed capital formation took place in manufacturing, much of it
because of opportunities opened up by the creation of the CACM.
Agricultural investment was, however, about one-third that of industry
and deteriorated even further after 1973 (Appendix A, Table II) .
Although the annual share of banking credit of agriculture was at least
70% that of industry until the mid-1970s, it was used mainly to purchase
current inputs rather than for capital investment (Banco de Guatemala,
1980b; IDB/IBRD/AID, 1977). Government lending to agriculture was very
limited and gave little support to smaller farmers.

Government consumption has tended to move with GDP, whereas govern-
ment investment has been much more volatile. During the 1960s the rate
of public investment was smaller than that of private investment,
whereas the reverse occurred after 1970 due mainly to the implementation
of the 1970-1975 Development Plan by the government. Following the
earthquake of February 1976, public sector investment almost doubled in
real terms as the government took the lead in the reconstruction process
(Appendix A, Table III) .

During the 1960s and early 1970s domestic prices remained remark-
ably stable and increased by an average of only 0.3% per year (IMF,
1978) . The conservative monetary policies of the government restricted
expansion of the money supply, and the openness of the economy allowed

imports to rise with export earnings, relieving demand-pull inflationary
pressures.

After 1973 Guatemala departed sharply from past patterns of
development. In contrast to the previous stable period, consumer prices
surged by 10 to 15% each year as a result partly of increased prices of
imported inputs after the oil shortage, and partly to the inflation
generated by the rapid growth of the money supply resulting from in-
creased export earnings— led by coffee whose price rose by over 35% in
1974 over 1970 (IMF). The resurgence of trade with other CACM countries
in 1973 and 1974 generated a surplus of $40 million each year. This
surplus combined with a boom in coffee export earnings in 1973 and one
in sugar export earnings in 1974 allowed the country to import at a
level sufficient to maintain growth, thus avoiding a recession (IBRD) .

Contributing to the inflationary pressures was a shortage of basic
grains, particularly maize, caused by a shift of areas planted with
basic grains toward cotton and sugar production in the South Pacific
region. To meet domestic demand, the National Agricultural Marketing
Institute (INDECA) was forced to import and sell at prices lower than
import cost. In 1974 the government reversed its strategy and took
several measures to stimulate production (see below) . The favorable
crops of 1975 and 1976 (Appendix A, Table IV) helped dampen inflationary
pressures, but by the end of 1976, the exceptional demand created by the
earthquake reconstruction efforts combined with a massive influx of
foreign exchange from coffee and cotton exports pushed the rate back to
previous levels. After 1976 moderate government measures to limit the
money supply and control the domestic prices of major export commodities
have helped control inflation.

During the past 20 years there has been little change in the rela-
tive importance of agriculture in Guatemala. It still accounts for
about 28% of GDP, about three-fifths of total employment, and over two-
thirds of the value of exports. Moreover, savings from export agricul-
ture have provided a large share of investment resources, and much of
the industrial expansion of this period has been based on agricultural
raw materials (e.g., sugar cane and cattle). During the same period,
however, the share of agriculture in the national fixed capital forma-
tion has fallen from 15% in the early 1960s to about 8% in the 1970s
(IBRD). Limited investment in agriculture is a major cause of lagging
productivity in traditional crops and stagnating incomes for small
producers. Public investment has concentrated on minor irrigation
works, some grain storage facilities, and rural roads.
K/ In an effort to raise the income of small producers and landless
agricultural workers, and to secure sufficient production of basic
grains, the government has attempted to implement several programs as
stated in its development plans. A lack of adequate storage facilities
for staple crops by the private sector, leading to marked seasonal price
variations, prompted the government to intervene. The government initi-
ated price stabilization programs for staple crops in the early 1960s.
It purchased the crops during harvest time at fixed prices, stored them,
and sold them during off-peak seasons. But these programs did not pro-
duce the expected results because market prices remained above the pro-
ducer prices set by the government. As a result, grain prices continued
to fluctuate (Fletcher et al., 1970).

In the early 1970s, the government reformulated its price stabili-
zation program and initiated a series of measures to promote production

10

within the context of the National Development Plan of 1971-1975. One
of the major recommendations of the Plan was to strengthen the public
agricultural sector by consolidating existing agencies and establishing
new ones under the general authority of the Ministry of Agriculture. A
government decree of July 1, 1974 (Diario de Centroamerica, July 1,
1974) made it compulsory for farmers to plant at least 10% of the area
in basic grains in plots of 70 hectares or more, made credit through the
National Agricultural Development Band (BANDESA) more easily available,
announced a prohibition to export grain for the next two years, and
raised guaranteed prices by as much as 100% (Appendix A, Table V) .
Production, however, increased because of higher yields rather than
because of expanded areas. INDECA took a more realistic role as a stabi-
lizer of market prices rather than trying to maintain artificially high
prices for producers and artificially low prices for consumers. But
insufficient and unsuitable government storage facilities and a lack of
coordination of the agencies involved have blunted the original
intentions. Participation of the government in the market has been
about 5%, well below the targeted level of 20% (Appendix A, Table V) ,
and the costs of the price stabilization program during the 1971-1974
period were over $11 million. Prices of staple crops have continued to
fluctuate and costs of inputs have increased. Consequently, the area
allocated to the production of staple crops decreased. The National
Development Plan of 1975-1979 (SGCNPE, 1975) acknowledged that much
remained to be accomplished in making the concept of the public agricul-
tural sector a viable one for planning, policy and operational purposes,
and reemphasized the need to strengthen its institutions.

11

The main activities of the government in the agricultural sector
are technical assistance and training through the Institute of Agricul-
tural Science and Technology (ICTA) and the General Directorate for
Agricultural Services (DIGESA) , marketing of basic grains through INDECA,
land colonization and distribution through the National Institute for
Agrarian Transformation (INTA) , and agricultural credit through BANDESA.

Producer organizations, such as the National Coffee Association
(ANACAFE) and the National Cotton Council (CNA) which offer marketing
and technical assistance to their members, receive partial support from
the government. These activities have generally been quite limited and
coordination among these organizations has been inadequate because of
their autonomous nature.
\jf Another area where the government has intervened is the wheat
market. The wheat pricing program started in 1952 and has worked rea-
sonably well because of a high support price made possible by a "bread
tax" that transfers income from the urban consumers to wheat growers
and millers. The high proportion of imports (60% of domestic consump-
tion) allows the flour mills to maintain a lower average price for
flour than would otherwise be possible. This, in turn, allows for a
high support price. Self-sufficiency in wheat, however, is not
possible because Guatemala produces only soft wheat and would still
need to import hard wheat.

The highly skewed distribution of land ownership in Guatemala is a
major factor behind the country's unequal distribution of incomes; 7% of
the population accounted for 60% of the GDP in the late 1960s (Fletcher
et al., 1970). In 1970, 83% of the people in rural Guatemala lived on

12

plots too small (less than 7 hectares) to produce the income needed to

support a family without outside employment (Table 1) . Within the

Central American area, only El Salvador has a higher proportion of

people on sijnilar-size plots of land because it is more than three times

as densely populated as Guatemala. At the other end of the scale, 80%

of Guatemala's agricultural land is held in units larger than 7 hectares,

and these farms are owned by only 2% of the farm families. The high

concentration of the indigenous population in the Western Highlands

accounts for much of the inequality of land distribution, with 26% of

the total area and 60% of the population (SGCNPE, 1978a). The situation

is made more acute by the fact that the land is rugged and unsuited for

2
cultivation. Erosion of the land and low productivity are common

problems. In contrast, the fertile plains of the South Pacific are for

the most part held by wealthy owners and dedicated mainly to export

crops .

Although an agrarian reform law has existed since the 1950s and the
National Institute for Agrarian Transformation (INTA) has existed for
nearly as long, negligible progress has been made toward improving the
equality of land distribution in Guatemala.

The lack of access to adequate credit at a reasonable cost con-
tinues to be a barrier to improved output and productivity, particularly
for small farmers. It is unlikely that more than a third of the farmers
in Guatemala make regular use of institutional credit even though
BANDESA has greatly expanded its operations since 1974. BANDESA now

2
Studxes have revealed that this land is better suited for forestry
(SGCNPE, 1978b).

13

Table 1. Estimated Land Tenure Pattern in Guatemala, 1970

Size of Holding

Share of
Farms or Families

Share

of

Area

(%)

(cum. %)

(%)

(

cum. %)

Small

83.3

83.3

12.3

12.3

Landless

26.5

26.5

Less than 0.7

ha

14.8

41.3

1.0

1.0

0.7 - 4.0 ha

42.0

83.3

11.3

12.3

Medium

14.1

97.4

21.4

33.7

4.0 - 7.0 ha
7.0 - 35.0 ha

6.8
7.3

90.1
97.4

6.3

15.1

18.6
33.7

Large

35.0 - 350.0 ha
Over 350.0 ha
Administrators

2.7

100.0

66.3

100.0

1.4

98.8

23.9

57.6

0.5

99.2

42.4

100.0

0.8

100.0

Families without land.
SOURCE: IBRD (1978, p. 73).

14

serves over 80,000 farmers, many of whom are members of cooperatives
which receive its funds.

The agricultural sector has played an important part in the earn-
ing of foreign exchange. Exports of traditional products (i.e., coffee,
cotton, sugar, and bananas) accounted for 60% of the total value of
exports during 1970-1977 (Directorate General of Statistics, DGE, 1970-
1977). The expansion of production of export crops and favorable condi-
tions in world markets have contributed to this outcome. Export crops,
with the exception of coffee (which still uses traditional methods of
production), are produced with sophisticated techniques. Coffee exports
alone account for 30% of total exports, and the government has encour-
aged its production by making credit available (Banco de Guatemala,
1976, 1980b).

Although Guatemala has reduced its dependence on coffee exports
very substantially, coffee clearly remains the largest single export
commodity. Changes in overall export earnings have traditionally been
and continue to be very closely linked to changes in the value of
Guatemalan coffee exports. Some export diversification as well as
favorable movements in the cotton and sugar prices helped dampen the
impact of changes in coffee export growth on total export earnings
(IMF) .

Cotton has been the second most important crop since the 1960s.
Production has been stimulated by improved technologies, a growing
domestic textile industry, and increasing external demand. Sugar has
traditionally been the third largest export product of Guatemala.
Production achieved record high levels in 1975, with exceptionally high
international prices, and stabilized at pre-1975 levels thereafter

15

(Banco de Guatemala, 1976, 1980a). Bananas and meat are the remaining
major agricultural export products of Guatemala. The policy of
BANDEGUA, a subsidiary of Del Monte Corporation and the major exporter
of Guatemalan bananas, has been to maintain production for export more
or less constant, and in the past few years BANDEGUA has tended to
diversify into other fruits such as pineapples and papayas. During the
past 15 years increases in meat production reflect increased numbers of
animals and hectares of pasture rather than increased productivity per
animal or per hectare (IDB/IBRD/AID) . The present plan of the govern-
ment to shift cattle production from the Pacific coast to the northern
slopes and lower Peten region should allow the freed lands of the
Pacific south to be diverted to cotton and basic grain production.

In summary, prospects for Guatemala's agricultural exports are
generally quite good, though efforts could be made to raise productivity,
particularly in coffee. Non-export agriculture, however, suffers from
fragmented land holdings and low productivity, resulting in inadequate
incomes for farmers. This, in large part, stems from a limited ability
to analyze agricultural development problems and to formulate appro-
priate solutions in terms of policies and investment programs. The
conditions for agricultural development in the overall context of the
Guatemalan economy include some potentially favorable factors. Some
balance of these factors could work well for overall economic growth and
the development of the country's diversified agriculture. They include
(a) increased and more diversified agricultural exports, (b) favorable
international prices for export commodities (c) comfortable interna-
tional reserves, (d) low external debt service ratio and long maturity
at low interest, and (e) restrained monetary policy to cope with

16

inflation (AID, 1978). Other factors could be added to the preceding
list such as the large untapped natural resources potential, including
petroleum and forestry, and strong rural cooperative agreements. These
factors appear to offer considerable scope for undertaking medium- and
long-range commitments with the goal of increasing output and rural
welfare. This goal would require greater participation by the govern-
ment in such things as increasing credit supply and price regulation.
Given the high rate of population growth of nearly 3% per year, it
appears, as stated in the Development Plan for 1979-1982, that the only
way to increase production levels of basic grains and the incomes of the
rural poor is through technological improvement. Policies must be
directed to stimulate new technologies and their rate of adaptation
without ignoring the adverse effects on employment that they may bring
about.

CHAPTER III
THEORETICAL BACKGROUND

Mathematical Programming Models

Traditionally, mathematical programming models have been used in a
normative sense, by maximizing a set of goals. Goods are assumed to
face infinitely elastic demands, usually justified by the country's
price-taker position in international trade. For a large number of
products that do not enter international trade, price determination
depends on domestic demand. Mathematical programming models can, of
course, incorporate product demand functions which yield endogenous
prices, thus providing a large degree of generality to the system. As
such, these models are used in a descriptive sense to simulate the
behavior of a competitive or monopolistic market.

Several authors have tried to provide solutions to Samuelson's
(1952) competitive equilibrium formulation. He pointed out that maximi-
zation of the net social payoff function (the sum of the consumers' and
producers' surplus) led to a competitive equilibrium solution. He used
this function to try to solve Enke's (1951) problem of interspatial
markets by relating it to the Koopmans-Hitchcock minimum transport cost.
He used this artificial magnitude to cast the problem mathematically
into a maximizing problem. His suggestions on solutions were, however,
iterative procedures.

17

18

Fox (1953) proposed an iterative solution for the case of a multi-
regional feed grain economy, given estimated parameters of the regional
demand functions. Tramel and Seale's (1959) reactive programming and
Judge and Wallace's (1958) methods are iterative heuristic methods that
solve the product shipments problem with given demands and supplies in
each region. Their methods do not formulate the problem as a mathe-
matical programming one with an objective function. Schrader and King
(1962) were the first to introduce price responsive demand functions
into LP models. Their method maximized producers' revenue and obtained
a market clearing solution with iterations.

Takayama and Judge (1946a, b) introduced quadratic programming to
solve the regional flows problem under independent linear demand
functions. The objective function was specified as the sum of consumers'
and producers' surplus and was given a welfare connotation. Iterative
solution procedures for the competitive and monopolistic cases are based
on Wolf's modified simplex algorithm. Yaron et al. (1965) treated three
cases (a) independent demands, (b) , interdependent demands with fulfill-
ment of the integrability conditions, and (c) interdependent demands
without fulfillment of the integrability conditions. For case (a) they
used step-wise approximated demand functions using linear programming.
For case (b) they used quadratic programming. For case (c) they used a
primal-dual formulation and concluded that the welfare interpretation of
the objective function no longer holds, which lends force to satisfying
the integrability conditions. They did not, however, present any
computations.

Martin (1972) proposed a noniterative equilibrium solution with
independent demands. He used a piece-wise linear specification of

19

product demand and factor supply functions. At the same time, similar
procedures were being used to build the French national model (Fahri and
Varcueil, 1969) and a regional model for the Soviet Union (Mash and
Kiselev, 1971). Neither of these, however, considered interdependence
in demand.

Interdependence in demand and the specification of a variable that
would measure producers' income at endogenous prices were first explored
by Duloy and Norton (1973, 1975) when they formulated the programming
model for the Mexican economy, CHAC.1 One advantage of their specifica-
tion is their use of Miller's (1963) separable programming to approxi-
mate nonlinear functions without significantly increasing the number of
rows. With this improvement nonlinearities in both the objective func-
tion and constraint set could be easily handled.

Incorporating demand functions into planning models, rather than
assuming exogenous product prices, allows the model to correspond to a

market equilibrium. It also permits an appraisal of the benefits

_ i

accruing to producers and consumers, and it gives the model greater
flexibility in that changes in the input side can take place not only
directly through changes in the technology set but also through changes
in demand due to relative price changes of given input intensive
commodities. •

The methodology followed in the present study is that developed by
Duloy and Norton. The basic optimizing market equilibrium formulation
assumes that producers are profit maximizers and that consumers'

A name which means "Rain God of the Mayas."

20

behavior is adequately described by a set of demand functions in the
space of prices and quantities.

In Duloy and Norton's (1975, pp. 593-594) general model, the demand
function was specified as

(D P = f (q, Y),

where p is an n x 1 vector of prices, q is an n x 1 vector of quantities,
and Y is lagged permanent income. In the unconstrained case, the objec-
tive function for the competitive market situation may be written

(2) Max Z = |f (q> Y) dq - c (q)
0

where c(q) is an n x 1 vector of total cost functions. Setting the
first derivation of Equation (2) with respect to q equal to zero yields
the equilibrium conditions of marginal revenue equals marginal cost.

(3) P = c'(q)

In the constrained resource case the model would include the condi-
tion Aq < b, where A is an m x n matrix of resource coefficients, and b
an m x 1 vector of resource availabilities. The Kuhn-Tucker necessary
conditions are

8Z
(4a) ~3q~ = f' ~ c'(cl) - P'A < 0

(4b) q°< *2- = 0
9q

(4c) \— = Aq - b < 0

3p -

21

(4d) u ' ^r— = 0,

where p is the dual variable vector and the ° superscript means that
derivatives and vectors are evaluated at the point of the optimum.
Equation (4a) means that marginal profits must be zero or negative.
Marginal profits are equal to price minus marginal costs, where the
latter have two components; the explicit market costs of inputs, c'(q),
and the economic rents which accrue to fixed factors, u 'A. Equation
(4b) is the complementary slackness condition, which together with
Equation (4a) means that if profits are nonzero the activity is zero,
and if the activity level is positive marginal profits are zero.
Equation (4c) is the complementary slackness condition for the dual,
which with Equation (4d) means that if a resource's shadow price is
nonzero its slack is zero and vice versa.

The linear programming formulation for the model described assumes
a linear demand function, although this need not be the case, as long
as the matrix of demand coefficients is negative semi-definite to insure
convexity. Equation (1) may be rewritten as

(5) p = a + Bq

where a is an n x 1 vector of constants and B is an n x n negative semi-
definite matrix of demand coefficients. Y has been dropped since this
is a static formulation. Equation (2), the objective function, then

22
2

becomes in the competitive case

(6) Max Z = q'(a + .5Bq) - c(q)

and the equilibrium conditions

(7) p = a + Bq = c'(q).

