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FACULTY WORKING
PAPER NO. 935

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Optimal Plant Size and Industrial Structure
Before the Modern Industrial Corporation

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Jeremy .Mack

College of Commerce and Sussnes-s Administration
Bureau of Economic and Business Research
University of Illinois, Urbana-Champaicn

BEBR

FACULTY WORKING PAPER NO. 935
College of Commerce and Business Administration
University of Illinois at Urbana-Champaign
February 1983

Optimal Plant Size and Industrial Structure
Before the Modern Industrial Corporation

Jeremy Atack, Associate Professor
Department of Economics

Not to be quoted or cited without the permission of the author.

Abstract
The transition from small, seasonal businesses meeting local needs
to the large scale corporation serving a national market in America took.
less than a hundred years from 1840 to 1920. Alfred Chandler explains
the change as a response to high-speed, continuous production processes
and mass distribution (especially from 1880 onward) and the interaction
between these two factors. This paper emphasizes the crucial role
played by external economies of scale in the transition since production
economies in many processes were rapidly exhausted. At the same time,
the changes for many firms at this time stemmed from taking advantage of
the factory system and more completely exploiting the production
economies available from pre-Civil War techologies, post-1880, rather
than from the adoption of the revolutionary mass production methods then
being pioneered.

Optimal Plant Size and Industrial Structure
before the Modern Industrial Corporation*

According to Alfred D. Chandler, Jr. (1977, esp. pp. 287-314), the
modern industrial corporation evolved from the technological imperati-
ves of the late nineteenth and early twentieth centuries. High-speed,
continuous production processes and the ever-expanding markets needed
to absorb their output demanded new and specialized management forms
to oversee their operation. The small scale, individually owned and
managed manufactory became economically obsolete and was replaced by
the large scale, investor-owned and professionally-managed factory.
The transition from the small, seasonal business, meeting local
needs, to the large corporation serving a national market year-round
took less than a hundred years, from 1840 to 1920 (Chandler, 1977).

This paper examines the extent and universality of this change by
determining what scale of plant survived during the early stages of
the transition and the implications that this had for the industrial
structure in the latter half of the nineteenth century. In most
industries, production economies were rapidly exhausted, but plants
continued to benefit from mass distribution and it was the conjunction
of mass production with mass distribution by a few firms that
increased concentration and radically altered industrial structure.
Nevertheless these changes were limited to relatively few firms and
the small firm continued to survive and remained the typical producing
unit in spite of these changes. Indeed, these changes may have even
added to small firm vigor. Specifically, I will determine what size
of plant survived during the period 1850-1870 before most of the new
technologies were innovated and how many of these plants would have

-2-

been needed to satisfy demand with no changes in technology or the
extent of the market during the subsequent period.

I. Constraints on Factory Production

Faced by scarce labor and capital, limited power resources, and
poor transport facilities, most manufacturing firms in the first half
of the nineteenth century remained small (Bateman and Weiss, 1975 and
1981). The wage labor supply was small in a country with few large
urban areas (Williamson and Swanson) , and ample opportunities to set up
as a yeoman farmer (Danhof, 1941). Large firms had to resort to
various devices to create a captive labor force. The New England tex-
tile mills, for example, tapped the pool of unmarried farm girls by
offering a supplementary source of income to the impoverished farm sec-
tor and education and strict moral guidance to their employees
(Abbott, 1908-1909). In the South, slaves were often used, especially
in the iron "plantations" (Bradford, 1959), or else manufacturers such
as William Gregg or Daniel Pratt resorted to building model com-
munities to tie labor to the mill (Mitchell, 1928; Miller, 1972).
Capitalization, too, remained small so long as the investor's liabi-
lity was unlimited. Businesses had to rely upon the personal resour-
ces of the owners, their relatives, and friends and the good offices

2
of their suppliers for investment funds. It also meant that

investors were unwilling to relinquish day-to-day supervision to pro-
fessional managers, preventing the division of labor within firms and
the division of talent between firms. Where power was needed, it was
usually water. Yet the power capabilities of most water rights were
quite small and usually seasonal; unusable in the winter's Ice or

-3-

summer's drought and flooded out in the freshets of spring. Even
along the Fall line where quite large water powers were available and
which were less plagued by seasonality, the demands for more power
from growing firms exhausted the hydraulic potential of the site
(Atack, Bateraan and Weiss, 1980). Poor transport facilities com-
pounded the problems of seasonality and more importantly, the high
cost of transportation limited the distance over which goods could
profitably be shipped to market.

