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Full text of "The survivor technique and identification of optimal plant size using individual plant data"

UNIVERSITY OF 

ILLINOIS LIBRARY 

AT URBANA-CHAMPAIGN 

BOOKSTACKS 



Digitized by the Internet Archive 

in 2011 with funding from 

University of Illinois Urbana-Champaign 



http://www.archive.org/details/survivortechniqu383atac 



Faculty Working Papers 



THE SURVIVOR TECHNIQUE AND IDENTIFICATION OF 
OPTIMAL PLANT SIZE USING INDIVIDUAL PLANT DATA 

Jeremy Atack and Fred Bateman 

#383 



' 



College of Commerce and Business Administration 

University of Illinois at Urbana-Champaign 



FACULTY WORKING PAPERS 
College of Commerce and Business Administration 
University of Illinois at Urbana-Champaign 

March 8, 1977 



THE SURVIVOR TECHNIQUE AND IDENTIFICATION OF 
OPTIMAL PLANT SIZE USING INDIVIDUAL PLANT DATA 

Jeremy Atack and Fred Bateman 

#383 






■ " :•>.;,-.' , 



-■■■■! ■ ■ :■ 



: ' t •• 1 



: :\ ' 






■ ■ '• •• ' '. '.' • •■ ■ 



THE SURVIVOR TECHNIQUE AND IDENTIFICATION OF OPTIMAL 
PLANT SIZE USING INDIVIDUAL PLANT DATA 



Jeremy Atack 
University of Illinois 



Fred Bateman 
Indiana University 



Comments welcomed 



ABSTRACT 

The Survivor Technique and Indentif ication of Optimal Plant Size Using 

Individual Plant Data 

George Stigler's survivor technique has been gaining increasing 
acceptance in recent years as a heuristic method for identifying minimum 
long-run average costs or the range of plant sizes operating under 
conditions of approximately constant returns to scale. The authors 
investigate this hithertoo untested equivalence using micro-data and 
conclude that the method has considerable merit but is not infallible. 



Jeremy Atack 
University of Illinois 

Fred Bateman 
Indiana University 



The Survivor Technique and Identification of Optimal Plant Size 

Using Individual Pl ant Data 

George Stigler's "survivor technique" has never been applied 
in its "ideal" form, using individual plant data. Nor have the results 
been compared systematically with those applying alternative methods to 

Che same figures, which as William Shepherd has stressed is crucial 

2 
for interpreting survivor technique results. Recently available samples 

of plant-level data drawn from early federal census documents, and newly 

completed work relying upon alternative methods, provide the first 

3 

opportunity to test the survivor technique under "ideal" conditions. 



The Technique 

The survivor technique seeks to identify that size class or those 
classes of plant that not only survived the rigors of competition and 

the test of time, but also succeeded in increasing their share of industry 

4 
value-added. That is, it seeks to identify plant sizes that grew in 

relative importance through the long-run adjustment process. A number 

of assumptions are implicit. The time span between observations must 

be sufficiently long to permit long-run scale adjustments and for a 

clear pattern to emerge. The long-run average cost curve is assumed to 

retrain fixed, thus excluding major technological advances which may 

shift the long-run average cost curve. Similarly, constant cost industry 

conditions must be assumed so that the long-run adjustment process itself 

doss not induce shifts in the long-run average cost curve through changing 

factor prices. Finally, atomistic competition must be assumed so that 



long-run demand shifts leave price unchanged due to compensating supply- 
shifts through the adjustment process. 

Collectively these assumptions ensure that optimally adjusted 
plants will produce at minimum long-run average (private) cost. If there 
are only internal economies of scale, then the optimally adjusted plant 
produces under constant returns to scale as defined by the production 
function and the long-run average cost curve. On the other hand, if 
there exist substantial external economies which can only be achieved by 
large scale operations, it is possible that a plant might be producing 
under conditions of decreasing returns in production, but that the rise 
in the value of long-run average costs is postponed by the realization 
of these external economies. Thus, rising costs in the production process 
say be offset by decreasing costs in the purchase of inputs or in marketing 
and distribution ar i once again optimal plant size would appear to be 
located under constant returns to scale identified with minimum long-run 
average costs but not by production function estimates. The converse 
of this argument would apply in cases where there is reason to suppose 
that large scale operations encounter external diseconomies of scale 
despite internal economies in the production process. 