Equation (6) corresponds to Samuelson's net-social-payoff functj
except for transportation costs which are not included.

onsumers

Equation (6) can be decomposed into producers' and c

3

surplus (Duloy and Norton, 1975, p. 593)

(8) _CS_ = .5q' (a - p) = -,5q' Bq

(9) JPS_ = q'p - c(q) = q' (a + Bq) - c(q)

Finally, the area under the demand function and the revenue function are
respectively, Equations (10) and (11). Both are sketched in Figure 2.

(10) W = q' (a + .5Bq)

(11) R = q' (a + Bq)

2

In the monopolistic case, Equation (6) becomes

(6*) Z* = q'(a + Bq) - c(q)

which yields equilibrium conditions identical to (4a) to (4d) , except
that the vector p is replaced by the term a + 2 Bq, the vector of
marginal revenues

(7') a + 2Bq = c'(q),

or marginal revenue equals marginal cost.

3
There has been a long debate over the use of Marshallian surpluses
as welfare measures (Mishan, 1960, 1968; Winch, 1965; Burns, 1973), but
in the context of sector models the interest is primarily in their 'use
to simulate a market equilibrium and not in their welfare interpretation.

23

Figure 2. Area under the Demand Equation (W) and
Total Revenue Function (R)

24

The maximum for both the competitive and monopolistic cases
involves a quadratic term in q. Two linear approximations have been
developed by Duloy and Norton; one based on previous knowledge of B
(interdependence in demand) and the other where B is diagonal (separa-
bility assumed) . In this research only the latter case will be
considered.

Let Wj denote the area under the demand curve for product j, then

(12) q'(a - .5Bq) = E W.. j = 1, ..., n

J J

W is a quadratic, concave function when plotted against q , and since

the programming model is a maximization problem, W. can be approximated

by a series of linear steps and conventional LP computer codes can be

used to obtain an approximation to the maximum. Duloy and Norton (1973)

introduce additional variables, W, . , where k = 1, . . . , s for each W •

kj - j'

assign upper bounds wk_. on q^ over which interval W applies; and
assign a single value for W , say d , which approximates W over the
interval q.. < w^ . Define q = xy, where x is a vector of aggregate
production areas and y is a diagonal matrix of yields. They then sug-
gest that the quadratic term q' (a - .5Bq) be replaced in the maximiza-
tion problem as follows for the case of product j produced under h
(h = 1, ..., t) technologies:

(13) Max -E c, . x, . + E d W

h hJ hj k kj kj

such that

(14) -E c, . x, . + Z r, . W. . > Z

h hJ hj k kj kj -

25

(15) £ y v . - I w. . W, , > 0

kj "kj -

(16) Z W4t < 1. k = 1, ..., s

h - 1, ..., t

k Jk

This method adds two rows for each product, but permits inclusion of
as many W activities as desired to increase the accuracy of the
approximation. The segmented approximation of W and R for a single
product is shown in Table 2.

Because of the concavity of W, no more than two of the W selling

kj

activities will appear in the solution. It is clear that the approach
can be readily extended to the multi-product case. International trade
can also be incorporated through well behaved nonlinear import demands
and export supplies.

This specification of demand functions is convenient in the
analysis of comparative statics solutions from demand rotation.
Demand functions can be rotated simply by varying the value of the
convexity restriction. The matrices W and R are invariant under this
class of transformations. The upward rotation of the demand function
is expressed as a proportional lengthening of the segments with
prices constant. In Figure 3, D D represents the function p = f(q)
and D^ represents p = f(Xq), and the slopes of the linearized func-
tion W1 and W2 are equal for corresponding segments. A similar condi-
tion holds for the linearized R function. Thus, the coefficients of
the W and R matrices can be expressed as simple multiples of the
corresponding quantities. The selling activities of the transformed
tableau would be similar to those of Table 2 where all rows except
the convexity restriction are multiplied by A . By dividing

26

A|

fi

C

H

•H

o

rt

a

n

j-i

X

en

<D

C

>

o

C

a

27

28

all the elements of each activity by X , the problem with the transformed
demand function is reduced to a problem with coefficients in the con-
straint matrix identical to those before the demand transformation, but
with X replacing unity in the right-hand side of the convex combination
constraint.

The underlying assumptions of the aggregate LP model are

(a) integrability of product demand and factor supply functions, and

(b) a partial equilibrium setting.4 Integrability refers to conditions
in which the matrices of first derivatives of the factor supply and
product demand functions must be symmetric. This implies that the cross
price effects are equal over all commodity pairs, and also that the
effect of income on consumption is identical across all commodities of
interest or zero. How restrictive this symmetry condition is depends on
whether one is dealing with supply or demand. For the supply functions,
the classical assumptions of the theory of production yield this
condition. Zusman (1969) notes that, in empirical studies where the
supply functions are derived from observed behavior, the symmetry condi-
tion is still highly restrictive. In the case of the demand functions,
the situation is different; aggregate demand functions satisfy the
symmetry condition only if the individual demand functions do. The
price derivative of individual demand functions (under constant money
income) consists of a symmetric substitution term and an income effect
term. For the latter term to also be symmetric it would be necessary
that the income elasticity of demand of all commodities be zero. This
condition would be only approximately satisfied if the income effect is

4
See also McCarl and Spreen (1980)

29

small relative to the substitution term. This would happen if the goods
are closely related in demand, have low income elasticity, and consti-
tute a minor share of the consumer's expenditures. In all other cases
the symmetry requirement is not even approximately met. Models that do
not require the integrability assumption have, however, been formulated
by incorporating price and quantity variables into the primal
formulation. The objective function no longer represents the sum of
producers' plus consumers' surplus, but rather the excess of consumer
expenditure over the sum of factor incomes plus outlays on purchased
inputs. The objective function includes a quadratic term, but since it
is not derived from an integration process, the symmetry assumption
(integrability requirement) may be dropped. The disadvantage of this
approach is that it requires a much larger constraint set.

The second assumption of a partial equilibrium setting refers to
the fact that the model does not take into account the effect of income
generated by the system on the demand function. If the sector modeled
is small enough relative to the entire economy, this shortcoming would
be unimportant. If, however, the sector considered is large relative to
the entire economy, the income it generates would be expected to have a
major impact on consumer demand.

Risk Considerations

It has been established that, in general, agriculture is a risky
process, especially in LDCs. Several studies5 support the hypothesis

See, for example, Behrman (1968), Dillon and Anderson (1971)
Francisco and Anderson (1972), Linn et al. (1974), Pomareda and Simmons

30

that farmers do behave in risk averse ways. Neglect of risk averse
behavior in agricultural planning models had led to overstatements of
the output level (usually overspecialized cropping patterns) of risky
activities and to overestimates of the value of basic resources.

In modern decision theory, uncertainty is a state of mind in which
the individual perceives alternative outcomes to a particular action.
Risk, on the other hand, has to do with the degree of uncertainty in a
given situation. Some define risk as a measurable probability, for
example, as variance. Others define it as the probability that returns
will not fall below a given "safe" level. Others, such as John Dillon
(in Boussard, 1979) state that one should avoid using the word risk as
if it were a definite measure of anything. He feels, though, that one
should speak of "risk aversion" without causing confusion.

Two basic traditional approaches for incorporating risk into agri-
cultural programming models have been used: (a) the "theory of games"
approach, where the decision maker is supposed to play a game against an
unknown opponent called "nature," and (b) the "portfolio selection"
approach where risk is taken into account through the objective function.
Only the latter approach and its alternative simplified Minimum of Total
Absolute Deviations (MOTAD) model will be discussed because of their use
in this research.

r

Alternative (E - V) models have also been developed, e.g. the
safety first" model proposed by Roy (1952) . Its optimizing criterion
is

Min P { e < e }
— o '

where P represents probability and e0 is a specified level of disaster
(risk level). If the distribution of E is fully described by e and al,
then this criterion is equivalent to

e - e0

Max

31

The portfolio selection or expected income-associated income vari-
ance (E-V) approach, which leads to a quadratic programming formulation,
is attributed to Markowitz (1952) . His problem was to select an optimal
portfolio of stocks solely on an (E-V) criterion such that V is minimum
for an associated E under a budget constraint. It is also assumed that
the farmer is a risk averter, i.e., faces quadratic iso-utility func-
tions which are convex from above, and the conditions — > 0 and
3v2 > 0 hold. Since short-run planning models assume constant overhead
costs, the income distribution of a farm plan is totally specified by
the total gross margin distribution. For n activities and m resource
constraints, the Markowitz' s quadratic programming model minimizes
expected variance V, subject to expected income and resource avail-
ability constraints

(1) Minimize V = Z Z x. x a

j k 3 k jk

Baumol (1963), without rejecting Markowitz' approach, used an (E-$o)
formulation. The decision maker is assumed to subjectively establish a
confidence limit and a floor on expected returns to which the limit is
applied. Other approaches which depart from the (E-V) approach, but
whose practical usefulness is not questionable are (a) the flexibility
constraints approach (Day, 1979), and (b) the focus loss constrained
program (FLCP) . The first one imposes special constraints to the LP
problem. These constraints reflect all the unknown constraints not
explicitly taken into account in the analysis but which prevent farmers
from changing their year to year plans quickly. The shortcoming of this
model is that it does not give very much information on how to choose
the level of the bounding constraints. The second approach was devel-
oped by Boussard and Petit (1967). The basic assumption is that the
expectations of farmers are described by two concepts, (a) the focus of
gams (expected gains), and (b) the focus of losses (the most unfavor-
able outcome). The average gains are maximized subject to the usual
constraints of the model and a special focus-loss constraint. The
advantage of this model is its ability to be implemented in an ordinary
LP framework, whereas its main criticism is its lack of theoretical
foundation (Boussard, 1979).

32

such that

(2) I e. x. > E
j J J -

(3) I a. . x. < b
1J J ~ j

i = 1,

J j, k « 1, ..., n

(4) x. > 0,

J -

where

.th

is the level of the j activity,

.th

ajk is the variance of the j activity when j = k,

and the covariance of activities j and k when j ± k,

e.. is the expected gross margin of the jth activity,

aii is the amount of the i resources per unit of the
jth activity,

• 4.u -th

is the x resource constraint level, and

is a positive scalar of total expected gross income.

b.

i

E

By parameterizing E from zero upward a sequence of solutions is
obtained of increasing total gross margins and variance until the high-
est possible total gross margin is attained. Solutions are obtained for
critical changes in the basis such that for the current total margin E,
the variance is minimum. These solutions define the efficient (E-V)
boundary. The acceptability of any one particular plan on this boundary
depends on the farmer's preference determined by his (E-V) utility
function. When this function can be measured, a unique farm plan can be
rigorously identified which offers the farmer highest utility.

This model has several shortcomings at different theoretical levels.
Some ammendments have been proposed in order to improve its significance

33

and its feasibility. From a practical point of view, the necessity of a
quadratic programming routine has been cited as a problem, even though
several codes have been developed by RAND corporation, IBM, and others.
For that reason, a number of approximations of quadratic functions have
been proposed. The most general case is the separable programming
approach which approximates nonlinear functions in the model at the
expense of an enlargement of the initial matrix. The Duloy-Norton
approach has many similar features to the separable programming approach.
Another drawback of the model is that the variance symmetrically weighs
positive and negative deviations from the mean. This would be true only
in the exceptional case where the population total gross margin distri-
butions are symmetric. Nevertheless, when income deviations are weighed
on a quadratic basis it is not likely that any disutility will be
attached to positive income deviations. Thus, using an (E-V) criterion
may lead to conservative farm plans. Markowitz (1959) has suggested
minimizing the negative semi-variance subject to constraints (2) through
(4).

The estimation of the variance-covariance or semi-variance matrices
presents some problems. The model requires a priori estimates of the
mean gross margins for each activity and the corresponding variances and
covariances.

In most cases, time series data are used to estimate variance-
covariance matrices under the assumption that the dispersion of gains is
independent of time. Few empirical studies seem to have been devoted to
the verification of this assumption. Errors in estimating the variance-

7C
See, for instance, Sharpe (1963, 1967) and Thomas et al. (1972)

34

covariance matrices do shape the final solution of the Markowitz
problem. In Thomas et al. (1972) an attempt was made to drop statis-
tically insignificant covariance terms. A number of these were found to
be relatively high, and differences between the "significant covariance
model" and the "all covariances model" did not exceed 3 to 5% of the
optimal activity levels. The significant covariance model yielded lower
expected incomes for each permitted level of income variance.

Hazell (1971) suggested the "minimum of total absolute deviations"
approach (MOTAD) as an alternative to the (E-V) formulation. This
criterion retains most of the desired properties of the latter and is
easier to handle computationally. Let c . (h = 1, . . . , S; j = 1
n) be the h observation in a random sample of gross margins of

activity j. The sample mean is g = - E c An unbiased estimator of

J s h nj

the population mean absolute income deviation is

A - ^ I \ (CM " V *: I-

Using A as a measure of uncertainty, Hazell considers E and A as the
crucial parameters in the selection of a farm plan. Efficient (E-A)
farm plans are those having minimum mean absolute income deviation for
given expected income level E. The (E-A) criterion has an important
advantage over the (E-V) criterion in that it leads to a linear pro-
gramming formulation.

Hazell 's model is as follows:

Minimize As = £ y
h h

such that

35

1 (Chj " Sj} Xj + yh - ° h = 1, ...,

S e x = E e > 0

J J

I a. . x. < b. i = l. m

xj> yh 1 0 all h and j

where E yh is the sum of the absolute values of the negative total gross
margin deviations around the expected returns based on sample mean gross
margins. The efficiency locus is obviously different from the (E-V)
locus, but according to Thomson and Hazell (1972), the differences are
small enough so as to definitely accept the MOTAD formulation as a
reasonable approximation of the (E-V) formulation. They found that for
large sample sizes the relative asymptotic efficiency of the estimated
mean absolute deviation is 88%. That is, it is 88% as efficient as the
estimated standard deviation in estimating the population standard
deviation.

Risk can be incorporated into an LP model by simply subtracting the
risk term in the objective function and introducing appropriate changes
in the constraint set. The general case of the Markowitz criterion will
be treated before discussing the MOTAD risk model.

Assuming that farmers behave in a risk- averse way, according to the
Markowitz (E-V) criterion, the endogenous price programming formulation
can be modified into a risk formulation. The objective function of such
a model is

(1) Maximize U = X'Y (A - .5BYX) - C'X - $ (X'fiX)

36

where

X is an n x 1 vector of crop area,

Y is an n x n diagonal matrix of average yields

C is an n x 1 vector of cost coefficients per unit of
crop area,

A, B are coefficient matrices of the linear demand struc-
ture P = A - BYX, where P is expected price and B is
assumed to be diagonal with nonnegative elements,

<J> is an aggregate risk parameter of farmers, and

R is an n x n covariance matrix of activity revenues
of farmers.

This new objective function is the same as that of the Duloy and
Norton model except for the addition of the risk term. The rationale
for this function is found in Hazell and Scandizzo (1974) . When the
risk factor <j) is set equal to zero, we have the familiar profit maximiz-
ing objective function. The effect of ignoring risk-averse behavior
depends on the properties of the term (X'fiX) .

Letting the linear programming constraints be denoted by DX < b,
where D is an m x n matrix of resource requirements and b is an m x 1
vector of resource supplies, the Lagrangian of (1) is then

(2) L = X'Y(A - .5BYX) - C'X - <j> (X'GX) - v' (DX - b) ,
where

v is an m x 1 vector of dual variables.

The solution to this problem is a saddle point, which satisfies the
Kuhn-Tucker conditions. The necessary conditions are

37

8L
^ = y. (a. - b. y. x.) - Cj - 2* Zw.. x. - ZvR dkj < 0 ,

i, j = 1, ..., n

k = 1, . . . , m

where the lower case letters denote the elements of the corresponding
matrices. Complementary slackness conditions require that (3) holds as
an equality for every nonzero x. in the solution. Thus, from (3) and
using the fact that B, the matrix of slopes, is diagonal, we can solve
for expected prices, p:

(4) P = ~ t c + Z v, d1 . + 2<J, Z w. . x
yj J k k kJ i « i

P. = a. - b. y. x.
J J J J j

This equation states that for each nonzero activity the expected
marginal cost per unit of output must equal expected price. The
expected marginal cost is the sum of the expected own marginal cost,
, plus expected opportunity costs ~- E vk d for the resources used

J J J j£ J

in activity j, plus a marginal risk factor — 2<j> E w. x.. When risk

yj i XJ 1
neutrality is assumed, i.e., f = 0, as in the deterministic model, this

latter term would disappear. The appearance of the risk factor as a
marginal cost provides the rationale for the expectation that deter-
ministic models tend to overestimate the supply response of high-risk
crops. This is because <J> 1 jg x± is positive and the marginal cost
curve must lie above the marginal cost curve of a risk neutral deter-
ministic model. Crops v/ith large revenue variances and/or whose

38

revenues are positively correlated with those of other crops will have a
positive marginal risk term. The converse holds for the case of those
crops with small variances, and/or whose revenues are negatively cor-
related with those of other crops. This will result, under risk
behavior, in smaller outputs in the first case and larger ones in the
latter (Hazell et al., 1978).

To analyze the effect of risk behavior in the valuation of scarce
resources it is helpful to see that since (X'flX) > 0 in the model objec-
tive function, the value of the objective function is smaller than under
risk neutrality. The total valuation of resources thus must also be
smaller. While it is still possible that some resources increase in
value, others must decline by sufficiently large amounts so that, as a
whole, farmers would be willing to pay less for their production inputs.

The aggregate risk model as specified in (1) is a quadratic
programming problem. Duloy and Norton have shown that the quadratic /
teimX<YjA_-_.5BYX) can be linearized (pp. 22-25). Following their
methodology, Hazell and Scandizzo (1974) linearized the second term
(X'flX) of the risk objective function. They do not, however, linearize
the classical variance estimator

(1) est (X'flX) = nix[fLE(t.-r.)(r..ifj],

ij J t J1^ i

but the less efficient variance estimator

(2) est (X'flX) = Ll\ I | E (r. - r.) x. I ] 2,

T t j Jt J J ' '

as suggested by Hazell, where rjfc is the tth observation of the revenue

39

of the j activxty x , r is the sample mean revenue for r over T

J J

uT
years, and A = 2(T - 1) » wnere n is a constant.