Machines, particularly cheaply built machines, could be substituted
for some of the scarce labor, but so long as work was seasonal and the
geographic boundaries of the market were limited, there was little
incentive to adopt the technology, improve it or adapt it to new appli-
cations. Although Oliver Evans' highly mechanized, continuous process
flour mill was widely adopted by the industry, its principles were not
applied to other activities during the antebellum period (Chandler,
1977). Similarly, although the New England textile mills had
pioneered the integrated factory system, there were few imitators
until just before the Civil War when the sewing machine began to be
adopted by the boot and shoe industry (Ware, 1931; Hazard, 1921).

From 1840 onward these constraints were progressively eased by the
railroad and the substitution of steam for water power. The spreading
railroad network significantly reduced the costs of distribution and
banished the seasonal dependency of other transportation media. By
I860 the east coast and midwest had a basic, albeit not fully inte-
grated, network but which did include direct links between the midwest

-4-

and major eastern cities, and, by 1370, 52,922 miles of track were in
use nationwide (Poor, 1890).

The adoption of steam power, made possible and economic by new and

cheaper supplies of coal, freed firms from the locational constraints

of waterpower, its seasonality and the difficulty in expanding the power

3
available. Steam-powered plants could be located in towns and cities

4
rather than alongside the nearest feasible water-right. Labor supply

problems were at once eased and the urban environment not only consti-
tuted a larger market for manufactured products, but was also usually a
node in the railroad network. Lastly, the steam engine permitted the
use of power intensive machinery on an extensive scale and the factory
system came into being in more and more industries.

II. Economies of Scale and Factory Production

Factory production did not necessarily imply large scale opera-
tion; the technology of the day was not one that demanded high rates
of output to realize lowered production costs. Indeed, what evidence
we have suggests that the potential economies of scale were often
realizeable by relatively small plants.

The usual method of estimating production functions, ordinary least
squares, disguises the rapid exhaustion of scale economies as it implies
a linear cost function and scale economies independent of plant size.
k number of alternative production function forms have been developed
which have the property that scale elasticity varies with plant size.
Within certain parameter limits, these are consistent with a U-shaped
long-run average cost curve. I do not, however, impose prior constraints
upon the parameters.

-5-

Consider Che following Cobb-Douglas version of the Zellner and
Revankar (1969) function:

ln(VX) = In A + (I • In L + g • In (K/L) [1]

where: V = value-added
L = labor
K = capital
and ln(V ) = In V + 0V, a monotonic transformation of V.
This production function is estimated using the Box and Cox (1963)
non-linear maximum likelihood method.

Returns to scale, e, depend upon the parameter, 0, the estimate,
U , and upon the level of value-added, V:

e = u/(l + 0V)

For 0 > 1, returns to scale are decreasing with increasing plant size
measured by value-added and, when y > 1 and 0 > 1, at low levels of
value-added, plants are subject to increasing returns to scale which
eventually give way to a range of approximately constant returns
followed by decreasing returns to scale as the value of V increases.

Production functions using this non-linear maximum likelihood method

Q

were estimated for plant data from the 1870 census of manufacturing.
Analysis focused upon twenty-four industries which in 1870 produced
over 50 percent of all manufacturing value-added and represented about
a quarter of the identifiable industries at the time.

The production function estimates of u and the value of 0 which
maximized the likelihood function are shown in Table 1.

-6-

Table 1

Interpretation of the results was not, however, straightforward. In
approximately a third of the twenty-four cases, the value of 0 which
maximized the likelihood function was negative. This would imply
scale economies that increased with plant size, a notion generally
contrary to our theory of the firm. However, in none of these instances
was the estimate of 0 significantly different from zero suggesting that
the variable scale elasticity production function methodology was not a
significant improvement over fixed scale elasticity forms. Indeed,
only two estimates (woolen mills and steam engine manufacturer)

Q

yielded values for 0 that were significantly different from zero.
Although none of the scale parameters, 0, was estimated to be
significantly less than zero, negative values for 0 should not be
dismissed as a statistical irregularity. Other researchers using
different data sets have encountered similar results but have not
investigated the phenomenon more closely (Ringstad, 1974). The
problem appears to be that not only is the scale elasticity parameter,
e, a function of plant size but also 0 itself is a function of plant
size. A simple verification of this can be made. If the data are
dichotomized by plant size into two mutually exclusive groups, "small"
and "large" plants in each industry, and equation [1] re-estimated for
the separate groups, then 9 is often significantly positive (and never
negative) for "small" plants and negative, often significantly so, for

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9
large plants. The hypothesis that 6 was the same for both "small"

and "large" plants in an industry was almost always rejected.

For "small" plants, scale elasticity decreases rapidly, so that
even quite modest growth by "small" plants exhausts the potential scale
economies available to such firms. For "large" firms the puzzle is why
scale economies appear to increase for larger and larger firms. The
answer, I believe, lies in unidentified cost curve shifts which invali-
date the results based on the estimation of a single production function.
The source of such shifts may have been technological discontinuities
between "small" and "large" plants.