Results showing a single size class of plants gaining in relative 
importance, therefore, suggest a U-shaped long-run average cost curve 
and a determinate optimal plant size. The persistence of a wide range 
of size categories with no clear gainers is suggestive of the presence 
zi constant returns to scale ever a wide range of outputs and, hence, 
of a relatively flat long-run average cost curve. Either result would 
be consistent with cost function studies. 



Application of the technique to monopolistic industries yields 
imperfect results due to changes in optimal plant size over time with 
shifts in demand since, under such a market structure, optimal plant 
size is jointly determined by demand conditions and technology. In an 
attempt to circumvent this problem, Weiss, rather than identifying the 
optimal range (s) of plant size, identified only the "minimum efficient 
plant size" defined to be the smallest plant size that increased its 
relative contribution to total value-added. 

The advantages, drawbacks and limitations inherent to the technique 
have been detailed by previous users' but its most commonly-cited advantage — 
its ability to analyze changes in optimal plant sizes over long time 
spans rather than in a purely static context — is worth emphasizing. 
Application of the survivor principle further "finesses the problem of 

the capitalization of rents into costs, a process which drives disparate 

g 

measured average costs towards eauality." There are several recognized 

limitations. Social costs are not captured by the method. Moreover, 
it may embrace other effects, such as externalities or technological 
change, which could lead to false impressions regarding internal scale 
economies. 

Application of the S u rvivor- Technique 

The data used in this study wei e drawn from the 1850, 1860 and 1870 
United States censuses of manufactures. Since the population from which 
the random samples were selected was the state rather than the entire 
nation, these data may not be representative of United States manufacturing 
in general. However, the hypothesis that the pooled data were significantly 



different from that expected from a random sampling of plants in the 
entire nation was rejected at better than the five percent level. Neither 
the industrial distribution of plants nor the characteristics of those 

plants, particularly those with respect to size were significantly 

9 
different from those for the entire nation in any census year. 

The availability of data from these census years permitted three 
separate applications of the survivor technique to the periods 1850-1860, 
1860-1870 and 1850-1860-1870. All other studies with the exception of 
that made by Shepherd were limited to examining the possible existence 
of optimally sized plants between only two years. In the absence of 
externalities and technological change under conditions of atomistic 
competition the availability of this additional observation should improve 
the survivor technique results, but technological change, the accretion of 
externalities or the existence of market power would lead to a clouding 
of the results. 

Twenty-five industries, or approximately one-fourth of the identifiable 
industries existing during this time period were studied. Since the 
results were not unequivocal in designating the presence or absence of 
an optimal range of plant sizes across these industries the "quality" 
of the results is shown in Table 1. Other practitioners of the technique 
have not been consistent in thier choice of the appropriate index of 
plant size, so the results in Table 1 offer four different measures of 
size; capital assets, employment, gross output and value-added. These 
results permit us to discriminate between the possible options. In 



Table 1 

THE QUALITY OF SURVIVOR TECHNIQUE RESULTS MEASURING PLANT SIZE 
BY CAPITAL, EMPLOYMENT, GROSS OUTPUT AND VALUE-ADDED 
1850-1860, 1860-1870 AND 1850-1860-1870 



Percent of Survivor Technique Result of Each Type Measuring Plant Size By 

Capital Employment Gross. Output Value-Added 
Result 1850- 1860- 1850- 1850- 1860- 1850- 1850- I860-' 1850- 1850- 1860- 1850- 
1860 1870 60-70 1860 1870 60-70 1860 1870 60-70 1860 1870 60-70 



Clear 


8% 


28% 


12% 


20% 


28% 


24% 


32% 


4% 


20% 


32% 


24% 


28% 


Clear After 

Adjustment 


24 


36 


44 


32 


24 


20 


36 


32 


20 


56 


40 


43 


Partially Clear 


4 


8 


12 











28 


44 


52 


8 


16 


20 


Partially Clear 


36 


72 


68 


52 


52 


44 


96 


80 


9'2 


96 


80 


96 






40 15 24 40 40 56 4 4 4 4 4 
Inconsistent 24 12 8 8 8 16 4 4 16 



.ear or worse 



64 28 32 48 48 56 4 20 8 4 20 



Clear - One or more adjacent size classes increasing their share of industry value-added. 