Following Hazell and Scandizzo's methodology, Hazell 's MOTAD formu-
lation can be approximated by defining new variables z > 0, for all t,
which represent negative deviations in total revenue for all activities
so that

(3) 2 Z z = E | Z (r. - r )
t t t j T f

"jt t' ~j

From (2) an estimator, s, of the population standard deviation can be
obtained

(4) s = A^z z
t

= A* A.
The problem of minimizing (X'ftX)"5 is then approximated by

Minimize $ s
such that

£ (r.. - r.) x. + z > 0 t = 1 T
Jt j j t-u c J-, ..., I

n z - j s = o
t t a"2

x , zt > 0

40

Figure 4 shows a complete LP tableau which approximates the quad-
ratic programming problem which incorporates this development on risk.
In the model if is a coefficient to be parametrically programmed.

Areas for Further Improvement

Mathematical programming models could be improved if they were
considered in the context of multi-level programming and if income were
explicitly incorporated.

Multi-level Programming

In a market economy most economic policy problems can be decomposed
into two related subproblems, (a) the behavioral problem of forecasting
(describing) the economy's (or sector's) response to policy changes, and
(b) the policy (normative) problem of choosing among possible
alternatives. Mathematical programming deals only with the maximization
of the behavioral objective function.

Higher level decision makers usually manipulate policy variables
(e.g., tax rates, the size of the budget deficit) in order to influence
a set of impact variables (e.g., employment level, rate of inflation),
and decentralized decision makers control behavioral variables (e.g.,
private investment) in the light of the levels of the policy variables.
Candler and Norton (1977) formally define this area of investigation as
"multi-level programming." Candler and Townsley (1979) attempted to
develop algorithms for the multi-level problem solution.

Multi-level programming assumes that the product possibilities open
to decentralized decision makers and the rules governing their choice of
variables under their control are known, and that the policy makers

41

42

objectives are also known. Little attention has, however, been given to
the definition of policy objectives, partly due to the fact that inves-
tigators have limited themselves to presenting policy makers a set of
alternatives (e.g., different product prices or investment levels) based
on their models and partly because of the difficulty of defining these
objectives.

In the two-level case, Candler and Norton state the multi-level
problem as follows: find vector x = x x x ) such that

(1) f2 = max (c2'x2)

such that

(2) f = max (c1 'xj
1 x, x„ 1 1

1»~2 1 V

(3) Al;L x- + A x 5 b

(4) -I xQ + A^ xx + A22 x2 = 0

(5)

x > 0

where

xQ, X;L, x2

f2

fl

All

A12

are vectors of impact, behavioral, and policy
variables, respectively,

is the policy makers' objective function,

is the behavioral objective function,

is the matrix of resource requirements,

expresses the effect of the policy variables
on resource availability,

b is the level of available resources prior to
policy intervention,

43

A21 is a matrix of the effects of the behavioral
variables x^ on the impact variables, and

A22 expresses the direct effects of the policy
variables x2 on the impact variables xq
(often this matrix is zero and policies would
have to achieve their impacts directly) .

For a given level of x^ (2) to (5) define an LP problem. However,
(1) to (5) is a multi-level problem. Because it implies multiple levels
of optimization, multi-level programming is a generalization of mathe-
matical programming. Since (1) through (5) is a two-level example,
there are two objective functions, (a) a "policy objective function"
which defines preferences at the aggregate level, and (b) a "behavioral
objective function" which drives the normative model to yield the kind
of market equilibrium that is felt to be most realistic. There are also
three feasible sets corresponding to each type of variable: (a) the
policy instrument set, (b) the feasible behavioral set which, for any
given set of policy instrument values, constrains the values to be taken
by the behavioral variables, and (c) the feasible policy set which is an
implicit feasible set for the impact variables — for example, given the
possible subsidy rates, the feasible policy range states the boundaries
for possible values of impact variables such as employment and output
growth. The frontier of the feasible policy set is the policy
behavioral frontier. The size of the feasible policy set depends on the
size of the policy instrument and behavioral sets, and on the nature of
the behavioral objective function.

Candler and Norton^ maintain that the frontier of the feasible
policy set normally lies very much interior to the corresponding tech-
nological (production possibilities) frontier, even in the absence of

44

market distortions. Parameterization of the policy objective function,
without recognition of a behavioral function will trace out points on
the technological frontier, but this solution is not of interest to
policy makers. The authors illustrate the use of multi-level program-
ming for the case of the Northwest Mexican agriculture and show that,
for a given set of policies, the policy behavioral frontier lies much
interior to the production possibilities frontier, and the behavioral
optimum, undisturbed by policy actions, lies interior to the policy
behavioral frontier. Consequently, gains in the impact variables could
be achieved with an appropriate policy mix. And, solving only a
behavioral programming model without concern for a wide range of policy
choices may not be very realistic.

Incorporating Income

A second area where mathematical programming models could be
improved is the incorporation of income effects in their formulation.
An increase in yields, for example, may have important shift effects on
food demand, with farm family food demands increasing as their incomes
rise, and nonfarm family demands increasing, partly in response to lower
prices (a movement down the demand function) , but also in response to
income increases arising from the multiplier effects of increased
incomes (a rightward shift of demand) .

A proper treatment of these income effects in agricultural models
has not yet been developed. In 1967 Yaron developed a programming model
into which the demand functions for the final outputs and the income
generated by the system are endogenously incorporated. He established a
lagged relationship between demand and income and set up a two-period

45

version of the model to show that the competitive equilibrium interpre-
tation still holds. However, he made initial income exogenous, thus
leaving out any effects on income of variations in the endogenous prices
and quantities of the model. Thus, as he pointed out, the approach is
limited to cases where the portion of the economy represented by the
model is small. Regarding LP solutions he used iterative procedures.
Norton and Scandizzo (1977) developed a procedure for obtaining general
equilibrium solutions for economy-wide models in the LP format so that
the computational power of the simplex solution algorithm could be
exploited. The LP framework can be adapted to the nongeneral equilib-

o

rium cases. Their static general equilibrium model assumes that there
exists a maximization problem whose solution is a general equilibrium
solution in prices, quantities, and incomes; demand is now a function of
prices and incomes. The quadratic programming formulation exploits the
Cournot and Engel aggregation conditions to make endogenous the process
of income formation in the computation of competitive equilibrium. The
assumption underlying the formulation is that consumers behave according
to an aggregate inverse demand function of the type

(1) P = A-BX + (f)y
n,l n,l n,n n,l n,l 1,1

(2) y > P'X,

where P is a price vector, A > 0, B is a nonsingular symmetric matrix of
demand coefficients, X is quantities demanded, and y is income. Their
model is as follows:

Some work in this direction is being undertaken by the World Bank.

46

(3) Max X* (A - .5BX) - C'Q
X,Q

such that

(4) X'* < 1

(5) DQ - b < 0

(6) X - Z < 0

(7) X,Q > 0

where C are the costs of all primary factors which are available in
infinitely elastic supply, Q is quantity supplied, and function (3) is
the sura of consumers' and producers' surplus over all product markets.
Inequality (4) is the Engle aggregation obtained by differentiating (2)
with respect to income and assuming that consumers are on their budget
lines; (5) are aggregate resource constraints; and (6) expresses the
requirement that quantities demanded cannot exceed quantities produced.
The motivation behind the introduction of (4) is not the assumption of
utility maximization by individual consumers, but rather the requirement
that the Engel aggregation must hold in the aggregate for the equilibrium
solution. Norton and Scandizzo (1977) show that a model specified in this
way yields the static market equilibrium conditions and can be linear-
ized with some transformations using log-derivative variables. An added
advantage of their formulation is that the Engel aggregation conditions,
(4), imply compensated quantity changes. This condition then guarantees
that utility is held constant by an appropriate change in prices. Their
model, then, maximizes the sum of the areas under the compensated demand
functions, overcoming the limitations of consumer surplus analysis and

47

its dependence on the assumption of constant marginal utility of income.
It also overcomes the problem of integrability, which requires that the
matrix of first derivatives in the demand function, B, be quasi-negative
definite, and also symmetric, and the cross price effects of the demand
functions do not need to be symmetric.

Empirical Applications: Supply Response

Several approaches have been used to estimate supply response in
agriculture. The most common are the linear programming and econometric
approaches. Linear programming is appealing because it permits consid-
eration of several products and inputs in the decision-making process.
Linear programming also has an advantage in less developed countries
where time-series data are unavailable but cross-sectional data may be
obtained. A brief discussion of the literature on supply response is
presented in this section, and an analysis of the supply response esti-
mation with MAYA is presented in Chapter V.

Estimating the supply responsiveness of agricultural commodities is
both difficult and important. Supply elasticities are useful in showing
how producers are likely to react to higher output and input prices, and
can give planners a basis for setting output prices to meet production
targets. In general, the extent of responsiveness measures the ability
of producers to adjust production to changing economic conditions con-
fronting them in a dynamic economy.

Most of the research on supply analysis has concentrated on the
development of a one-commodity supply function with little regard to the
influence of other commodity prices. According to Shumway and Chang
(1977) conceptual and empirical problems remain in understanding

48

own-price effects as well as cross-price effects; moreover, the number
of both econometric and LP studies is limited. Perhaps the most impor-
tant econometric study where direct and cross-price supply relations
were estimated is that of Gruen et al. (1968). In that study the
elasticities for six commodities were reported. Perhaps the most
important LP study on supply response is the Southern Farm Management
Research Committee's (1966) study of cotton supply in 17 regions in the
U.S. It estimates the impact of price changes of cotton on its own
supply and on the supply of substitute crops, tobacco, peanuts, and
rice.

Nerlove and Bachman (1960) outlined the setting of supply analysis ^/
and summarized models which derive optimum supply from production func-
tions and from linear programming. They found that linear programming
was seemingly a sound analytical approach for comprehensive estimation
of direct and cross-price effects. Interaction between alternative pro-
duction activities is captured in the analysis. The authors criticized
the time-series approach in that it takes only a few variables into
account, and substitutability and complementarity among products and
inputs could not be adequately measured. Furthermore, historic data do
not always give good inferences for the future. Looking to the future,
the authors mention serious gaps in the theory of aggregation and
adjustment .

Other studies show that the LP estimates are unreliable. Wipf and l/
Bawden (1969) evaluated the descriptive and predictive reliability of
production function estimates. They derived firm-level supply functions
from production functions for a variety of agricultural products and
farm types. Supply elasticities and profit maximizing outputs were

49

computed from these, and comparisons were made with actual output and
with elasticities estimated from regression results of alternatively
specified forms of production functions. They wanted to see if realis-
tic supply functions could be derived from statistically fitted produc-
tion functions according to the notion that a firm's supply curve is
that portion of marginal cost above average cost. They found that these
empirical estimates were not reliable. Their output prediction did not
exhibit a consistent magnitude or direction of bias but ranged from
slight underestimates to extreme overestimates — the latter being most
frequent.

Quance and Tweeten (1971) compared the results of positivistic *S
(time series) studies with those of conditionally normative studies for
cotton, wheat, feed grain, and livestock. They found that LP models
provide somewhat realistic long-term elasticity estimates for commodi-
ties characterized by well defined resource constraints. They believed
that their predictions were good for wheat, average for cotton, and poor
for livestock. The LP results showed more realistic regional shares of
production (based on comparative advantage) , but not so realistic
absolute levels of these shares or of supply elasticities. The LP
supply functions exhibited an "inverted lazy-S" shape, rising steeply at
very low prices where the commodity is not profitable, becoming more
elastic at higher prices as commodities become competitive, and finally,
becoming steeply sloped when resources become constraining and diminish-
ing returns is experienced. Their results showed that supply

9
In the sense that linear programming estimation is based on the
norm "what would be" if producers followed the profit norm.

50

elasticities are not at all constant, and supply functions are not
straight lines as assumed by regression analysis. The authors cautioned
against constant slope regression estimates, especially when examining
policy impacts that fall outside the range of experience reflected in
past data.

From Wipf and Bawden's and Quance and Tweeten's findings it is
apparent that both regression and LP estimates differ. It is not appar-
ent which one is more reliable. Shumway and Chang (1977) estimated
direct supply elasticities for 15 vegetable and field crops in California
using regression analysis, and both direct and cross-price elasticities /
with LP analysis. They compared the reliability of both methods accord-
ing to three criteria. First, they compared long-run LP direct supply
elasticities for each commodity (group) at the average 1961-1965 output
levels and lagged representative crop prices for 1960-1964 with regres-
sion elasticities for the same period computed by imposing certain
efficiency conditions for acceptability. The authors found a high
degree of comparability for individual crops. Secondly, they used the
LP derived parameters as prior information in time-series regressions to
predict 1974 and 1975 supply levels and found that this procedure did
not significantly reduce the accuracy of those equations. Finally, they
used LP estimated cross-price parameters in time-series regressions.
This procedure neither improved nor worsened the regression estimates.
Their findings do provide direct contrast to previous studies. The
authors suggested that LP estimates could be substantially improved if
the model specification better reflected the real world behavior of
producers. These estimates could be used to improve econometric models

51

where the latter are also appropriate.10 The introduction of endogenous
prices and of risk into linear programming models should add to the
realism of supply estimates.

Positive estimates have certain advantages. Where available and
where the structure of the economy has not markedly changed, these esti-
mates would give accurate predictions. Problems can arise, however, if
one or more of the statistical assumptions are violated, e.g., high cor-
relations among independent variables, aggregation errors, measurement
errors, omission of variables, or incorrect specification of the
relationship.

Errors can also arise when estimating LP supply functions. Stoval
(1966) considers three sources of error, (a) the specification error
(errors in technical coefficients, resource restrictions, or in product
and input prices), (b) the sampling error (when the distribution of the
model's parameters over all firms is unknown but estimated by sampling
techniques), and (c) the aggregation error (in finding the representa-
tive farm) . Programming estimates are also limited in that they are
based on the profit maximizing goal and pure competition assumptions.
Profit maximization may not be the only goal of producers. Risk con-
siderations are also important in their decision making process. Thus,
the closer these assumptions reflect the decision environment of pro-
ducers, the more accurate one would expect the estimates to be. Linear
programming models permit simulation of the effects of exogenous
policies not experienced in the past— hence, not available from

Sharpless (1969) also emphasizes the importance of combining
linear programming with time-series studies of the rate at which farmers
adjust under given circumstances.

52

positivistic models. Furthermore, as stated earlier, they permit the
analysis of supply response to LDCs, where time-series data are often
of poor quality or nonexistent.

The theory of supply response based on the linear programming
assumptions is well known. Most of the research on supply response at
the firm level or at the industry level has been based on the fixed-
price assumption of classical linear programming. On the aggregate
level, this assumption does not hold. When production is large, prices
are the result of the interaction of supply and demand. Hence, even
if the individual producer is a price taker, on the aggregate, product
prices cannot be given ex-ante. Aggregating firm supply functions has
been the usual approach to arrive at sector-wide or industry supply
functions.

The first econometric studies to consider supply and demand
simultaneously were those by Powel and Gruen (1968) and by Gruen et al.
(1968), where direct and cross-price elasticities were calculated.

Interaction of supply and demand was considered by Hall et al.
(1968) to simulate competitive equilibrium for six products in 144 pro-
ducing regions and nine consuming regions in the United States using
quadratic programming. At the time of their writing they did not report
results on the estimation of supply functions. Several studies of
supply response at the sector level have used LP models with endogenous
prices — the Duloy and Norton approach. Using the agricultural model
CHAC, Bassoco and Norton (1975) analyzed the aggregate response of the

The limitations of this approach are discussed in Nerlove and
Bachman (1960), Sharpless (1969), and Egbert and Kim (1975).

53

Mexican agricultural sector from 1968-1976. Short-run and long-run
elasticities were estimated from supply functions derived by shifting
the demand function. The extent of the shift in demand was based on
certain assumptions regarding annual GNP growth, the rate of increase of
factor endowments, the rate of technological growth (rate of change in
yields per hectare), and the rate of change in export bounds. Condos
et al. (1974) developed a four region agricultural model of Tunisia
which has been used to analyze the implications of achieving a self-
sufficiency objective. Pomareda and Simmons (1977) analyzed the com-
petitive position of northwest Mexico, Guatemala, and Florida in the
U.S. winter market for fresh vegetables. The model included annual
crops and vegetables in three regions in Mexico and two regions in
Guatemala. The authors included four types of labor, various planting
dates, monthly yields and use of land and irrigation water, and monthly
demands in the U.S. and Mexico. Risk was introduced by means of abso-
lute deviations matrices and a risk aversion parameter. This model has
been used to analyze the supply response of alternative policies such as
changes in the U.S. demand, changes in the tariff structure, adoption of
new technologies in Guatemala, and increasing wages in Mexico. Cappi
et al. (1978) used the MOCA model for Central America12 to estimate
direct and cross-price elasticities for four grains.

The Aggregative Programming Model of Australian Agriculture
(Monypenny, 1975) was developed as a vehicle for obtaining guidelines to
the micro and macro implications of changes in policy instruments. This
model incorporates risk and considers nonirrigated short-cycle crops,

12

This experiment was done only with the Costa Rican model.

54

pasture, and livestock activities. This model includes special activi-
ties to account for yearly cash-flows, maximum borrowing constraints,
and allocations of cash for taxes and family consumption.

The research done on the reliability of supply response estimates
in agriculture does not reveal that the LP approach is less reliable
than the econometric approach. Previous tests on this reliability used
fixed-prices for products and did not include risk. Inclusion of demand
functions and risk should improve the estimates. Even though both
approaches present difficulties due to their assumptions, mathematical
programming models which include risk offer a potential tool for improv-
ing the supply estimates. The most important strength of the LP
approach is that it can simulate the effects of exogenous forces and
policies for which historical observations are not available.

CHAPTER IV
THE LP MODEL OF GUATEMALA

The Guatemala LP model MAYA is structured like the CHAC-type
models. In MAYA the agricultural sector is disaggregated into three
subsectors according to farm size and technology. Group 1 includes sub-
sistence farms primarily in the Guatemalan Highland, Group 2 farms are
engaged in small-scale marketing primarily in the eastern half of the
country, and Group 3 farms are engaged in commercial agriculture and are
located in the South Pacific region. These subsectors are linked by the
objective function and by intersectoral transfers of products and inputs.

MAYA was adapted from previous partial models of Guatemala's agri-
cultural sector and contains data for 1976-1977. Input-output coeffi-
cients for Group 1 were obtained partly from raw data from a farm-level
survey of Guatemala (AID, 1975) which includes only basic grains, and
partly from tabulated data of an LP model for the Highlands (see ECID/
SIECA, 1980), the data of which are also based on the survey. Although
the data from the survey is for 1973, a comparison with data from ICTA
surveys revealed that, in most cases, it was still valid for 1976-1977.
Input-output coefficients for Groups 2 and 3 were adapted from (a) a
fixed-demand, risk LP model for the South Pacific region (see Pomareda
and Samayoa, 1978), which includes mostly export crops, some grains, and
the livestock sector; (b) a country model of Guatemala which is part of
a simplified, no-risk, CHAC-family model (MOCA) for Central American
agriculture that links five country models through international trade

55

56

activities (see Cappi et al., 1978); and (c) farm budgets kept on a
daily basis by the Institute of Science and Agricultural Technology at
several experimental areas scattered throughout the country, and which
concentrate mainly on basic grains and other staples (ICTA, 1976, 1977,
1978, 1979).