Production function estimates assume technological homogeneity
across the observations and although the period up to 1870 was not
characterized by significant or rapid technological change, except for
the sewing machine, subtle changes did take place at differential rates
between plants on the basis of size. One important change, for example,
was the adoption of steam power. Steam-driven plants, in virtually
every industry, were larger on average than waterpowered plants. For
example, steam driven saw mills produced an average of $5,400 (1860
dollars) value-added in 1870 compared with only $1,400 for waterpowered
mills and in iron blast furnaces and rolling mills, the averages were
$56,700 and $4,700 respectively for steam and water powered plants.
These differentials were preserved in each region including New
England which had abundant, large waterpower resources. The impor-
tance of steam power for the embodied technology in the machines is

-9-

not very well documented but we do know, for example, that steam-
powered spindles operated at higher speeds and produced a different
quality of yarn (Montgomery, 1840, pp. 69-71). Similarly, in saw mills,
the switch to steampower was often accompanied by a switch to a cir-
cular or band saw with dramatic decreases in the kerf and sharp
increases in the throughput of lumber (Reynolds, 1957). Under this
general heading of technological change too, one can also include the
transition from workshop to factory and the organizational changes
contingent upon that change. The switch lowered unit costs at larger
output levels and factory production was sufficiently different and
distinct from workshop/artisan manufacture to warrant classification
as a separate technology. We cannot, however, distinguish the
workshop from the factory using the data in the manuscript censuses.

A second factor may also have generated cost curve shifts for large
firms, most of which were to be found in New England or the Middle
Atlantic states. Higher population and transport densities, a more
skilled labor force, more sophisticated capital markets and a superior
supply of ancilliary and support services and products may well have
placed the plants in those areas on a different family of cost curves
and at the same time have contributed to their larger relative size.

Within a given technology, however, there is good reason to suppose
that unit costs were lower for larger plants. The large manufacturer
may have been able to exercise some monopsony power to purchase inputs
at lower prices than smaller competitors. Poor transport facilities
would have reinforced this power as raw materials with a low value-
to-weight would not be able to absorb the transport costs to distant

-10-

raarkets. \t the same time, any cost savings to large firms were
apparently passed along to consumers in lower prices as the return on
investment in large firms was often less (but more stable) than that
for small firms (Bateman and Weiss, 1980). Large firms also had
access to the imperfect captial market of the time at preferential
rates (Davis, 1960). For very large plants, cost could rise if only
from managerial difficulties in overseeing such a large operation and
controling costs with so imperfectly developed management tools.

Although the results in Table 1 do not lend much support for a
variable scale elasticity production function form in preference to a
homogeneous function, nevertheless we can use the results from Table 1
for these industries for which 8 > 0 and u > 1 to estimate the output
level for which average costs were a minimum, and the range of outputs
embraced by costs within 5 and 10 percent of the minimum. These can
then be compared with the average size of plant in the industry. The
results are shown in Table 2. Value-added has been adjusted using the

Table 2

Warren-Pearson price index to express the results in 1860 dollars.
This step is essential for the later results as the lingering effects
of the Civil War inflation were still apparent in the 1870 data and
prices generally fell over the period to the mid-1390s (U.S. Bureau of
the Census, 1975, Series E52-63).

The relationship between decreasing scale elasticity and the
average cost curve for woolen textiles is graphed in Figure 1.

Figure 1

-11

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Figure 1

Economies of Scale and Index of Average Cost by Value-Added (1860 dollars)

for Wool Textiles (SIC 2231)

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e = m/(1 + 0V) = 1.47/(1 + 0.0000059-V)

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AC(V) = k(V -e ) /M - AC(V)

min

= k(V{1/^1}.eQV/lJ)/0. 03731

10

15

I I

20 25

-T—
30

t—
35

min AC(V)

I $52,576

40 45 50

70

55 60 65

Value-Added

(thousands 1860 dollars

-13-

Average costs are defined by:

AC(V) « kCV1"^ • eQV)l/U

where u and 8 are from the variable scale elasticity production func-
tion estimates, V is value-added and k is a function of input prices.
Assuming competitive markets (as we must for our production function
estimates), k is a constant.