Clear After Adjustment - Two or more non-adjacent size classes increasing their share of 

of industry value-added, but the apparent inconsistency is re- 
solved by merging size classes. 

partially Clear - Only the lower bound of the surviving size classes is observable. 

f-rlear - Shifts in industry value-added between size classes erratic with no boundaries 



:r.5i3tant - Incompatible with survivor technique because middle size classes were 
shrinking relative to the smallest and largest size classes. 



nerns of allowing us to draw inferences about the existence of an optimal 
range of plant sizes. The results obtained using either capital assets 
:r employment are clearly inferior to the alternatives. Gross output 
cr value-added indices of plant size on the ether hand are approximately 
the same unless we have a marked preference for more definitive statements 
about the range of surviving plants in which case the value-added measure 
of plant size is to be preferred. Since disclosure laws have prevented 
use of the gross output measure for twentieth century data and because 
of the relatively stronger results that we have obtained using value-added, 
this represents our preferred measure of plant size. 

In keeping with the heuristic nature of the survivor algorithm, 
allocation of the results between the categories in Table 1 was not 
particularly rigorous. A more mechanical procedure, such as designating 
any result "inconsistent" where more than one intervening size class 
was declining relative to those on either side, would have reduced the 
number of results that were at least partially clear, particularly if 
plant size were measured by capital assets or employment. 

The results in Table 1 show little evidence that the use of two 
census years is to be preferred to only three. Indeed in almost every 
instance the use of 1850-60-70 data resolved some of the apparent incon- 
sistencies in the sub-periods as might be expected if movements towards 
an optimal range of plant sizes followed a random walk or if there were 
no clear optimum. 

The survivor technique implications for an optimal range of plant 
sizes classified by value-added over the three census dates are shown 



7 

in Table 2. The results for flour milling (SIC industry code 2041) were 

unclear and are therefore not shown in Table 2. In this industry six of 
the twelve size groups showed marked increases in their share of industry 
value-added but these were scattered across the entire spectrum of plant 
sizes. 

The results in Table 2 also reveal a wide range of optimal plant 

sizes in each industry, suggestive of fairly broad flat long-run average 
cost curves, with constant returns to scale prevailing across a wide 
variety of different plant sizes. This result is consistent with the 
conclusions of twentieth century cost function studies. 

The Consistency of Survivor Technique Predictions 

Although two alternative, and equivalent, methods of testing the 
accuracy of the survivor technique predictions are possible — the estimation 
of cost or production functions — analysis of these manufacturing data 
is limited to production functions due to data inadequacies for cost 
function estimation. 

Ordinary least squares estimates of a production function, however, 
imply linear cost functions and hence are inconsistent with the assumption 
of a U-shaped long-run average cost curve underlying the survivor principle. 
But in recent years a number of alternative production function forms, 
estimated by the maximum likelihood technique, have been developed 
that are consistent with a U-shaped long— run average cost curve within 

certain parameter limits. A Cobb-Douglas variant of the Zellner and 

12 
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Returns tc scale, f- , are then: 

e = y/(l + 6V) 

and depend upon the paramater, G , Che estimate u and upon the level of 
value-added, V. For G > 0, returns to scale are monotonically decreasing 
and for > and u > 1, this production function implies that at low 
levels of value-added, plants are subject to increasing returns to scale 
eventually giving way to a range of approximately constant returns with 
decreasing returns tc scale apparent for !»...-. ;;iough V. 

The logarithm of the liklihood function corresponding to equation 
[1] is: 

lnit = constant - -| lna 2 + In J(A;V) 

- i I i In (V X ), - InA - y • InL. - • ln<^ _ 

2.V- i=1 j 1 1 L ± j 

2 

where a is the variance of the nomally and independently distributed 

random error term with mean zero, n is the number of observations and 
J(X;V) is the Jacobian of the monotonic transformation. Ordinary least 
squares minimizes the last term of equation [2] for any predetermined 
value of , yielding a conditional maximum for the likelihood function. 
3y varying and evaluating (ln£ - constant) the global maximum of likeli- 
hood function can be determined. 

This non-linear maximum likelihood method was applied to the plant 
data for the twenty-four industries shown in Table 2. The results are 
given in Table 3 and are generally consistent with the survivor technique 
oredictions. 