Although MAYA is more inclusive than the models mentioned, it is
still not a complete model of the agricultural sector. It includes only
the (13) most important annual crops and excludes the livestock sector.
Approximately 90% of the value of total agricultural production is
accounted for in the model. Figure 5 gives an overview of MAYA and
Appendix A, Table VI a complete listing of the variables included.
Activities (columns) are classified into five major groups— production
and transformation activities, input supply, product demand, foreign
trade, and national accounts. The signs of the coefficients are
indicated. The matrix shows that basic inputs enter into the production
process as governed by the input balance rows and the resource avail-
ability restrictions. Crops are either sold directly or transformed.
Both are sold to the domestic market or exported. Imports are included
to complete the demand and supply process.

Specification of the Production and
Transformation Block

Production Groups

Group 1 producers are subsistence farmers with landholdings of less
than 10 hectares and a low level of technology who produce mainly staple
crops. Yields are low and labor is supplied by family members. Some
surplus produce is sold during market days or along the road. This type

Nv

COLUMNS

Production and Transformation

Input Purchases

ROWS >v

Group 1

Croup 3

Inputs Croup 1

Inputs Croups 2 6 3

Credit

Mult.

„„..

—

r,«.

—

— •-

,«,.

""*•

a--..

>„..

....

C2 i, C3

Cl

Cl

CJ

C3

Objective

-....s

-1

-, ~.

■*!

,-,.

*.

••>

««— -

National

National
Produce
Balances

ConveKlEy

National Labor
Constraints

Input
Croup 1

.„.,„....

Fl

.,_,„,.

™ --™

w

'■-,»

c.-.

♦ "..

*

-i

Croup 1
Farms

—

Ess.

-_

>—

*-"-■»

-1

und

faltal.

£2L

; ;

F,

-1

5""

"*"

~1

-1-1-1

"""

*

Croup 2

.«-.

ES.

,»

"*°'

—

JIL'!.

-1

Croup 3
Farms

,™

ESS.

u».

M

,22.

-1

Bound.

1

! !

Figure 5. Overview of the MAYA Model'

Does not include risk (see Figure 4) .

A detailed labor matrix is shown in Figure 6,

58

Cmand International Trade

National Accounts

OU|.

"">"<•

Toial

»-

,.„

u„.

!"■

»

J

*HS

"

• C

C2

G3

CI C2 H3 1 Labo

'

'

-V

-1

-1

HA*

Ml

X

M2 1

1 1

.... ,

-,

-1

-,

-»

z

-I

■ |

I

I

I

I

!

I

I

I

< L

-,

< 0

1

' °

<0

< 0

<o

-1

< 0

-1

- 0

-1

...

■

— '

.K,

1',

- "'.

<0

<o

< 0

I«.

.0

-1

< a

< 0

•I

-1

-'

< 0

< *,

'- 'l

-1

<0

,o

-I

-I

-!

-I

-1

.0

i*l

- rlJ

h

| j

ml

*

»:

*»

110

l4

-— —

EXPLANATION OF SYMBOLS

st coeffici
aft annuls

differentials

vectors of wag.
inport and export

Figure 5. Extended

59

of farm is found in the Guatemalan Highland. One important feature of
the producers in this group is that they migrate to the coastal area
during the harvest season, and thus becomes part of the labor force of
Group 3. Income generated through migration is an important component
of the total income of this group.

Group 2 producers are small-scale farmers with landholdings of
between 10 and 60 hectares who are increasingly adopting modern
technologies. They typically hold part of the production for their own
consumption and for animal feed and market the remainder. The labor
force is made up of family members although some outside labor may be
hired. This type of farm is characteristic of the eastern half of the
country where 90% of the sesame, 50% of the beans and maize, 70% of the
rice, 30% of the coffee, and 40% of the domestically consumed bananas
are produced.

Group 3 producers are engaged in commercial agriculture in land-
holdings greater than 60 hectares and with relatively advanced
technology. They produce export crops, viz., cotton, sugarcane, coffee,
and bananas, and most of the grain marketed in the capital. These
farms are found only in the South Pacific region and produce 95% of
the sugarcane, 60% of the coffee, 34% of the rice, 25% of the maize,
and all of the cotton produced in Guatemala. From the point of view
of agricultural production and employment, this region is the most
important of the country.

Groups 1, 2, and 3 account, respectively, for roughly 10%, 30%, /
and 60% of the total value of agricultural production.

60
Production Technologies

Sixteen technologies have been specified according to whether labor
is used alone, combined with draft animals and/or machinery and accord-
ing to the proportion of total variable costs that make up intermediate
inputs, viz., fertilizers, chemicals, and improved seeds.1 In Table 3
four basic ways of combining labor, machinery, and draft animals are
shown. Each of these can be associated with a given level of intermedi-
ate input use. Codes used appear in parentheses.

This classification is somewhat arbitrary and does not necessarily
represent the usual practices of farmers because changes in prices of
products and inputs influence farmers' decisions on the combination of
inputs to use from one crop cycle to the other. Production of a given
crop in each of the three groups of farmers may take place under any of
these possibilities. For example, rice is produced in Group 3 with
technologies Dl and D2 with yields of 2275 and 2800 kilograms per
hectare, respectively, whereas in Group 2 it is produced with technology
CI with a yield of 2242 kilograms per hectare.

Transformation Activities

The model includes transformation activities in order to make it
more complete. Transformation coefficients take into account the extrac-
tion rates of raw products into final products and waste in marketing
the crop. For example, in the case of rice, farm yield is specified for
paddy, while demand is specified for polished rice. The extraction rate

1. . ..
A similar specification was used in Pomareda and Samayoa (1978) .

61

CTl

<

g

w

3

a,

c

a

■H

e

rQ

^

•H

CD

01

4-1

en

G

0

H

PL,

•H 4J

en

CO

CO

60 -H

<J

M

o

R

iH -H

0 ,Q

«

A

„

,

C -H

^^

^-s

^-^

^^

X W

CM

CM

CM

O W

<

pq

u

P

en

u

a)

•H

^1

-H

-d

QJ

^

0)

PL,

CTl

f=

•H

i-l

C/l

^

oj

m

m

u

>

o .c

cfl cd

62

of rice is 65%, for bran, 8%, and waste is 4% (SIECA/FAO, 1974).
Therefore, from every ton of paddy produced, 64.3% polished rice and
7.6% bran are obtained. For some crops such as beans and maize, which
are consumed without transformation, only the waste coefficient applies.
Account has also been taken of a "transformation differential" which is
the price of the final product multiplied by the transformation coeffi-
cient less the producer price of the raw product. For example, in the
case of rice the transformation differential is Q.087/kg = .96
[(.67 x .463) +(.08 x .079)] - .217, where .96 is 1 less the waste rate,
.463 is the price per kilogram of polished rice, .079 is the price per
kilogram of bran, and .217 is the farm-gate price of paddy. The trans-
formation coefficients and differentials as used in MAYA for the three
groups are shown in Appendix A, Table VII. Differences in the figures
for the same product between groups are due to different producer
prices.

Specification of Inputs

Two types of inputs are used in MAYA, (a) inputs supplied at the
regional level (viz., land, labor, machinery, and draft animals), which
are assumed to be perfectly inelastic and are specified on a monthly
basis; and (b) inputs supplied at the national level (viz., fertilizers,
chemicals, seeds, and credit), which are assumed to be perfectly
elastic. Farmers from Group 1 receive special treatment by the govern-
ment in the form of subsidized credit and easier access to seeds and
fertilizer. a Farmers in Groups 2 and 3 are assumed to compete for inputs
primarily because of lack of disaggregated data.

63

Labor

The treatment of the labor market in the LP model is a difficult
task. In a country where dualism in agriculture exists, with family
labor making up a large proportion of the labor force and where migra-
tions occur during certain months of the year, two problems arise:
(a) how to value family labor (treated under input prices), and (b) how
to define the limits of the supply of labor. Figure 6 shows a structure
of the labor market and brings out the hiring patterns of the three
groups. The labor force of Groups 1 and 2 is made up mainly of family
labor and, to a lesser extent, of hired labor from adjacent rural and
urban areas. On commercial farms four kinds of field labor are used,
(a) resident laborers who are given housing, (b) wage laborers from the
area, (c) migrant workers from the Highland (who contribute up to 60% of
the total labor force during harvest time) , and (d) migrant workers from
Group 2. An upper bound was set on the supply of migrants from Group 2
equal to 10% of the labor force in Group 3 in order to allow the model
to hire migrants from the Highland at a higher cost, which is the case
during harvest time.

The data on labor used in MAYA are projected figures based on the
1973 Population Census. The economically active population in 1976 by
departments was 1,911,313. Table 4 shows the distribution by group.

Labor constraints have been estimated subject to several considera-
tions such as the contribution of family labor and the availability of
urban labor for agriculture. Total labor force was thus adjusted to
exclude labor employed in livestock and in other crops not considered in

64

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66

2
the model as well as to account for absenteeism and idleness. In MAYA

self-employed workers (family heads and adults) are assumed to provide
100% of their time, whereas nonwage family members are assumed to con-
tribute only 60% of adult-equivalent work. Hired labor in Groups 1 and
2 is assumed to be made up of rural and urban contracted labor in each
group. Resident labor in large farms is assumed to be made up of 70%
of the family labor force of Group 3. Temporal labor is provided by
wage laborers (both rural and urban) from the region. It was assumed
that only males migrate for temporal work in agriculture. Labor
restrictions expressed in full-time adult equivalent workers are shown
in Table 5 and in thousands of work-days per month in Appendix A, Table
VIII.

Other Inputs

The land input coefficient was one, implying the use of an entire
hectare. An exception is made at the beginning of the cropping cycle
when preparation of the land would not tie it up for a full month.
Preparation of the land with draft animals may require a full month,
whereas preparation with machinery may require less than a month. This
time savings is important when double cropping is feasible. The
restrictions on land were set equal to the area planted with the crops
considered in each group. The alternative of using the total land area
owned by each group of producers would have understated the restrictions
when two crops are grown per year. Ideally, idle land with a potential

2
Labor employed in livestock activities accounts for 15, 25, and
20% of the agricultural labor force in Groups 1, 2, and 3, respectively.
A further reduction of 10% was made to account for employment in crops
not included in the model.

67

Table 5. Labor Restrictions in MAYA

Labor
Category

Group 1

Group 2

Group 3

Residents

Temporal

Family labor
Hired labor

(Adult-equivalent workers)

32,604

120,100
66,400

203,100
185,800

TOTAL

186,500

388,900

92,404

68

for growing annual crops should be included; however, due to lack of
data this could not be done.

Machinery requirements were standardized for a tractor of 60 HP and
were expressed in hours of tractor use. The total number of tractors
available in 1976 was calculated from the total imports since 1967.
During this period 8,847 were imported, 5% of which were assumed to be
available to producers in Group l.3 A maximum of 180 hours of use per
month per tractor was assumed.

The technical coefficients for fertilizer in Group 1 were expressed
in terms of kilograms of urea and kilograms of "other fertilizers." In
Groups 2 and 3 the technical coefficients express nutrient requirements
in terms of kilograms of nitrogen, phosphorus, and potassium (N, P, K) .
Nutrient supplies, however, were expressed in kilograms of fertilizer,
i.e., simple and complex formulas with the model selecting the best
combination.

Four types of chemicals were specified (viz., soil insecticides,
foliage, insecticides, herbicides, and fungicides), and their coeffi-
cients were expressed in quetzales per hectare. Coefficients for local
and/or improved seeds were expressed in kilograms per hectare. Farmers
were assumed to use available credit to purchase seeds, fertilizers, and
chemicals.

Input Prices

Input prices used in the model are reported in Table 6. Input
prices in MAYA are market prices and include wages which vary over

3
The Agricultural Census of 1964 reports this figure and it is
taken to be still valid.

69

Table 6. MAYA Input Prices

Input

Unit

Group 1

Group 2

Group 3

(Quetzales per unit)

Labor

day

0.40

2.20

2.20

Machinery-

hour

5.00b

2.29

2.29

Draft animals

day

1.54

1.20

1.20

Fertilizers

ammonium nitrate

ton

154.00

154.00

ammonium sulphate

ton

120.00

120.00

urea

ton

153.00

173.00

173.00

diammonium phosphate

ton

236.00

236.00

(20-20-0)

ton

180.00

180.00

(12-24-12)

ton

188.00

188.00

(15-15-15)

ton

181.00

181.00

(16-20-0)

ton

168.00

168.00

other fertilizers

ton

168.00

soil insecticides

Q

1.00

1.00

1.00

foliage insecticides

Q

1.00

1.00

herbicides

Q

1.00

1.00

fungicides

Q

1.00

1.00

other chemicals

Q

1.00

Improved seeds

maize

ton

510.00

840.00

840.00

rice

ton

600.00

600.00

sorghum0

ton

350.00

350.00

wheat

ton

380.00

380.00

potatoes

ton

330.00

sugarcane

ton

30.00

coffee

ton

4,500.00

4,500.00

cottonc

ton

550.00

lemon grass teac

ton

6.00

Credit

.05

- .12

,08 - .12

The wage for Group 1 is the reservation wage. The market wage is

Q 1.40. Wages for Groups 2 and 3 are market wages.

b

Price of rented machinery.

c

Only the 1973 prices of seeds for sorghum, cotton, and lemon grass
tea were available.

SOURCES: BANDESA, FERTICA, DIGESA, and Banco de Guatemala.

70

farm groups. Prices for land were endogenously determined. The problem
of how to account for family labor in the objective function depends on
its opportunity cost. If one assumes that labor could be employed else-
where, its price in the objective function would be the wage received.
This potential wage, called the reservation wage, is lower than the
market wage because labor would then be abundant and jobs still scarce
resulting in a fall of the current market wage.4 This reservation wage
was set at 30% of the market wage in the model.

Prices for other inputs in Groups 2 and 3 were as follows: (a)
fertilizer prices were expressed in thousand quetzales per ton of a
given formula, (b) chemicals were expressed in quetzales and their
prices in the objective function were unity, (c) coefficients for
machinery were total costs per hour of operating and maintaining a
tractor of 60 HP assuming a useful life of 10,000 hours over a period of
10 years, and (d) credit was available to farmers in Groups 2 and 3 at
interest rates of 12, 10, and 8% for short, medium, and long term credit,
respectively. Credit to Group 1 farmers was assumed to be subsidized by
BANDESA at a fixed rate of 5%.

The Specification of Demand and
Product Prices

Demands are specified at the national level for 18 final products.
Demand functions for 12 of these products were estimated. The remaining
six products (including export bananas which are only sold abroad) were

4
See, for example, Bassoco and Norton (1975) and Candler and
Pamareda (1977).

Machinery in Group 1 is assumed to be rented.

71

assumed to sell at fixed prices. At present, no comprehensive study is
available from which one could derive demand functions. To estimate the
demand_functions the procedure used for the Central American model
(MOCA) was followed. Price elasticities were derived from expenditure
elasticities previously estimated.

The method used to estimate price elasticities is the one suggested
by Frisch (1959) according to which ^price__elasticities can be estimated
once income elasticities, expenditure weights, and the value of the
money flexibility coefficient— the elasticity of the marginal utility of
income with respect total income— are known. The basic assumption
behind Frisch's approach is that there is "want independence" (i.e., the
marginal utility of good i depends only on its own quantity) among
groups of commodities. Estimation of the Frisch coefficient for
Guatemala is based on the findings of De Janvry et al. (1972) and of
Lluch and Williams (1977) on the relationship of the value of the Frisch
coefficient and per capita income. De Janvry et al. estimated values of
w from income and price elasticities of demand for food in various
countries of various income levels; regressed these values on
real per capita income; and obtained the following relation:

(D log£ (-w) = 1.591 - .5205 log y/p,

where w is the money flexibility coefficient, y is per capita income,
and p is the price level. This equation was found to be statistically
significant and consistent with Frisch' s conjecture that w increases as

See SIECA/FAO (1974, Volume II).

This assumption may not be realistic for very disaggregated
commodity groups. See also footnote 9.

72

the level of income decreases. The same authors obtained w from the
estimation of the parameters of cardinal utility functions and from
systems of demand equations where the assumption of additivity was made.
They surveyed the literature of values of w estimated using this
approach and calculated the following regression equation:

(2) loge (-w) = 1.7595 - .5127 log y/p .

Lluch and Williams used time-series data on income and expenditures
for 14 countries with a broad range of incomes and four levels of com-
modity aggregation, and obtained the following regression equation:

(3) log10 (~^ = 1>434 ~ -331 los10 Y>

where Y is per capita GNP in 1969 dollars.

These three equations were applied to Guatemalan income data.
Values for w were obtained for four income strata, corresponding to 50,
30, 15, and 5% of the population, and for the average income level. The
results obtained were consistent with the theory and do not differ
notably between equations. Therefore, the average of all three values
of w obtained for the average income level (-2.0) was used in the calcu-

o

lation of price elasticities.

Frisch's equation for estimating the price elasticity of commodity

(4) n. = -E. (a. - a± i),

More traditional farmers have larger values of w because of their
lower incomes; consequently, their direct price elasticities would be
smaller, which reflects fewer alternative crops and technologies than
larger farmers.

73

where n± is the price elasticity, E± is the income elasticity, and a. is
the expenditure weight of commodity i. Since previous estimates of the
EjS were available, and w and the a±s could be estimated, this equation
was used to calculate direct price elasticities. Given income elas-
ticities and the consequent estimated direct price elasticities are
reported in Table 7.

The approach used to estimate demand functions is crude but has
been used for lack of better information. The analysis assumes a linear

9

When the "want-independence" assumption is dropped, it can be
shown that the direct-price elasticities estimated by Equation (4) would
be biased. Frisch's equation for estimating cross-price elasticities
is

CD n±k = -E.ak(l-|). i = l, ..., n

k = 1, ... , n
i * k

From Cournot's aggregation it follows that direct elasticities can
be calculated by (2)

By (1) we can write n, , as
kk

(3) nkk = {-^i[E.ak(l-^)]-^a.nik}/ak

Ek
- - (1 - — ) - I a. n., / a, ,
w .^ x ik k

by virtue of Engel's aggregation.

Equation (4) can also be written as

E. E.
n. = -E. a. (1 + -±) + — .
111 w w

The first term is clearly smaller than in (3) . The second term is
negative (since w is negative), whereas that of (3) can take either
sign. The bias of (4) thus cannot be known a priori.

Calculation of direct elasticities according to (3) does require,
however, previous knowledge of cross elasticities which are, usually,
not available in developing countries.

Product

74

Table 7. Given Income Elasticities and Calculated Price
Elasticities Using Frisch's Method

Given Income
Elasticity, E.

Direct Price
Elasticity, n.

Maize

Rice

Sorghum

Wheat flour

Beans

Potatoes

Cassava

Bananas

Sugar

Cotton fiber

Coffee

Vegetable oil

0.4
0.6

0.6
0.4
0.5
0.2
0.3
0.5

0.5
0.8

-0.231
-0.302
-0.300
-0.312
-0.208
-0.252
-0.100
-0.155
-0.260
-0.300
-0.267
-0.408

SOURCE: Income elasticities are estimated for 1965 and taken
from SIECA/FAO (1974, Vol. II).

75
demand function of the form
(5) Q = a - pp.

The price elasticity of demand is
rc\ P dQ „ P ,

(6) n = T "dp = 3T

and the slope and intercept parameters are

(7) 3 - n-f-

(8) a = Q + £P,

where Q is the observed quantity consumed, by definition equal to per
capita consumption times population, and P is the observed price.
Appendix A, Table IX reports the demand equations as incorporated into
MAYA.

Demand functions were then broken down into at least 12 segments.
The extreme values correspond to the observed price ± 60 to 100%. The
area under the demand curve and the revenue function were then calcu-
lated given the estimated parameters.

The incorporation of demand structures permits specification of
competitive and monopolistic market forms. For simulation purposes with
MAYA, the competitive market form was assumed since, with a few possible
exceptions in the export crops, no producer can influence the market
price through production decisions. The optimization feature of the
model is not used in a normative sense, to maximize some goal set, but
rather in a descriptive sense, to simulate the behavior of the

76

competitive market. In the model the sum of the Marshallian surpluses
for each product's market is maximized, except in the case of those pro-
ducts whose prices are assumed to be exogenous.

Since the observed data on prices and quantities refer only to
market data, the Marshallian surpluses in MAYA pertain only to the
marketed surpluses. In Guatemala not all the quantity of maize and
beans consumed is bought in the market. Many producers satisfy their
consumption needs first before selling the remainder. In MAYA this was
represented by subtracting farm-family requirements of those two crops
from total production to arrive at the marketed surplus. Data on home
retentions are available by district. It was further assumed that if a
farmer meets his consumption requirements through market purchase, he
must pay an opportunity cost equal to the difference between the farm
gate price and the market price.

In MAYA national demand curves pass through a point representing
observed prices and quantities. Information on some product prices on a
regional basis is available from the statistical office, but information
on production on a regional basis is incomplete. Therefore, it was not
possible to estimate a weighted average of consumer prices, and the
prices used were simple averages. Export and import prices were
exogenous to the model under the assumption that Guatemala is a price
taker in international trade. Prices of exports were fob prices.
Import prices were adjusted for transportation costs and were measured
in Guatemala City. Domestic and international prices used in MAYA are
shown in Table 8.

77

Table 8. Domestic, Import, and Export Prices in MAYA

Consumer
Price

Export
Price

Import

Prices

Product

Third

Central

Countries

America

(Quetzales

per ton)

Maize

168.0

158.0

157.0

Beans

476.0

566.0

460.0

Sorghum

145.0

145.0

Rice

463.0

384.0

427.0

Wheat flour

430.0

223. 0a

Potatoes

220.0

260.0

Cassava

153.0

Bran

79.0

Sugar

242.0

340.0

Molasses

90.0

Lump Molasses

300.0

Coffee (ground)

3060.0

Coffee (beans)

2040.0

Bananas (domestic

consumption)

225.0

Bananas (export)

151.0

Cotton fiber

1140.0

1162.0

Cottonseed cake

87.0

Lemon grass tea

3370.0

Vegetable oil

940.0

Price of wheat grain.
SOURCES: DGE (1978), CNA, and Banco de Guatemala.

78

The Risk Matrix

The risk matrix was built as shown in Figure 4 (p. 41), with the
variant that it consists of three blocks; each corresponding to one
group. The available data on revenue variations were 10-year time-
series of prices for each of Guatemala's 22 departments, from which
series on a par group basis were obtained (see Appendix A, Tablw X) , and
on yields at the national level (Appendix A, Table IV) . To derive per
hectare revenue series by technology per crop (single cropped or in
association) , yields for each technology were assumed to hold a constant
relation to national yields, equal to the ratio between the technology
yield and the average of national yields for 1975-1977. After defend-
ing the revenue series by linear regressions the matrices of deviations
were calculated for each group.

CHAPTER V
MODEL VALIDATION AND RESULTS

MAYA was designed to model actual 1976-1977 behavior of the
Guatemalan agricultural sector. Before using it for policy analysis,
its predicting ability was tested. There are no formal analytical tests
for validating a large scale LP model. Validation or verification of LP
models has been examined by several researchers. Nugent (1970) explored
the feasibility of validation tests of programming models. In his work
with a multi-sector, multi-time period model of the Greek economy, he
gave three reasons why a model may not perfectly simulate the actual
economy: (a) there may be errors of specification in the model's con-
straint set, (b) the underlying market structure may be incorrectly
represented numerically in the model, and (c) a programming model
optimizes a particular objective function, whereas the real world may
optimize several "micro" objective functions. To test the first two
distortions, Kutcher (1979) proposed two tests for the Pacifico model of
the Mexican northwest — a capacity test which forced the model to produce
at least the base period quantities and sell at base period prices, and
a competitive market assumption test by further redefining the objective
function to a cost minimization version and analyzing shadow prices of
the minimum output constraints. On the demand side, Kutcher tested the
model assuming perfectly elastic demand (price taker assumption) , and
then assuming downward sloping demands. An analysis of activity levels
and shadow prices revealed that the latter version was perf erred.

79

80

Rodriguez (1978) did similar validation tests with an agricultural model
for the Philippines. The basic validation tests used in most planning
models involve analyzing how well the model solution simulates the base
period situation, (a) whether the model can produce the base period
demand quantity, (b) how well the model replicates the base period quan-
tity (whether price equals marginal cost) , and (c) how well the model
replicates base period quantities with prices fixed at base period
values. The validation tests which have been used generally relate to
aggregate results. This is most likely because results from an aggre-
gate model generally do not compare well to disaggregate regional
production patterns (McCarl and Spreen, 1980).

In validating MAYA the average absolute deviation criterion was
used to check how closely the model predicts consumer prices, volume of
production, and areas planted. The fact that MAYA does not reflect the
actual levels of prices and quantities on a group basis, as closely as
it does on the aggregate, does not discredit its usefulness in predict-
ing the general behavior at the group level. Before showing the
results, a number of validation issues need to be mentioned.

All of the parameters in MAYA were agronomic coefficients from
published surveys, farm budgets kept on a daily basis, previous partial
models, and government publications. The competitive market structure
was used on the assumption that it accurately describes the behavior of
Guatemalan farmers. Two modifications were, nevertheless, introduced to
make the model more realistic. First, Groups 1 and 2 farmers were per-
mitted to choose between keeping a minimum amount of maize and beans for
family consumption at home at farm-gate prices or buying them at a
higher price that takes into account an acceptable buying-selling margin.

81

This is equivalent to shifting the price axis to the right. The demand
function for these two products, then, only reflects the demand for the
marketed surplus by the nonfarm population. Second, risk was introduced
to explain observed behavior more realistically.

An important question in validating the Guatemalan model was what
to validate the base-period solution against. How confident can one be
of the base-period data? With regards to product and area levels, large
discrepancies were often encountered in published documents where the
source of the data was the same. An effort was then made to use the
data believed to be most reliable based on the opinion of experienced
authorities.

To recapitulate, the basic conditions under which the model was
solved for the base period were as follows:

(a) Each producer group had a limited amount of land equal to
the average of the area planted during 1976 and 1977.

(b) Most crops were produced under different technologies.

(c) Labor-use constraints were specified monthly by group.

(d) The areas planted with coffee and export bananas were
restricted.

(e) Inputs supplied at the regional level were fixed and
those supplied at the national level were available in
infinitely elastic supplies.

(f) Commodity demand functions were specified at the national
level.

(g) Upper bounds were set on imports from and exports to the
rest of the world (except on exports of cotton), as well as
on imports from other Central American countries.

82

The model was solved under these conditions and its predictive
ability was tested against actual base-period data. In the absence of
any empirical data from which to estimate the risk parameters <f> , the
basic procedure followed was to search through post-optimality tech-
niques the values of <J> for each group which best described the base-
period prices. Research done by Pomareda and Simmons (1975), Hazell and
Scandizzo (1977), Dillon and Scandizzo (1979), and Pomareda and Samayoa
(1978) indicate that values of between .5 and 2.0 best describe the
level of risk aversion in Brazil, Central America, and Mexico. These
studies also reveal that smaller, less sophisticated farmers are more
risk averse. Based on these studies, the assumption was made that the
value of the risk parameter <j> differed by .75 between Groups 1 and 2,
and by .5 between Groups 2 and 3. It was found that the set of <}> values
(2.0, 1.25, .75) for Groups 1, 2, and 3, respectively, performed best.
These values represent risk aversion at the aggregate group level.

Solving the model for different sets of cj> values provides direct
information about the effects of different levels of risk aversion on
equilibrium prices and quantities, for quantifying the actual values of
<j>. Table 9 reports the result of different sets of <J> values on domestic
equilibrium prices. The prices of maize, beans, sorghum, sugar, lump
molasses, potatoes, and vegetable oils tended to rise with increases in
<j>, which indicates that there are corresponding reductions in the
quantities produced for the domestic market. On the other hand, the
prices of rice, wheat flour, cassava, and export bananas decreased as <j>
increased, indicating that production of these crops for the domestic
market would increase as producers become more risk averse. The prices
of cotton fiber, bananas for domestic consumption, and lemon grass tea

83

Table 9. Price Response to Different Values of

Product

Risk Levels'

Actual

0-0-0 1. 5-. 75-. 25 2-1. 25-. 75 2.5-1.75-1.25

(Quetzales per ton)

Maize

168

143

157

159

159

Beans

476

357

445

498

558

Sorghum

145

108

128

144

159

Rice

463

412

403

385

363

Wheat flour

430

453

418

415

411

Potatoes

220

169

193

201

210

Cassava

153

117

116

114

112

Bran

79

79

79

79

79

Coffee

3060

2472

2474

2474

2474

Sugar

242

218

227

240

255

Molasses

90

90

90

90

90

Lump molasses

300

275

285

301

317

Cotton fiber

1140

1261

1261

1261

1261

Cottonseed cake

87

87

87

87

87

Bananas (export)

151

113

111

110

108

Bananas (domestic

consumption)

225

234

237

235

233

Lemon grass tea

3370

3370

3370

3370

3370

Vegetable oil

940

813

831

842

850

m.a.d.

70.7

60.7

57.8

64.1

The first, second, and third values correspond, respectively, to
groups of farmers Gl, G2, and G3 .

m.a.d. is the mean absolute deviation of the solution value with
respect to the actual value.

84

showed little or no response to risk. The results on quantities are
shown in detail in Table 10.

The first columns of Tables 9 and 10 show the base-year values
(1976-1977 averages) of prices and quantities. By comparing the model
solution for different values of risk with the base-year values, we have
a basis for selecting the best-fitting values of <j>. Clearly, the solu-
tion corresponding to risk neutrality (<J> = 0) is unsatisfactory. There
is a definite improvement in both prices and quantity fits as <j> in-
creases, but it deteriorates again as the values reach 2.5, 1.75, and
1.25. These results are better visualized at the group level in
Appendix A, Tables XI and XII. In selecting the set of <f> values it is
more appropriate to concentrate on the commodity prices because the
market structure of the model can only be expected to work best at the
demand level. The last row of Table 9 reports the sample mean absolute
deviation, m.a.d., of the price fits and demonstrates the superiority of
the risk set (2.0, 1.25, .75). The results suggest a useful definition
of riskiness in crop production which takes into account intercrop
relationships. High (low) risk crops can be defined as those where
production decreases (increases) as producers become more risk averse,
whereas risk neutral crops are those whose production is unaffected by
(j). Thus, it can be concluded that introduction of risk averse behavior
in MAYA improves its predictive power compared to the more common
assumption of risk neutrality.

The results of this section suggest that the model solution is
improved with the incorporation of risk and that the risk set (2.0,
1.25, .75) most closely represents the real world situation. This risk
set was selected as the basis for further policy simulations.

85

Table 10. Quantity Response to Different Values of <J>

Product

Maize

Beans

Sorghum

Rice (paddy)

Wheat

Potatoes

Cassava

Bran

Coffee

Sugarcane

Molasses

Lump molasses

Cotton (raw)

Cottonseed cake

Bananas (export)

Bananas (domestic
consumption)

Lemon grass tea

Vegetable oil

Risk Levels'

Actual

0-0-0 1. 5-. 75-. 25 2-1. 25-. 75 2.5-1.75-1.25

(Quetzales

per ton)

850

905

896

851

97

103

100

92

51

59

55

54

26

27

27

27

57

55

57

57

63

66

65

65

10

8

8

8

»,.

31

32

32

469

431

431

431

5705

6042

6042

5705

216

205

205

203

...

21

21

326

309

310

316

79

79

80

336

348

348

348

194

4
27

194

194

194

28

28

28

852
89
47
27
57
64
8
32

431
5651

201

318

81

348

194

28

The first, second, and third values correspond, respectively, to
groups Gl, G2, and G3.

CHAPTER VI
EMPIRICAL TESTING

One of the important uses of LP models is to obtain insights into
supply response, a fundamental question of production theory. MAYA was
built using cross-section microeconomic data and behavioral assumptions
which appropriately define the conditions for supply response to differ-
ent policies. The purpose of the results presented in this chapter is
not to provide concrete recommendations to policy makers, but rather to
present some issues and broad qualitative results of the Guatemalan
agriculture, using MAYA. In this chapter direct and cross-price elas-
ticities for selected crops and the supply response to changes in the
price of maize and cotton are explored in detail. The effect of risk on
supply response and some comparative advantage calculations are also
presented.

Estimation of Supply Elasticities

Supply elasticities are estimated for six products — maize, beans,
rice, sorghum, wheat, and cotton. These products were selected because
their input data in the model are more complete and are believed to be
more reliable. The results of this estimation for maize and cotton are
explored in detail in following sections. The supply response functions
obtained are, given the static formulation of the model, "equilibrium
short-run" functions; equilibrium in the sense that the points along a
given function are implicit intersections of supply and demand, after

86

87

all adjustments are allowed to work themselves out; and short-run
because investment and technology remain fixed. These response func-
tions, then, are not the traditional supply functions since, when the
price of one product is varied, the prices of all other products are
also allowed to vary.

The procedure for tracing out the functions consists of rotating
the product demand functions rightward, one at a time by varying the
right-hand side value of the convex combination constraint (see Chapter
III). Following this procedure, supply response schedules of maize,
other grains, and cotton were calculated as reported in Table 11.
Figures 7 and 8 portray these results graphically. Increased production
of maize due to higher prices took place at the expense of decreases in
the production of other crops. Since the demand for other products was
held constant, resources were reallocated away from these crops into
maize; the prices of these crops thus tended to rise in all cases except
in the case of cotton whose domestic price remained constant, and beans
whose production increased because of double cropping with maize.
Similar results were obtained when the international price of cotton was
gradually increased as in Table 12. Expanded production of both crops
thus draws resources away from others, and as production of the latter
declines, their prices tend to rise unless they are complements in
consumption.

It is evident from these results that the elasticity of supply is
not at all constant.

In

See footnote 4 on page 99,

89

a

w e
3 o

90

Price of Maize
(Q/ton)

210 .

200 -

190

180

170

160
150

140 '
130

120

110

100

Group 1

Group 3

Group 2

Thousand

tons

50 100 150 200 250 300 350 400 450 500 550 600

Figure 8. Maize Supply Response by Group as Estimated with MAYA

92

Direct and cross-price elasticities for the six products selected
were calculated taking as reference the highest and lowest production
recorded between 1970 and 1977 (Table 13). These points are only
approximate limits since by rotating the demand we are controlling
demand shifts not output shifts. It is, therefore, not possible to find
exact reference quantities. It may be seen from Figure 9 that the arc
elasticity of supply between points a and b can be calculated ex-post as
follows :

(q2 " V/(q2 + V

(P2 " P1)/(P2 + Px)

The direct price elasticities in Table 13 are reasonable in view of

2
prevxous econometric studies of less developed countries. The cross-
price elasticities show that some crops were more likely to drop in
production than others when prices of competing crops were raised.
Sorghum, for example, is more responsive in a negative direction to an
increase in the price of maize. Since maize, cotton, and rice compete
for resources in the more productive Group 3, an increase in the price
of rice caused a decrease in both area and volume of production of maize
and cotton — the estimated cross-price output elasticity of maize is
-1.038 and that of cotton is -1.664. The increase in cotton production
also took place at the expense of sharp decreases in the rice producing
areas (a cross-price elasticity of -1.003). Cotton is a very profitable
crop in Guatemala, and cotton responsiveness to maize price change
is only -.104, wherease maize responsiveness to cotton price change

2
See, for example, Askari and Cummings (1977)

93

Table 13. Arc Elasticities of Supply of Selected Products3 as Computed
from Estimates Obtained with MAYA

Price

Quantity

Response of

Change for

Maize

Beans

Sorghum

Rice

Wheat

Cotton

Maize

0.619

0.030

-0.785

0

-0.199

-0.104

Beans

0.135

4.975

0

0

0

-0.322

Sorghum

-1.821

0

65.189

0

0

-0.452

Rice

-1.038

0

0

33.746

0

-1.664

Wheat

-0.177

0

0

0

4.078

-0.014

Cotton

-0.193

-0.037

-0.247

-1.003

0.059

0.408

In calculating the direct and cross-price elasticities of maize
and beans, only the marketed quantities of both commodities were taken
into account. Total elasticities are smaller.