10 



Table 3 

DECREASING SCALE ELASTICITY ESTIMATES OF RETURNS TO SCALE 
IN MINIMUM EFFICIENT PLANTS, 1870 



[ndustry Description 



Returns 
To Scale 



SIC 
Code 



Industry Description 



Returns 
To Scale 



2 Gil y.eac Packing 
2C51 Bread and Bakery Products 
£032 Halt Liquors 
2GS5 Distilled Liquors 

21 - Tobacco 

2211 Co c tons 

r 

Voolens 

Hen's Clothing 
2351 Millinery 
2-21 ? Savnills 
2431 Milivork 
2511 Vcod Household Furniture 



1.55* 
1.48* 
1.21 
1.25 

-86 
1.00 
1.06 

.93 
1.04 
1.13* 
1.19 

.91 



27 
2892 



>799 



i Printing and Publishing 

i 

• Explosives 



; Leather Tanning 






! 3131 j Boots and Shoes 

3199 j Other Leather Products 

!| 3251 | Brick and Tiles 

f i 

j 3312 I Blast Furnaces 

!! ] 

3321 1 Iron Foundaries 

'•I I 

|i 5444 ; Sheet Metal 

j; 3511 Steam Engines 

i 1 

! : 

3522 Agricultural Implements 



Transportaion Equipment 



_I 



.96 

1.41 

1.06 

.94 

.76* 

.92 

.87 

1.06 

1.05 

1.09 

1.17 

.73* 



indicates returns to scale parameter significantly different from 1.00 at the 
fivs percent level (2-tailed test). 



11 



As the results indicate, standard errors were large, but the 
minimum efficient size plants in nineteen of the twenty-four were 
operating in the range where returns to scale were not significantly 
different from unity. Of the five industries that failed the test, 
three — Meat Packing, Bread and Bakery Products and Sawmilling — exhibited 
significantly increasing returns to scale in the minimum efficient size 
plants but larger plants, still within the ranges identified as optimal, 
were operating under constant returns to scale. However, the minimum 
efficient size plants in both the manufacture of miscellaneous leather 
products and transportation equipment were estimated to be operating 
under conditions of decreasing returns to scale. These results directly 
contradict the predictions of the survivor technique, particularly 
since these results were classified as "clear after adjustment" and 
"clear" respectively in Table 1 and applying more rigorous standards 
would not affect these categorizations. At the same time the decreasing 
scale elasticity estimates for these two industries lead us to suspect that 
there may have been unidentified cost curve shifts in both industries as scale 
elasticity was estimated to be increas ing with increasing plant size. 

The survivor technique predictions of the range of approximately 
constant returns to scale were less consistent than those for the 
minimum efficient scale of plant. According to the decreasing scale 
elasticity production function estimates, the largest surviving plants 

in nine industries were operating outside of the range of approximately 

13 

constant returns to scale/" 1 which suggests that Weiss 1 choice of the 

criterion of minimum efficient plant size rather than an optimal range 

of plant sizes might be correct albeit for the opposite reason to that 

, . . 14 
given by him. 



Some Supplementary Evidence Upon t he C onsistency of Survivor Technique Prediction s 

In the process of sampling the manufacturing manuscript censuses, 
the accounts of the operation of forty-six steamboats during the 1850 
census year were uncovered. These data differed substantially from those 
of the manufacturing plants and provided sufficient information, when 
supplemented by other sources, to estimate a steamboat cost function. 

During the antebellum period, the western river steamboat was 
the principle supplier of transportation services to the agricultural 
trans-Appalachian West. From an early date after its first successful 
trial on the Ohio and Mississippi Rivers in 1811, the western river 
steamboat took on certain structural characteristics which made it 
unsuitable for coastal navigation, and this has allowed us to apply the 
survivor technique to this mode of transportation. By examining a 
listing of all steamboats constructed in the United States between 1804 
and 1868, it was possible to isolate those constructed for use in the 
Mississippi basin on the basis of where they were built and their first 
home port. The size distribution of newly constructed western river 
steamboats by decade is shown in Table 4. Due to the short average, life- 
span of the western river steamboat of between five and six years, if 
there existed an optimal range of vessel sizes, a rapid convergence 
towards this optimal can be expected. 