94

Price

Quantity

ql q2

Figure 9. Hypothetical Graph Showing Response Associated
with the Increasing Slope of the Demand
Function

95

is -.193. The cross-price elasticities between maize and beans, as
expected, are positive since they are mostly double cropped. The size
of the elasticities of these two crops appear to be small when taken for
the country as a whole; they conceal, however, important changes which
take place at the group level. An analysis of the elasticities at the
group level would be of more interest to policy makers. Table 14
reports the direct and cross-price elasticites for maize and beans by
group. The own-price elasticities of maize for small, medium, and large
farmers are, respectively, 3.18, -.10, and 1.07, whereas the average for
the country is .62. The own price elasticity of beans is .51 for Group
1, and 4.98 for Group 2, whereas the average elasticity for all groups
is 4.98. The high price elasticity of maize of Group 1 indicates that
small farmers are much more responsive to changes in the price of maize
than are medium and large farmers.

Direct and cross-price elasticities for maize and beans have
expected magnitudes and signs in Groups 1 and 3. Maize price
elasticities — direct and cross-price — for Group 2, although small, are
unexpectedly negative. Moreover, the direct price elasticity of beans
for Group 2 has the expected sign but the cross-price elasticity of
maize, -.15, is negative. Group 2 farmers grow one-third of maize and
one-half of beans in association. Since maize and beans are complements
in consumption one would expect that an increase in the price of one of
them would produce increments in the production of both crops. In the
next section it will be shown that competition for resources between
Groups 2 and 3 is responsible for these results.

96

Table 14. Arc Elasticities for Maize and Beans as Computed from
Estimates Obtained with MAYA, by Group

Price
Change for

Maize

Quantity Response of

Beans Sorghum Rice

Wheat

Cotton

Maize

Gl
G2
G3

3.180

0.711

0

0

-0.200

0

0.100

-0.100

3.180

0

0

0

1.068

0

-0.785

0

0

-0.104

Beans

Gl
G2
G3

0.268

0.506

0

0

0

0

0.154

4,976

0

0

0

0

0.885

0

0

0

0

-0.322

97

Supply Response to
Changes in the Price of Maize

Tracing the supply curve by shifting the demand permits an overview
of the technological change and crop substitution that takes place at
the group level. In Table 15 and Appendix A, Table XIII, it is shown
that an increase in maize output in Group 1 takes place through in-
creases in area and yields. At a price of Q 209 per ton single-crop
maize is grown with more input-intensive, higher-yielding technologies
A4 and D2.

Maize output in Group 2 declined slightly. Output in this group is
the sum of that from a single-cropped technology and technologies
associated with beans and sesame — each showing a different behavior.
The area planted with maize-beans declined sharply from 56,200 to 4,300
hectares, whereas that planted with maize-sesame increased from 18,800
to 26,300 hectares. The area planted with single-cropped maize in-
creased by one-fourth as more and more farmers switched to lower yield-
ing technology B3 . Total area planted with maize (single-cropped and in
association) increased by 3.1%. Group 3 farmers respond to the price
rise by planting more maize with higher-yielding technology Dl. Maize
production becomes quite profitable in Group 3 and is substituted for
export cotton and sorghum (cross-price elasticities are -1.04 and -.785,

respectively). There is, clearly, a great competition for resources

3
between Groups 2 and 3, with the latter benefitting from the price rise

because of their more efficient use of resources. In Group 2 sorghum

3

As indicated in Chapter IV, in MAYA Groups 2 and 3 compete for
intermediate inputs.

Table 15. Production, Yield, and Employment Response to Variations in
the Price of Maize as Estimated with MAYA, by Group

Farm Group
and Crop

Group 1

Group 1

Price of Maize per Ton in Quetzales

Group 1
Group 2
Group 3

109.0

124.0

142.5

159.3

165.0

180.0

(Production in thousand tons)

(Yield in kilograms per hectare)

(Employment in thousand man-days)

10,878
43,373
32,171

13,982
42,936
32,272

16,739
41,856
32,233

16,507
41,833
32,002

18,048
41,429
31,974

21,366

41,797
31,963

209.0

maize

98.0

132.1

167.3

168.6

187.0

226.4

236.7

beans

15.4

19.6

22.0

23.0

22.4

20.6

20.7

wheat

62.6

59.8

59.8

56.6

56.6

56.6

55.2

"oup 2

maize

496.6

502.6

500.3

496.4

492.5

491.2

476.1

beans

75.0

70.8

68.4

69.1

69.6

71.4

71.3

rice

27.4

27.4

27.4

27.4

27.4

27.4

27.4

sorghum

12.3

maize

153.0

173.2

177.8

185.6

193.3

196.0

239.0

sorghum

55.3

55.3

53.7

53.7

48.9

47.3

33.4

cotton

319.5

316.5

313.8

316.1

313.7

313.8

299.2

maize

1227

1233

1245

1242

1254

1275

1324

beans

393

393

393

393

393

393

393

wheat

1540

1404

1371

1388

1388

1388

1396

oup 2

maize

1848

1785

1780

1763

1750

1745

1724

beans

593

610

669

674

723

711

712

rice

2242

2242

2242

2242

2242

2242

2242

sorghum

3000

maize

2040

2132

2151

2162

2212

2221

2320

sorghum

2900

2900

2900

2900

2900

2900

2900

cotton

3194

3194

3194

3194

3194

3194

3194

21,178
41,960
31,782

99

production benefits from these crop areas and input substitutions (with
a cross-price elasticity of 3.18). It is also interesting to note that
the area planted with single-cropped beans increased by 37%. This
result seems to indicate that as the price of maize rises and resources
become scarce, farmers in Group 2 are willing to take more risk and
prefer to grow single-cropped beans, a high risk activity, rather than
to grow associated maize-beans, a less risky activity. Total area
response function for maize and beans, and group yield response func-
tions for maize are shown in Figures 10 and 11, respectively.

Similar results were obtained when the price of beans was allowed
to vary. The signs of the elasticities of Group 1 are positive, as
expected, and the magnitudes are reasonable (Table 14) . The direct
price elasticity of beans of Group 2 has the expected sign, but the
cross-price elasticity of maize, -.15, is negative. Again, there is
competition for resources with Group 3. More maize is produced by Group
3 (the cross-price elasticity is .88) even at the expense of cotton
production.

Appendix A, Table XIV shows the degree of input use, yield, and

4
risk of the technologies of interest for each group of farmers. This

table and Appendix A, Table XII indicate that, in general, higher prices
motivate farmers to adopt more input-intensive, higher-yielding tech-
niques which are also riskier. Thus, Group 1 farmers plant larger areas
of single-cropped maize and of associated maize-beans. Group 2 farmers,
on the other hand, plant smaller areas of associated maize-beans

4
Risk is represented by the sum of absolute deviations of total

returns per hectare from the fitted regression over a 10-year period.

100

CD

en

N

e

•H

-■■■■

at

CIJ

S

«

TJ

a

ca

a)

N

•H

(D

si

<;

T)

>H

4J

a)

•H

.c

CJ

u

n

•H

CD

!5

en

<

T)

C1J

•n

C

c

•H

cfl

crt

4J

~

^

CO

o

C

«

en

a)

QJ

pa

4-1

a

■H

en

rrt

(!)

5^

Pi

4-1

01

O

<1)

U

QJ

<

U

101

P. 0)

u
6 j-i

CO CJ

102

(initially adapted to avoid risk) , and larger areas of intercropped
maize-sesame, and of beans alone (a more risky activity). Group 3
farmers grow only single-cropped maize and respond positively to price
increases; their risk taking behavior is evident as they quickly adopt
more advanced and more risky technologies.

Another area affected by the foregoing price policy was employment.
On the one hand, an increase in the price of maize brought about tech-
nological improvement which is labor reducing. On the other hand, an
increase in areas planted is labor creating. Overall employment in-
creased by 9.8% as the price increased from Q109 to Q209 per ton.
Table 15 reports that employment in Groups 2 and 3 decreased by 3.3 and
1.2%, respectively, whereas employment in Group 1 almost doubled mainly
due to large increases in areas planted. This result is interesting
given the serious problem of employment in agriculture.

Supply Response to
Changes in the Price of Cotton

To trace the supply function for cotton the same procedure of
shifting the demand function around its intercept, as explained earlier,
was followed with the additional assumption that exogenous international
prices also increase. The domestic consumption of cotton grew at
average annual rates of 9.4% from 1959 to 1973 (IDB /IBRD /AID, 1977), and
of 9.0% from 1973 to 1977 (Banco de Guatemala, 1979). During 1974-1977
average annual consumption accounted for 11% of total production.

With international prices unchanged, rotation of the demand curve
around its intercept yields a perfectly elastic domestic supply. This
is explained by the small domestic demand relative to international
demand .

103

International prices of cotton experienced an upward trend after 1973
and Guatemalan export prices reflect that trend. For purposes of
calculating supply elasticities and of tracing supply response functions,
it was assumed that export prices varied in increments of 10% of the
1975-1977 price of Q 1140 per ton (as assumed in the model), within the
range -20% to +30% of this price. At the same time, domestic demand was
assumed to change by 9.5% of the equilibrium quantity with each export
price change. The idea was to reflect the trend in domestic demand and,
at the same time, the situation that prevailed from 1973 to 1977 when
export prices varied within the range considered. The assumed price
changes imply smaller domestic demands coupled with lower international
prices, which in general would not necessarily hold true.

A domestic and an export supply function were obtained (Figure 12) .
The domestic supply function is very inelastic since domestic consump-
tions is a small fraction of total supply. The export supply function
exhibits some interesting features. Its shape resembles an inverted
lazy-S; at low prices it is quite elastic, and at higher prices it
becomes more and more inelastic as resources become constraining. The
most restricting resource is credit which is assumed fixed in the model.
It was interesting to find that an increase in credit of 5% was fully
allocated to cotton, and the consequent increase in production was
greater than the credit increase in percentage terms. This result shows
that the supply elasticity with respect to credit is greater than one.
This finding should be of interest to policy makers in formulating a
credit policy.

Table 16 shows direct and cross-price elasticities of cotton by
farm group. The direct price elasticity of cotton of .41 seems

104

Price of Cotton
(Q/ton)

1700 -•

1600 ■•

1500 -

1400 -■

1300 -
1200

1100 -■
1000 -■

900 "
800

— l 1 r

10 20 30

40 50 60 70 80 90

— I —

100

Thousand
tons

Figure 12. Supply Response Functions for Cotton as Estimated
with MAYA

105

106

reasonable when compared to results of studies by Quance and Tweeten
(1971) and Tweeten and Quance (1969), which revealed a supply elasticity
of .3 to .4 for the U.S. and of .3 for the world excluding the U.S. and
communist countries. The cross-price elasticity of maize in Group 3 is
-1.09 which implies that maize growers are the most affected by an in-
crease in cotton prices; and Table 17 reports that the area planted with
maize in Group 3 decreased by 21%. The cross-price elasticity of maize
for Group 1, -.55, is relatively large as labor is scarce because migra-
tion into cotton production is intensified. Group 2 farmers benefit
directly from these area reductions. Because farmers in Group 2 compete
with those of Group 3 for intermediate inputs, as less maize is produced
by Group 3, some of the resources formerly used to produce maize on
large farms are shifted to maize production on medium-sized farms. It
is interesting to note that maize area decreased on Group 2 farms and,
at the same time, more maize was produced. This occurred both due to
the adoption of more input-intensive, riskier technologies of maize and
to increased production of maize associated with beans. Production of
beans by Group 2 farmers remained rather stable, whereas rice production
decreased. The shadow price of cotton for the domestic market is also
reported in Table 17 and is always greater than the export price. This
result makes sense in view of the nature of the maximization of the
model; more exports are preferred because this adds foreign exchange and
export takes to producer surplus. The discrepancy between domestic and
export prices becomes smaller as the latter increases. This may be due
to the fact that the tax rate was allowed to increase with higher export
prices.

107

Table 17. Area, Production, and Domestic Price Response to Variations
in the Export Price of Cotton as Estimated with MAYA, by
Group

Farm Group
and Crop

Group 1

maize

maize-beans

wheat

Group 2

maize
beans

maize-beans
rice

Group 3

cotton

maize

sorghum

Group 1

maize
beans
wheat

Group 2

maize
beans
rice

Group 3

cotton

maize

sorghum

912

Price of Cotton per Ton in Quetzales

1026 1140 1254 1368 1482 1596

(Area in thousand hectares)

(Production in thousand tons)

1710

81

79

77

76

76

78

78

78

72

59

58

57

57

56

56

53

40

41

41

41

41

41

41

41

43

264

249

226

226

232

232

182

88

94

85

68

68

69

69

36

—

1

18

43

43

43

43

100

13

12

12

12

12

7

7

4

82

97

99

100

100

102

102

106

97

84

85

85

85

84

84

77

19

19

19

17

17

17

16

16

189

171

169

166

166

167

166

163

28

23

23

23

23

22

22

21

55

57

57

57

57

57

57

57

476

499

496

496

497

505

505

523

64

69

69

68

68

68

68

70

28

27

27

27

27

16

16

10

263

311

316

321

321

326

326

338

238

181

186

186

186

181

183

153

55

54

54

49

49

49

47

47

(Shadow price in quetzales per ton)
1016 1127 1261 1338 1436 1530 1622

1712

108

Effects of Expanding the Cotton Area

Cotton is the second largest export commodity in Guatemala after
coffee. It contributed 20% of the foreign exchange earnings of agricul-
tural exports during 1975 to 1977. Spurred by attractive world prices,
production and exports of cotton in Guatemala started in the 1950s
despite unsettled political conditions. Following a phenomenal rise
during the early 1960s, cotton area and production trended lower in the
late 1960s. During 1960-1961 the area planted was only 26,000 hectares,
it reached a peak of 115,000 hectares in 1965-1966, and declined sharply
to 80,000 hectares in 1968-1969 (Harness and Pugh, 1970). The decline
in cotton production followed lower prices in foreign markets, some
increase in production costs, especially pest control, and difficulty
in maintaining yields. This trend reversed itself in the 1970s with
more favorable international prices. In 1975 the area planted with
cotton reached 110,000 hectares which was again close to the peak level
of 1965-1966. The adoption of new techniques and effective plague
control also contributed to this outcome. The rapid upsurge of prices
and the consequent expansion of areas caused the Ministry of Agriculture
to intervene by fixing the area planted to protect smaller producers
from being displaced by the larger ones, and by fixing the quantities
to be sold in the domestic market.

Despite the competition of artificial fibers, world demand for
cotton shows an upward trend. International demand for Guatemalan
cotton was estimated to grow at an average of 1.6%, and domestic demand
at an average of 7.3% for the period 1980 to 1985 (IDB/IBRD/AID, 1977).

109

Cotton farming in Guatemala is dominated by large scale commercial
enterprises. Some farming operations combine cotton and cattle.
Generally speaking, a farmer who obtains high yields with reasonable
efficiency finds cotton much more profitable than most alternative crops,
From the stand point of land availability there is no close competition
among commercial crops. One reason for this is that land is still rela-
tively plentiful although there is considerable expense in clearing and
developing it. Another reason for the lack of competition among the
chief commercial crops is different growing requirements — for example,
cotton is grown in the lowlands, sugar cane usually at slightly higher
elevations, and coffee in the highlands. However, there are some over-
lapping labor needs between these crops, especially during harvest time.
Major enterprises most likely to continue to compete with cotton for
investment capital and management are cattle, bananas, and sugar cane.
More recently, tropical fruits and essential oil crops such as lemmon
grass and citronella have shown to be potential competitors of cotton.

Like coffee and sugar cane, cotton production is a highly labor
intensive crop. The supply of unskilled laborers, especially migratory
workers, has been inadequate especially during harvest time since often
the harvest season of all three crops overlap. However, increases in
wages coupled with increasing export prices have alleviated this problem
in the short run.

Migratory labor mainly from the Guatemalan Highlands make up about
60% of the total labor employed during harvest time in export crops.
Since the Guatemalan government has emphasized the need to improve the
economic conditions of small and medium-size farmers, it should be of
particular interest to policy makers to analyze the impact of policies

110
aimed at promoting exports on incomes and employment of these groups.

r

MAYA was used to simulate an 8% increase in the cotton area. Results
on labor supply response are shown in Table 18. Total labor use in-
creased by 1.4%. The reduction in migrant labor from Group 2 was more
than compensated by an increase in migrant labor from Group 1. Both
family and hired labor use decreased in Group 1, whereas in Group 2,
family labor decreased and hired labor increased. Figure 13 portrays
the total labor use in Group 3 on a monthly basis. The seasonality of
labor is immediately apparent. More labor was hired during December and
January, the cotton harvest period, and less labor was hired during
April to June, the sugar cane harvest period. Indeed, the sugar cane
area decreased by 1,200 hectares and production decreased by 107,500
tons (Table 19) .

Maize and sorghum area and production decreased in Group 3. In
Group 2 the area for single-cropped maize and for beans decreased,
whereas that planted with maize-beans increased. This change resulted
in an overall increase in the production of maize from 496,400 to
528,800 tons — due partly to adoption of higher yielding technologies and
partly to the increase in the area planted with maize associated with
beans. Total cropped area, however, decreased by 9%. Total area
planted decreased by 4.4% in Group 1 because both the area planted with
maize and that planted with maize-beans decreased as labor is in short
supply.

6
The area authorized for cotton production increased by 25% from
1973 to 1979, with great yearly fluctuations. The 8% increase assumed
is an arbitrary magnitude.

Ill

Table 18. Labor Supply Response to an 8% Increase in Cotton
Area as Estimated with MAYA, by Group

Labor by
Category

Basic
Solution

8% Area

Increase

%
Change

(Thousand man-days)

Group 1 Labor

family
hired

14,869
1,617

14,441
1,407

-2.9
-13.0

Group 2 Labor

family
hired

37,238
4,522

36,793
6,401

-1.2
41.6

Group 3 Labor

Group 1 migrants

6,455

7,158

10.9

Group 2 migrants

2,873

2,684

-7.0

regional

22,674

22,627

-0.2

Total Labor

90,247

91,511

1.4

112

Labor Use
(thousand man-days)

3700

3600
3500 -

3400 '

3300

3200 1

3100
3000 -

2900 '

2800

2700

2600 -f

2500

2400 ~

2300

2200
2100 -

2000 -

1900 *

1800

Coffee

Harvest

(N-J)

Sugarcane

Harvest

(M-M)

ft Land

Cleaning

(J-s)

basic solution

8% increase in cotton

area

Month

July Aug Sep Oct Nov Dec Jan Feb Mar Apr May June

Figure 13. Monthly Distribution of Labor Use in Group 3 with Base
Solution and with an 8% Increase in Cotton Area as
Estimated with MAYA

113

Table 19. Area and Production Response to an 8% Increase in
Cotton Area as Estimated with MAYA, by Group

Farm Group
and Crop

Basic Solution

Area Production

8% Area Increase

Area Production

Group 1

Group 2

(Area in thousand hectares ,
production in thousand tons)

maize

77.3

168.6

75.5

159.3

beans

23.0

14.3

maize-beans

58.4

52.2

other

45.8

45.8

maize

249.1

496.4

185.3

528.8

beans

84.7

69.1

29.9

52.2

maize-beans

17.8

104.8

other

153.1

129.9

Group 3

cotton

99.0

316.1

106.9

341.4

maize

85.0

185.5

75.0

153.0

sorghum

18.5

53.7

15.4

44.6

sugarcane

62.7

5705.2

61.5

5597.7

other

121.3

127.2

114

The welfare effects of a policy aimed at increasing cotton produc-
tions, employment, and incomes of farmers through an increase in the
area planted with cotton are shown in Table 20. Such a policy was
effective in raising producers income in Group 3, hired-labor income in
Group 2, migrant-labor income, and foreign exchange earnings.7
Producers income of farmers in Groups 1 and 2, however, decreased and
agricultural prices rose by 6%. The latter occurred mainly because of
higher consumer prices of those crops whose production diminished as a
consequence of this policy— e.g., sorghum, beans, and sugar.8
Producers' welfare, measured by producers' surplus, increased by 24%,
whereas total welfare (the sum of consumers' and producers' surpluses)
decreased by .3%.

Although the magnitudes of the results presented in Table 20 may
not be realistic, they are, at least, indicative of the likely effects
of controlling the expansion of the area planted with cotton in order to
benefit small farmers.

A very important implication for planning of this policy, as well
as of others aimed at achieving given targets of production, is that
trade-offs in consumption and production cannot be ignored and must,
therefore, be properly evaluated. The supply response analysis of the
last two sections showed that farmers react to price stimuli in

Foreign exchange earnings increased by Q 5.1 million. Additional
earnings from cotton exports alone amounted to Q 9. 7 million. The dif-
ference of Q 4. 6 million account for foreign exchange foregone by import-
ing additional quantities of maize, rice, and sorghum, whose production
declined since resources were drawn away from these activities into
cotton.

Q

Sugar exports remained constant but domestic supply decreased.

115

Table 20. Welfare Indicators in the Base Period and After an
8% Increase in Cotton Area as Estimated with MAYA

Indicator

Basic
Solution

8% Area
Increase

%
Change

Hired-labor Income

(Millions of quetzales)

Producers Income

Group 1
Group 2
Group 3

41.26

39.02

-5.7

101.65

98.42

-3.3

271.58

276.44

1.8

Group 1

2.26

1.97

-14.7

Group 2

7.69

10.88

41.5

Group 3

71.42

72.53

1.4

Group 1 migrants

(14.85)

(16.46)

10.8

Other

(56.57)

(56.07)

-0.1

Balance of Trade in

Agriculture

501.81

506.93

1.0

Producers ' Surplus

89.53

111.07

24.1

Objective Function Value

934.18

931.45

0.3

Consumer Price Index

in

Agriculture

100.00

105.97

6.0

116

accordance with their attitudes toward risk. Their ability to adopt new
technologies and the availability of resources influence their cropping
patterns. Moreover, on the consumption side, product prices are deter-
mined by the interaction of supply and demand. Appropriate evaluation
of substitution effects in production and consumption should thus con-
tribute to effective policy making.

Effect of Risk on Supply Response

In Chapter III it was shown that the introduction of risk into an
LP model leads to different levels of production and prices than those
obtained with no risk. In this section an attempt was made to explore
the slope and location of the supply function for selected crops with
and without risk. Since prices are endogenous supply, functions are not
derived by changing a given price ceteris paribus but by allowing other
prices to change also. Thus, the functions obtained must be considered
as total supply response relationships. Supply response functions
derived in this manner are portrayed in Figures 14A to 14F for six
crops. The points on these functions are numbered so that points 1, 2,
etc., correspond to the same demand shift under risk and under risk
neutrality. The end points represent low and high production levels
observed during 1970 to 1977. Contiguous points represent a 10% shift
in demand except in the case of sorghum and rice whose demands were
shifted by 20% intervals.

9
The risk set (2.0, 1.25, .75) for Groups 1, 2, and 3, respectively,
was assumed.

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The supply functions are all upward sloping. Production increased
less than proportionally with demand, causing prices to increase. Wheat,
beans, and cotton supplies show a rather inelastic portion at higher
prices. Clearly, there is keen competition for resources from other
crops in the model. In some cases risk affected the slopes of the func-
tions and, in most cases, it shifted their location. It caused the
supplies of maize, sorghum, and beans to shift up and to the left, which
means that lower quantities are produced at higher prices. Taken as a
whole, cotton is risk neutral. Wheat presents an interesting case; it
appeared to be a risky crop at low prices and became less risky and more
elastic in the price range Q 383 to Q414. In contrast the supply
response function of rice, a low risk crop, shifted down when risk
averse behavior was introduced. The analysis indicates that the bias of
ignoring the risk averse behavior in planning models could be
significant.

Comparative Advantage

Comparative advantage in international trade has been quantified in
terms of Bruno's (1965, 1972) domestic resource cost (DRC) or exchange
cost measure — i.e., the level of production costs in quetzales required
to earn a dollar of foreign exchange via exports. This concept can also
be used in the case of imports to measure the gains to Guatemala from
additional units of imports in order to save a dollar of foreign
exchange via import substitution.

The numerator of the domestic resource cost formulation is the
opportunity cost of an additional unit of production, and the

121

denominator is the net foreign exchange earned (in the case of exports)
or saved (in the case of imports).

Since the LP solution directly provides a measure of opportunity
costs, it is a straight forward matter to calculate the domestic
resource costs (the numerator of the DRC) of exports and imports. For
the present study it is desirable to know the exchange costs of incre-
mental exports and imports from the existing levels and, therefore, for
this experiment all exports and imports were upper bounded at the 1976
to 1977 levels. For imports from the Central American countries
governed by international agreements, these bounds were set equal to
those quantities. In the case of exports of a given product, the
domestic resource cost, excluding profits but including the "normal"
returns to land and labor, was found by subtracting the export bound
shadow price (representing the amount of producer's excess profits per
incremental unit exported) from the exogenous export price (Bassoco and
Norton, 1979). Normal factor returns refer to the rates of return
accruing from production for sale in domestic markets. The procedure
followed in the case of imports is essentially the same except that in
this case this measure can also be interpreted as the (potential)
domestic resource savings of not importing one additional unit.

The shadow price column, shown in Table 21, represents the marginal
profits (when positive), or losses (when negative), for export and
import crops, respectively. A distinction between imports from the
Central American countries, which are tariff exempt, was made. To
obtain a measure of the exchange cost the DRC is simply divided by the
export or import price. By comparing this cost with the prevailing
exchange rate, a ranking of crops according to the degree of comparative

122

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123

advantage in international trade is possible; that is, in order of the
marginal domestic cost of earning a dollar in exports (or import
substitution) . Crops whose exchange cost in quetzales is greater than
the exchange rate in quetzales per dollar would require subsidies for
additional exports (import substitution) at the margin. The exchange
costs calculated in this manner are given in Table 22. The average of
the exchange costs weighted by the proportion of the value of exports
during 1976 to 1977 for all crops exported turned out to be Q .88 per
dollar (12% less than the official exchange rate) , for imports from
third countries Q .84 per dollar, and for imports from Central American
countries Q .96 per dollar. These figures indicate that Guatemalan
export agriculture is quite competitive in world markets. It also means
that export crops could have been taxed up to 12% without becoming
unprofitable. Imports from third countries appear to be more favorable
than imports from other Central American countries. Guatemala would
certainly be better off importing wheat from third countries than pro-
ducing it domestically.

These results provide a basis for establishing the relative com-
parative advantage on a group basis. Group 3 is clearly better off
than Groups 1 and 2 since export crops, which are mostly produced by
Group 3 farmers, are very profitable in international markets.

124

Table 22. Ranking of Products According to Exchange Cost
Calculations Using Estimates Obtained with MAYA

Product

% of
Production

Value
(million Q)

Exchange
costa

Rank

Exports

Bananas

100.0

45.66

0.46

1

Potatoes

44.5

6.24

0.64

2

Sugar

64.8

106.76

0.69

3

Coffee

84.5

265.20

0.98

4

Cotton

88.0

127.82

1.00

5

Imports from Third Countries

Wheat
Maize
Rice
Beans

137.0

16.50

13.1

9.48

33.0

2.11

2.9

1.13

0.68

1

1.00

2

1.12

3

1.21

4

Imports from C.A.

Beans
Maize
Sorghum
Rice

1.8
9.7
9.9

2.76

0.92

1

1.26

0.99

2

0.65

1.01

3

0.43

1.10

4

The exchange cost in quetzales is equal to the marginal
cost of production over the export or import price of Table 21.
The exchange rate is 1 quetzal = 1 US dollar.

CHAPTER VII
SUMMARY AND CONCLUSIONS

Summarv

The purpose of this research was to build a mathematical program-
ming model for the agricultural sector of Guatemala which could be used
to simulate the consequences of different policies. The basic optimiz-
ing market equilibrium formulation of the model assumed that producers
are profit maximizers and that consumers' behavior is described by a set
of demand functions in the space of prices and quantities. This assump-
tion implies that prices are endogenously determined by the intersection
of the demand and supply schedules and is, thus, more realistic than the
fixed-demand assumption of traditional mathematical programming models.
The model formulated in this manner was modified by adding the assump- u
tion that producers behave in a risk averse manner.

MAYA modelled three subsectors of agriculture according to farm
size and technology — subsistence, small-scale marketing, and commercial
agriculture — which produce 13 annual crops representing about 90% of the
total value of agricultural production during 1976-1977. These crops
could be transformed into 18 final products which could be sold directly
in the domestic market or exported.

Some of the data sources of MAYA included (a) the South Pacific
regional model of Guatemala which is a risk model but assumes fixed
demands, and (b) the Central American model, MOCA, made up of five

125

126

country-models which assumes downward sloping demands but no risk.
Conceptually, thus, MAYA is a much improved, more inclusive version of
previous partial models of the Guatemalan agricultural sector because
of its more realistic theoretical assumptions and because it covers a
wider range of products. Market equilibrium models can be useful for
policy analysis in that they define an equilibrium, toward which the
market system tends, conditional upon specific policy instrument values.
Several different equilibria of this type were obtained with MAYA in
order to compare the relative impetus given to the economy by alterna-
tive policy actions. The introduction of assumptions about producers '
decision rules and consumers' behavior may, however, also increase the
scope of errors in specification and estimation.

To demonstrate the uses to which the Guatemalan model MAYA can be
put, several experiments were conducted. Supply response to variations
in the prices of maize and cotton was analyzed by rotating their
respective demand functions around the intercept to trace out the
supply. Matrices of direct and cross price elasticities for six major
crops (viz., maize, beans, rice, wheat, sorghum, and cotton) were esti-
mated and the results were interpreted. Technological change resulting
from these price variations was also analyzed in detail at the subsector
level. Another experiment was done to evaluate the results of a policy
designed to increase incomes and employment of small and landless
farmers through an increase in the area planted with cotton. The extent
of the bias involved when risk averse behavior is ignored was also
evaluated by tracing out risk and no-risk supply functions. Finally,
MAYA was used to obtain schedules of comparative advantage in

127

production. Export and import products were ranked according to their
degree of comparative advantage in international trade.

Conclusions

In this study it has been demonstrated that the responsiveness of
farmers to changes in the price of a given commodity are dictated by the
availability of resources, particularly land and family labor, employ-
ment possibilities outside the farm, choice of crops and techniques,
relative product prices, and uncertainty of product prices and yields.
The study emphasized the importance of the yield and area components of
output elasticity in evaluating supply response. This approach is
relevant in underdeveloped agriculture where land and family labor are
scarce. It has been shown that increases in maize and cotton production
take place through increases in areas and yields — intensifying the use
of inputs such as chemicals, seeds, and machinery. In general, in
response to price increases, farmers tended to adopt higher yielding,
more input intensive techniques which are also riskier. The less
advanced farmers behaved no differently from the more advanced ones.
This result supports Behrman's (1968) findings that farmers in underdevel-
oped agriculture respond quickly and efficiently to relative price t,
changes. Another consequence of policies desinged to increase production
of a given commodity is that the prices of those commodities whose pro-
duction is not increased tend to rise as inputs are drawn away from those
products toward those whose production increases. It was found that a
policy to increase incomes and employment of small farmers through an
increase in the area planted with cotton could be effective in the
short run. In the long run, there are adverse effects caused by an

128

increase in the price level which could cancel out the initial favorable
results unless other policies designed to alleviate or present this
price increase were implemented.

Different methods to measure supply response, i.e., econometric
analysis, linear programming, and production functions, have been dis-
cussed in the literature. The results of this study support Shumway and
Chang's (1977) prediction that linear programming can be an effective
tool for simulating the behavior of farmers if downward sloping demand
functions as well as risk-averse behavior are explicitly introduced into
the analysis.

It has been demonstrated that the descriptive performance of agri-
cultural planning models can be considerably improved by introducing
risk-averse behavior, even when based on Hazell's (1971) MOTAD model
which yields results 88% as efficient as those which use unbiased esti-
mators of the variance-covariance matrix in the Markowitz's (1952)
portfolio selection approach of quadratic programming. Estimates of
risk aversion coefficients were obtained at aggregate levels using post-
optimality techniques of linear programming. Finally, it has been shown
that biases in estimates of supply response and resource valuation may
be quite significant in planning models which ignore risk-averse
behavior.

Areas for Further Research

Much improvement still remains to be done to increase the useful-
ness of MAYA. Livestock activities as well as tree crops production
activities need to be incorporated. Regarding the actual data base,
some improvement needs to be introduced through field work in the area

129

of export crops, particularly sugarcane and coffee for which insuffi-
cient data were available.

There are some areas in which the methodology of market equilibrium
programming model is, in general, deficient. Two topics which are
usually ignored are land tenure systems and factor markets. Apart from
the Kutcher-Scandizzo (1976) and Ferreira (1978) studies of northeast
Brazil, there has been no attempt to capture the influence of land
tenure considerations in the specification of a mathematical programming
objective function. Factor prices are, generally, not as specified
endogenous in sector models. Different kinds of land and labor need to
be specified. Some work in this direction has been done by Hazell
(1979).

The usefulness of mathematical programming models could further be
improved if they were considered within the multi-level framework and
if income was explicitly incorporated in their formulation. The
descriptive nature of mathematical programming models restricts their
use within the more broad policy context. Even though a policy objec-
tive function is sometimes attached to the constraint set of the
descriptive problem, it should be clear that such a model does not
represent completely either the policy problem or the descriptive
problem. In most cases optimization of the objective function given by
the sum of producers' plus consumers' surpluses need not be "the
optimum" policy. Mathematical programming when used to simulate the
behavior of markets for single products and complete sectors, particu-
larly in agriculture, deals only with the maximization of a behavioral
function.

130

Insofar as MAYA does not go beyond solving the behavioral sub-
problem of multi-level programming, its results should be interpreted
within the limitations and assumptions of mathematical programming.
It also means that a solution nearer real world optimality could be
found by formulating the model within the multi-level programming
framework. Several policy options can be considered to arrive at more
realistic solutions. Some of the policy variables directly affecting
agriculture, which the Guatemalan authorities control, are import
quotas, import and export taxation, credit, and interest rates. With
these variables they can influence the level of foreign exchange, farm
incomes, employment, and GNP growth. In the international trade sector,
for example, it could be of interest to maximize the level of foreign
exchange subject to given levels of import and export taxation and
agricultural credit. Another objective may be to maximize small
farmers' incomes and employment levels subject to given levels of
credit, interest rates, and volume of trade. Formulating MAYA in the
multi-level programming framework would, thus, permit a more realistic ^
representation of the policy making process, which could be quite useful
for planners.

The second shortcoming of mathematical programming models is that
their partial nature ignores income effects which act to shift con-
sumer demands under different policies. If the sector modelled is u—
small enough, ignoring income effects should be unimportant. But if
the sector is relatively large, the income it generates must necessarily
influence demand patterns. Given that the agricultural sector of
Guatemala represents one-third of GNP, income effects are very likely to
play a role in the demand for agricultural commodities. Thus, the

131

incorporation of income into the model would add to the realism of the
results.

APPENDICES

APPENDIX A
STATISTICAL TABLES

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141

Table VI. Variables Included in MAYA

1. PRODUCTION AND TRANSFORMATION BLOCK

Production Activities

Product

Maize

Late maize

Maize-sesame

Maize-beans

Beans

Rice

Sorghum

Cassava

Potatoes

Wheat

Bananas (domestic
consumption)

Sugarcane

Coffee

Cotton

Bananas (export)

Lemon grass tea

Group 1

Group 2

Group 3

Transformation Activities

Primary Product
Raw cotton

Sugarcane

Coffee nuts

Units Processed Product Group 1 Group 2 Group 3

1000 ha

Cotton fiber
Cotton seed
Cottonseed cake
cottonseed oil

Molasses
Refined sugar
Lump molasses

Ground coffee

X

X

X

X

X

X

X

X

X

X

X

X

142

Table VI. Continued

Transformation Activities (Continued)

Primary Product Units Processed Product
Wheat

Rice

1000 ha Wheat flour
Wheat bran

" Polished rice
Rice bran

Group 1 Group 2 Group 3

2. INPUT PURCHASES

Input Purchases (Groups 2 and 3)

Units

Units

Input

(thousands)

Input

(thousands)

Resident labor (G3)

Man- days

Family labor

Man-days

Urban labor (G3)

ii

Rural labor

ii

Family labor (G2)

ii

Machinery

hours

Migrant labor (Gl) ,

Draft animals

days

(G2), (G3)

M

Credit

Quetzales

Urban labor (G2)

ii

Urea

tons

Machinery

hours

Other fertilizers

ii

Draft animals (G2)

ii

Soil insecticides

Quetzales

Draft animals (G3)

ii

Other chemicals

ii

Credit

Quetzales

Ammonium nitrate

tons

Ammonium sulphate

ii

Urea

"

Diammonium phosphate

ii

(20-20-0)

ii

(12-24-12)

ii

(15-15-15)

n

(16-20-0)

ii

Soil insecticides

Quetzales

Foilage insecticides

ii

Fungicides

ii

Herbicides

ii

Local seed

tons

Improved seed

ii

143

Table VI. Continued

DEMAND

Product Demand Functions Estimated

Products Sold at Fixed Prices

Maize
Rice
Beans
Sorghum
Cassava
Potatoes
Wheat flour
Sugar
Coffee
Cotton fiber
Cottonseed oil
Bananas (domestic
consumption)

Lump molasses

Molasses

Rice and wheat bran

Cottonseed cake

Lemon grass tea

4. INTERNATIONAL TRADE

Imports from the ROW Exports to the ROW Imports from Central America

Maize

Coffee

Maize

Beans

Cotton

Sorghum

Wheat

Sugar

Beans

Rice

Bananas (export)

Rice

NATIONAL ACCOUNTS

Labor income (six groups of labor)
Income by group (three groups)
Foreign exchange
Tariffs and taxes to exports
Transformation differential
Total income

^est of the World.