Table 4 shows such a convergence. Prior to 1840, steamboat operators 
showed a clear preference for steamboats of 200 gross tons or less. 
However, after 1830 an increasing number of vessels of over 300 gross 
tons were constructed, coinciding with renewed efforts to improve 



13 



Table 4 

DISTRIBUTION OF WESTERN .STEAMBOAT TONNAGE BY VESSEL TONNAGE 
AND DATE OF CONSTRUCTION, 1810-1859 



Decade 




Percent of Total Tonnage of Western 
; Constructed Each Decade by Vessel 


River 
L Size 
501-6C 

Tons 


Steamboats 
Class 1 




1-100 

Tons 


101-200 

Tons 


201-300 
Tons 


301-400 
Tons 


401-5G0 
Tons 


)0 


bUi-ZUU 
Tons 


Over 
700 Tons 


1810-1819 


2% 


26% 


29% 


28% 


10% 


0% 




0% 


0% 


1820-1329 


9 


47 


27 


12 


6 













1830-1839 


12 


49 


17 


14 


4 


2 




1 


1 


1840-1849 


8 


34 


28 


17 


7 


4 




1 


2 


1350-1359 


4 


23 


22 


17 


13 


8 




7 


6 



Percentages nay not add to 100 due to rounding 

Source: Reconstructed from William M. Lytle, Merchant Steam Vessels of the United 
States, 1804-1868, Mystic, Conn.: The Steamship Historical Society of 
America, Publication No. 6, 1952, pgs. 1-208. Otherwise known as the 
"Lytle List". 



•14 



navigation of the western rivers and the percentage of total tonnage of 
western river steamboats represented by these larger steamboats increased 
each decade from 1830. Apparently the removal of naviational constraints 
upon steamboat size, permitted steamboat operators to build more 
optimally sized steamboats and these were of at least 300 gross tons. 
However, remaining impediments to navigation particularly on certain 
stretches of the river prevented steamboat operators from replacing the 

entire fleet with optimally sized vessels from the standpoint of 

■ - - 15 

OTn iiiumi long-run average cost. 

The 1850 steamboat data from the manuscript census, supplemented 
by other evidence on freight rates and technological characteristics 
defining steamboat capacity were used to estimated an envelope long-run 
average cost curve of the form: 

AVC = a + b-T + c-T 2 + d-T-C + e-C + f"C 2 [3] 

as suggested by Johns ton 1 , where AVC = average variable costs per one 
thousand ton-miles, T = steamboat gross tonnage and C = steamboat 
capacity in thousands of ton-miles. The resultant estimate of equation 
[3j for the forty-six steamboats is shown in Table 5 and the envelope 
of short-run average variable cost curves for steamboats with a capacity 
of between five and forty million ton-miles is shown in Figure 1. This 
envelope curves declines sharply at first but begins tc flatten out between 
400 and 500 gross tons, reaching a minimum for vessels of about 675 
gross tons. This result is entirely consistent with the data presented 
in Table 4. 



15 



Table 5 

COST FUNCTION ESTIMATE FOR FORTY-SIX WESTERN RIVER STEAMBOATS, 1850 

(Standard Error) 



Constant T T 2 T-C C C 2 R 2 



24.767 0.065880 3 0.000494 b -0.000021 b -0.002581 b 0.0000002 b .57376 
(0.037719) (0.000214) (0.000008) (0.000837) (0.0000001) 



3 Significant at the 10% level (2-tailed test) 
Significant at the 5% level (2-tailed test) 



16 



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17 



Conclusions 

Although our test results of the consistency and accuracy of the 
survivor technique predictions vis a vis those from alternative methods 
of estimating scale economies confirm William Shepherd's c aveat that 
the survivor estimates "need to be screened against alternative evidence.., 
even where its numerical results are perfectly deal," our conclusion 
is much less pessimistic about the value of this method. The survivor 
technique does indicate the range of plant sizes operating under con- 
ditions of constant returns to scale and minimum long-run average cost. 
Out of twenty-five opportunities to test the survivor principle using 
different methods to estimate the numeric significance of scale economies, 
only two industries "failed" the test of consistency. Given our use of 
the ninty-five percent confidence interval we would have expected at 
least one rejection due to random error even if the hypothesis that the 
different methods yield identical results is true. Further, in both 
instances, there is reason to suspect that the production function 
estimates may be in error due to unidentified shift-parameters and hence 
it is quite possible that the survivor technique gives superior results. 

Not only might the survivor technique be superior to other methods 
in identifying constant returns to scale, but the method also enjoys 
s:-~e unique advantages. Although the method i^ not sLeg^nt and involves 
considerable elements of judgment, the data which it uses are precisely 
those which the census authorities currently make available albeit at a 
:=cre aggregated level than might be desired. The researcher is therefore 
not constrained by disclosure laws or data deficiencies. 