144

Table VII. Transformation Coefficients and Transformation Differentials
Used in MAYA

Transformation
Coefficients

Product

Raw
Product

Maize

0

.930

Rice

polished rice

bran

Sorghum

0

950

Wheat

wheat flour

wheat bran

Beans

0

980

Cassava

0

870

Potatoes

0

900

Bananas (domestic

consumption)

0

720

Bananas (export)

0

870

c a
Sugarcane

sugar

molasses

lump molasses

Sesame

vegetable oil

Cotton

cotton fiber
cottonseed cake
cottonseed oil

Coffee

ground coffee
Lemon grass tea

0.930

Transformed
Product

0.643
0.077

0.718
0.194

0.084
0.036
0.074

0.391

0.329
0.255
0.074

0.323

Transformation
Differentials

Group 1 Group 2 Group 3

(Quetzales per kilogram)
0.019

0.076

0.077

0.055

0.030
0.104

0.017
0.068

0.077
0.068

0.122

0.189

0.815

0.022
0.104

0.016

0.122

0.014
0.012

0.122
0.800

Sugarcane can be processed to obtain refined sugar and either
liquid molasses or lump molasses as byproducts.

145

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146

Table IX. Demand Functions in MAYA

Product Demand Equation3

Maize p = 895 - 1.385 Q

Beans p = 2,764 - 30.110 Q

Rice p = 1,996 - 92.356 Q

Sorghum p = 628 - 9.477 Q

Wheat flour P = 1,808 - 14.260 Q

Potatoes P = 1,093 - 29.100 Q

Cassava p = 1,683 - 214.713 Q

Bananas p = 1,677 - 10.369 Q

Sugar p = 1,173 - 5.604 Q

Cotton p = 4,940 - 309.698 Q

Coffee P = 14,521 - 531.325 Q

Vegetable oil P = 3,244 - 86.325 Q

Price is expressed in quetzales per ton, and quantity in
thousand tons.

147

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149

Table XI. Cropped Area Response to Different
MAYA, by Group

Values as Estimated with

Farm Group
and Product

Actual

Risk Levels

0-0-0 1. 5-. 75-. 25 2-1. 25-. 75 2.5-1.75-1.25

Group 1

(Thousand hectares)

maize

92.0

125.7

118.2

77.3

76.3

beans

2.0

maize-beans

31.0

53.0

53.2

58.4

58.3

potatoes

38.0

39.5

40.8

40.8

40.8

Group 2

maize

208.0

237.1

240.0

249.1

251.3

beans

39.0

97.1

94.3

84.7

81.2

maize-beans

29.5

27.5

24.5

17.8

16.4

maize-sorghum

18.0

maize-sesame

9.0

22.7

22.4

20.1

19.3

sorghum

7.3

rice

9.0

11.8

12.2

12.2

12.2

wheat

5.0

cassava

1.0

0.8

0.8

0.8

0.8

bananas

26.9

coffee

131.0

120.0

120.0

120.0

120.0

Group 3

maize

88.2

81.9

82.7

85.0

87.1

rxce

4.2

sorghum

4.5

20.2

19.1

18.5

16.3

bananas (domestic

consumption)

21.2

20.8

20.8

20.8

20.8

bananas (export)

5.5

5.5

5.5

5.5

5.5

cotton

102.0

96.7

97.0

99.0

99.6

coffee

117.4

95.0

95.0

95.0

95.0

sugarcane

65.0

66.4

66.4

62.7

62.1

lemon grass tea

4.4

_

...

150

Table XII. Production Response to Different
MAYA, by Group

Values as Estimated with

Farm Group
and Product

Risk Levels

Actual

0-0-0 1. 5-. 75-. 25 2-1. 25-. 75 2.5-1.75-1.25

Group 1

(Thousand tons)

maize

159.0

227.8

217.9

168.6

167.0

beans

16.0

20.8

20.9

23.0

22.9

wheat

50.1

55.2

56.6

56.6

56.6

potatoes

62.5

65.8

64.7

64.7

63.5

Group 2

maize

471.0

501.9

500.1

496.4

493.0

beans

45.0

82.2

78.9

69.1

65.9

sorghum

49.0

rice

15.0

26.6

27.4

27.4

27.4

sesame

11.8

11.6

10.4

10.0

wheat

6.0

cassava

9.7

8.3

8.3

8.3

8.3

bananas

27.0

coffee

166.0

163.7

163.7

163.7

163.7

Group 3

maize

220.0

175.4

178.2

185.6

192.5

rice

7.6

sorghum

5.0

58.5

55.3

53.7

47.3

bananas (domestic

consumption)

180.0

194.4

194.4

194.4

194.4

bananas (exp

ort)

336.0

347.6

347.6

347.6

347.6

cotton

318.0

308.9

309.7

316.1

318.2

coffee

295.0

267.6

267.6

267.6

267.6

sugarcane

5910.0

6041.7

6041.7

5705.2

5651.0

lemon grass

tea

0.2

151

Table XIII. Area and Technology Response to Different Maize Prices as
Estimated with MAYA, by Group

Product and

Price per

Ton (qu

etzales)

(Technology)

109.0

124.0

142.5

159.3

165.0

180.0

209.0

(Thousand hect

ares)

Group 1

Single-crop maize

40.7

57.3

78.3

77.3

92.2

125.0

126.1

(Al)

40.7

57.3

78.3

77.3

92.2

125.0

119.0

(A4)

1.5

(D2)

5.6

Maize-beans (Al)

39.2

49.8

56.1

58.4

57.0

52.4

52.6

Wheat

40.7

42.7

43.6

40.9

40.8

40.8

39.6

(A3)

6.0

18.2

4.1

1.2

1.2

1.2

(B3)

13.9

(B4)

3.7

18.7

18.9

18.8

18.8

18.8

(C2)

1.8

1.8

1.8

1.8

1.8

1.8

1.8

(C3)

9.5

9.5

9.5

9.5

9.5

9.5

9.5

(D3)

9.5

9.5

9.5

9.5

9.5

9.5

9.5

Other

5.0

5.0

5.0

5.0

5.0

5.0

5.0

Group 2

Single-crop

maize

199.5

221.7

246.6

249.0

265.5

261.3

252.3

(B3)

91.8

121.8

148.5

153.9

173.3

170.2

168.6

(C2)

107.7

99.9

98.1

95.1

92.2

91.1

83.7

Associated maize

75.0

65.2

40.3

37.9

21.5

25.6

30.6

Maize-beans

(Al)

56.2

45.3

19.4

17.8

0.6

4.7

4.3

Maize-sesame

(Al)

18.8

19.9

20.9

20.1

20.9

20.9

26.3

Beans (Al)

70.2

70.9

82.8

84.7

95.7

95.8

95.9

Rice (CI)

12.2

12.2

12.2

12.2

12.2

12.2

12.2

Sorghum (D3)

4.1

Other

121.0

121.0

121.0

121.0

121.0

121.0

121.0

Group 3

Single-crop

naize

75.0

81.2

82.6

85.0

87.4

88.2

97.6

(CI)

75.0

75.0

75.0

75.0

75.0

75.0

75.0

(Dl)

6.2

7.6

10.0

12.4

13.2

22.6

Sorghum (D3)

19.1

19.1

18.5

18.5

16.9

16.3

11.5

Cotton (D3)

100.0

99.1

98.2

98.9

98.2

98.2

93.7

Other export

crops

187.1

187.1

187.1

184.0

184.0

183.7

183.7

152

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APPENDIX B
EQUATIONS OF THE MODEL

Equations of the Model

MAYA contains 325 structural equations. Except for a few strictly
accounting equations, they are set out fully in algebraic form in this
appendix.

Capital letters represent variables and right-hand values, and
Greek letters and lower case letters indicate parameters. A description
of each term is also given for some equation sets, and the number of
equations within each set is given on the right-hand side.

All of the equations are written in inequality form. Obviously,
many of them will be binding in any solution, and hence, those equations
could have been written as strict equalities. However, writing them as
inequalities reduces the computer time associated with each solution,
for it eliminates the need to pass through phase I of the simplex
algorithm; and by appropriate use of the signs for equations with zero
right-hand side elements, one can be sure that restrictions will be
binding when exact equalities are desired (Cappi et al., 1978).

The initial step in preparing the model's computer version was to
design a nomenclature for columns and rows, assigning certain fields to
group indices, others to product and input indices, and so forth. This
convention is not readily apparent in the equation names given below
because empty fields are ignored. Special symbols were also used to
designate restrictions (R) and balances (B) . Product and input symbols
(two characters) and all other abbreviations were dediced upon at

154

155

the outset. The equations were then developed in sets, beginning with
group specific equations, and then moving to national balances and
restrictions. A description of the notation used follows in Table XV.

MAYA Equations

1. Objective Function (FOB)

e m

E 0). D. + Z p. XR. - Z p. MR. - Z v- SMF •= . , .

j>g J,g J,g j J J j J J t £ £,h=l,2 t,£,h=l,2

1/ *

Z w» SMH - - Z c5 SF- - Z c, SF^ - Z SQ , .
t £ h ' t,£,n | f f,h=l f f q,h=l

- Z SQ - Z c- , . S- , . - Z c S - c' SMQ, . - c'* SMQ*

^q - s,h=l s,h=l s s h=l Hh=l xq
q n s ' s H

- TCRh=1 - TCR* - TR - TA —*■ max (1)

[area under the domestic demand function for final products] +
[gross revenue from sale of exports] - [c,i,f value of imports] -
[reservation wages of family labor Gl, G2] - [market wage costs
of hiring labor] - [total cost of fertilizers Gl] - [total cost
of fertilizers of both G2 and G3] - [total cost of chemicals Gl]

- [total cost of chemicals of both G2 and G3] - [total cost of
seeds Gl] - [total cost of seeds of both G2 and G3] - [total
cost of machinery use Gl] - [total cost of machinery use of both
G2 and G3] - [total cost of credit, Gl] - [total cost of credit,
G2 and G3] - [total processing cost differential] - [total trade
taxes] — y max

Detailed in equations 11-14.

t)

W)

QJ

OJ

to

CO

to

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a)

o

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<)

)-J

u

3

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a

-a

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c

cfl

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156

l=N> -G

T3

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rt

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0

rt

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crj

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03

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163

2. Processing costs accounting row (RTRRI)

- TR + £ c. Q. < 0 (1)

i,h

- [total processing cost differential] + £ [unit costs

i,h

times quantity processed of raw product i] < 0

3. Trade taxes accounting row (RTARI)

- TA + £ a. MR. + £ a XR < 0 (1)

j 3 3 j 3 3 -

- [total trade taxes] + £ [import tax rate times quantity

J

imported] + £ [export tax rate time quantity exported] < 0
j

4. Consumer level commodity balances for endogenous price products
(BjBP)

- £ ]i3. Q. + £ 6. D. - MR. + XR. < 0 (12)

- £ [net output of final good j from the processing of farm-gate
h

product i] + £ [quantity of final product j demanded] - [total

g
imports of product j] + [total exports of product j] _< 0

5. Consumer level commodity balances for fixed price products (BiBP)

- £ yJ. Q. , + D. - MR. + XR. < 0 (5)

6. Convex combination constraints on the interpolation weight
variables for the demand function (RjRC)

£ D < 1.0 (12)

„ J)6

164

7. Family-labor constraints for Groups 1 and 2 (hRMF)

SMFt)h + SMGt}h < RMFt>h h = 1, 2 (24)

[Supply of family labor in month t] + [Supply of migratory
labor in month t] <_ [Total availability of family labor]

8. Hired-labor constraints (hRMR)

SMRtjh < RMR^ (36)

9. Regional temporal labor constraints of Group 3 (RMU)

SMUt,h i ^t.h (12)

10. Hired-labor income balances (1BINBI)

I W£,h SMRt,£,h - CIN£,h 1 ° l = h = l> 2 <2>

E [wage coefficient times total number of man-days of hired
labor] - [total income earned by hired labor] <_ 0

11. Migratory-labor income balances (1BINBI)

E w„ SMG^ . , - CIN„ . < 0 h = 1 , h = 2 ,„.
t £,h t,£,h l,h - ^ = 3 and ^ = 4 (2)

Z [wage coefficient times total number of man-days of
migratory labor] - [total income earned by migratory
labor] < 0

165

12. Resident-labor income balance (1BINBI)

Z w SMRt - CIN„ £ 0 £ = 5 and h = 3 (1)

E [wage coefficient times total number of man-days of
resident labor] - [total income earned by resident
labor] <_ 0

13. Temporal-labor income balance (1BINBI)

Z w- SMU . . - CIN„ , < 0 I = 6 and b = 3 (1)

j_ -c t ,£, n -t-jh

Z [wage coefficient times total number of regional-
urban labor man-days] - [total income earned by
regional-urban labor] <_ 0

14. Producer level product balances (hBiBP)

- y. t. p- i. + iooo Q. u < 0 (27)

x,h i,h i,h —

[yield per hectare times total number of hectares planted
with crop i] + [scale factor times total number of tons
produced] £ 0

15. Producer income balances (hBINBI)

Z P. , Q. , - INC, < 0 (3)

i,h i,h h —

Z [farm gate price of product i times quantity produced]
i

- [total income of producers] <^ 0

166

16. Land constraints (hRTI)

Z P±,t,h * RTIt,h <36>

E [total number of hectares planted with product i]
i

<^ [total area planted]
17. Labor input balances for Groups 1 and 2 (BMh)

ZA- -up- ,. v " SMFt . - SMR , < 0 h = 1, 2 (24)
. i,t,h x,t,h t,h t,h — ' v '

I [labor requirements per hectare times total number of
i

hectares planted] - [supply of family labor] - [supply of
hired labor] <^ 0

18. Labor input balances for Group 3 (BMh)

Z X. fc . P. . - SMR . - SMU , - SMG . < 0 (12)

. i,t,h i,h t,h t,h t,h -

h = 3

£ [labor requirements per hectare times total number of
i

hectares planted] - [supply of resident labor] - [supply
of urban labor] - [supply of migratory labor from Groups
1 and 2] £ 0

19. Fertilizer balances for Group 1 (hBF)

Z <J>r , P. , - SF7 , < 0 h = 1 (2)

. Yx,h i,h f,h —

167

20. Fertilizer balances for Groups 2 and 3 (hBF)

^/i,hPi,h "^kf SFf * ° h = 2> 3 0)

21. Chemicals balances for Group 1 (hBQq)

^i,qPi,h-SVn ± ° h = 1 (4>

22. Chemical balances for Groups 2 and 3 (hRQq)

^hKisqPi,h'S% <- ° h = 2' 3 (4)

23. Machinery use restrictions (hRMQ) for Group 1

^i,t,hpi,t,h i SM(\,h h-1 (11)

24. Machinery use restrictions for Groups 2 and 3 (hRMQ)

^hTi,t,hpi,t,h <- m% h = 2-3 <8>

25. Draft animals restrictions (hRBU)

2a-., P. , < RBU. , (17)

. l , t , h l , h — t,h v;

26. Seeds balances for Group 1 (hBiS2)

^iPi5h-Ss,h ± ° h = l (3]

168

27. Seeds balances for Groups 2 and 3 (BiS2*)

E a. "P. , - S < 0
. , x i,h s —
i,h

h = 2, 3

(8)

28. Credit balance for Group 1 (hBCR)

E c^ SF, , + E SQ , + I c S , + c ' SMQ^
ft f,h Hq,h ss,h h xh
f q,h ^' s

- SCR, < 0
n —

h = 1

(1)

29. Credit balance for Groups 2 and 3 (BCR*)

E c. SFr , + E SQ ,_ + E c S , + c' SMQ
c u f t>h u q5h , s s,h
f,h q,h H' s,h '

- (CRS + CRM + CRL) < 0

h = 2, 3

(1)

30. Risk balance rows (hRRI)

a. Revenue balances

£y. r ,P. ,_ - zr r. > 0
. i,t,h i,h t,h —

E [coefficient of income deviations from the mean
i

times area planted with product i] - [total of income
deviations in period tj > 0

(30)

b. Total sum of negative deviations

I 2z- , - 7569 s = 0
t t>h

E [constant times total of income deviations over t]
t

- [constant times the population income deviation
estimator] = 0

(3)

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BIOGRAPHICAL SKETCH

Hilda Yumiseva was born in Quito, Ecuador, on June 13, 1948. She
completed high school in 1967 and obtained her B.A. degree in economics
in 1970. During 1971-1972 she did the course work for the master's
degree at the University of the Americas in Puebla, Mexico. In 1973
she obtained an OAS scholarship and enrolled in the Ph.D. program at the
University of Florida. She completed her course work in 1976 and has
since worked at the World Bank and the Secretariat of Central American
Economic Integration in Guatemala City. Upon the completion of her
doctorate she plans to continue working in Washington, D.C.

177

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.

q^ s4?. cXa^j tut/-*"

Max R. Langham, Chairman
Professor of Food and Resource
Economics

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.

Chris 0. Andrew, Co-chairman
Professor of Food and Resource
Economics

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.

W-U. IKS.

W. W. McPherson

Graduate Research Professor of Food
and Resource Economics

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.

/C'&Lt t/ J/&n.

David A. Dens low, Jr
Associate Professor

This dissertation was submitted to the Graduate Faculty of the College
of Agriculture and to the Graduate Council, and was accepted as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.

December, 1981

a 6 tl <* C/-/W
icuutu

Dean. .College of Agriculture

Dean for Graduate Studies and Research

UNIVERSITY OF FLORIDA

3 1262 08553 1530