18 



Finally, use of the survivor principle to indicate the minimum 
efficient scale of plant as suggested by Leonard Weiss proved to be 
superior in terms of accuracy in identifying constant returns to scale 
than the use of this method to specify an optimal range of plant sizes. 
This latter conclusion must be something of a disappointment to those 
who would urge use of the survivor technique for the resolution of 
public policy issues in the anti-trust field. It is apparently much 
easier to say what is optimal or efficient than to define what is sub- 
optimal or inefficient. 



19 



Footnotes 

"See George J. Stigler, "The Economies of Scale," Journal of Law and 
Economics , 1, 3 (October 1958), 54-71, 

•? 

"William A. Shepherd, What Does the Survivor Technique Show About Economies 

of Scale," Sou thern Econo mics Journal, 34, 1, (July 1967), 113-122. 
Says Shepherd, "the survivor technique cannot safely be used on its 
own. Its estimates need to be screened against other evidence... 
(T)he survivor technique may, under favorable conditions, yield 
preliminary or supplementary ic -.icstions of certain ranges in industry 
cost function. But as an estimator of scale economies its applicability 
is limited, even where its numerical results are perfectly dear." 

3 

The samples, drawn from the 1850, 1860 and 1870 censuses, contain data 

on ownership, invested capital, labor force, wages, quantity and value 
of inputs and outputs, location and motive power for 17091 firms. 
Tests of the samples' representativeness are given in Jeremy Atack, 
"Estimation of Economies of Scale in Nineteenth Century United States 
Manufacturing and the Form of the Production Function," (unpublished 
doctoral dissertation) Indiana University, 1976, chapter 3. 

See George J. Stigler, op. cit .; T. R. Saving, "Estimation of Optimum 
Size of Plant by the Survivor Technique," Quarterly Journal of 
Economics , 75, 4, (November 1961), 569-607; Leonard W. Weiss, "The 
Survival Technique and the Extent of Suboptimal Capacity," The Journal 
of Political Economy , 72, 2 (June 1964), 246-261; and William G. 
Shepherd, op. cit. 



20 



See the results summarized in A. A. Walters, "Production and Cost 
Functions," Econometric a, 31, 1-2, (January-April 1963); 1-66 
especially 39-52. 



See Leonard W. Weiss, op. cit. 



Especially by William G. Shepherd, op. cit . 



8 Ibid., 116. 



9 

Given our selection of the ninty-five percent confidence interval and 

the null hypothesis that the sample statistics and industrial 
distribution of plants were identical to those of the parent population, 
the number of "rejections" was no more than would be expected 
through random error. Copies of the sample tests are available 
upon request. 

See, A. A. Walters, op. cit . 

See Marc Nerlove, "Returns to Scale in Electricity Supply," in C. F. 

Christ (ed.), Measurement in Economics , Stanford: Stanford University 
Press (1963), 167-198; A. Zellner and N. S. Revankar , "Generalized 
Production Functions," Review o f Economic Stud ies, 36, 2, (April 1969), 
241-250; D. Soskice, "A Modification of the CES Production Function 
to Allow for Changing Returns to Scale over the Function," Review of 
Econo m ics and Statistics, 50, 4, (November 1968), 446-448; V. 
Ringstad, "Some Empirical Evidence on Decreasing Scale Elasticity," 
Econometric a, 42, 1, (January 1974), 87-102. 



21 

12 

Zellner and Revankar, op. cit . 

13 

Tae largest surviving plants in the following nine industries were 

operating outside of the range of approximately constant returns to 
scale: Woolens (SIC 2231), Men's Clothing (SIC 2321), Household 
Furniture (SIC 2511), Boots and Shoes (SIC 3131), Blast Furnaces 
(SIC 3312), Iron Foundaries (SIC 3321), Sheet Metal (SIC 3444), 
Steam Engines (SIC 3511) and Agricultural Implements (SIC 3522). 

14 

Leonard W. Weiss, op. cit . , 247. 

The structural evolution and operation of western river steamboats 
is discussed at length in L. C. Hunter, Steamboats on the Western 
Rivers , Cambridge Mass: Harvard University Press, 1949. 



John Johnston, Statistical Cost Analysis , New York: McGraw-Hill, 
1960, especially 71-73. 



William G. Shepherd, op. cit. , 116. 



jOUND^