In general, the range of plant sizes with average costs within
five or ten percent of the minimum average costs is quite broad except
for bread and other baked goods. In some instances, the average cost
curve is very flat, as, for example, with sawmills, leather tanning or
boots and shoes. A wide range of plants of different sizes could thus
be cost competitive with one another. Unfortunately, we do not know
what magnitude of cost differences would make firms non-competitive
with one another. In part, this would depend upon transport costs and
the firms' juxtaposition vis a vis the transport network and markets;
it would also depend upon the rate of return each owner-investor
demanded for the level of risk being borne. Unfortunately, production
functions do not address the issue of the costs of distribution,
although Chandler's (1977) thesis that the modern corporation emerged
from the conjunction of mass production with mass distribution assigns
them a critical role.

A relatively narrow range for low cost firms in the bakery
industry makes sense. Product perishability and the comparatively
undeveloped state of the market for commercially baked goods would
limit the growth of firms in the industry. The other products were

-14-

non-perishable and transportable, though given the ease of their manu-
facture and the sometimes low value-to-weight ratio, there was prob-
ably little point in producing more than necessary to supply the
market in the immediate vicinity. Nevertheless, since not all markets
were the same size and scale economies remained more or less constant
over a fairly wide range, the industries supported a variety of dif-
ferent sizes of plant.

The average size plant producing boots and shoes, pig iron, sheet
metal work, steam engines and woolen textiles was operating at a scale
very close to that which minimized average costs. Indeed, I would
argue that in only three of the industries in Table 2 were plants of
average size producing at a scale where costs were dramatically greater
than the minimum: meat packing, distilled liquers and sawmills. In
each case, the average plant in the sample (and also in the population)
was too small. With comparative statics analysis we cannot, however,
say anything about what happened to these small plants in the long-run:
Some may have grown and expanded into the range of constant returns
becoming cost competitive; some may have been driven out of business;
and others may have continued to survive if their (small) markets were
somehow protected, as, for example, by high transport costs.

III. The Survivor Technique

The static nature of the production function analysis and the
problems associated with the estimates which we have outlined above
limit the usefulness of that methodology for analyzing changes in

-15-

industrial structure and addressing the Chandler thesis of the con-
junction of mass production and mass distribution in the rise of big
business. Fortunately, there is an alternative means to determine
what size of plant was most efficient in 1870. We can examine changes
in the distribution of industry value-added (in constant 1860 dollars)
by size of plant over time. This approach is called the "survivor
technique." The survivor technique seeks to identify those size
classes of plant that not only survived the rigors of market competi-
tion and the test of time, but also succeeded in increasing their share
of total industry value-added (Stigler, 1958; Saving, 1961; Weiss, 1964;
Shepherd, 1967). That is, it seeks to identify those plant sizes that
grew in relative importance in an industry through the long-run compe-
titive adjustment process.

A number of assumptions are implicit in the technique and while
these have been discussed in detail by others, notably by Shepherd
(1967), there still appears to be some confusion about them. Shepherd
(1967), for example, argues that "survivor estimates for firm sizes
are likely to be more valid for atomistic industries. . .than for
highly concentrated ones," presumably because the assumptions of
atomistic competition insure that, in the long-run, market pressures
force all plants to operate at minimum long- and short-run average cost
if they are to survive. Profit maximizing behavior, however, also
ensures the survival of lower cost plants even under conditions of
monopolistic competition (Stigler, 1958). Moreover, demand changes
under conditions of atomistic competition affect only the number of

-16-

firras in Che industry while such changes for raonopolistically competi-
tive industries will permanently alter the market solution, including
the optimum plant size. Similarly, the assumptions of atomistic com-
petition presuppose no technological change and yet the movement towards
a deterministic surviving plant size may be most pronounced when tech-
nological charge is greatest.

Under certain circumstances, survivor technique results may lead
to erroneous conclusions. Consider, for example, the problems posed
by the existence of monopoly elements. Under conditions of monopo-
listic competition, long-run equilibrium is reached at some output less
than that which minimizes long-run average cost. Weiss (1964) avoids
this problem by emphasizing the "minimum efficient" scale of operation
rather than the range of optimal plant sizes emphasized by others
(Stigler, 1958; Saving, 1961). However, if the range of surviving
firms continues to be identified with minimum long-run average cost
then the results will be inconsistent with production or cost function
estimates which would show increasing returns to scale and decreasing
unit costs. Similarly, the presence of externalities in distribution
which alter the cost minimizing level of output for the product deli-
vered to the consumer will lead to inconsistent results between the
survivor technique estimates which take such factors into account as
a matter of course and those based upon production functions which
focus purely upon the production process internal to the firm.

-17-

There is no universal agreement on how plant size should be
measured, yet alternative measures such as value-added, output,
employment or capital can lead to quite different conclusions during
periods of technological change. Consider a (Hicks) neutral tech-
nological change (a horaothetic shift of isoquants towards the origin)
in an industry whose production function is consistent with a U-shaped
long-run average cost curve. Such a change leaves the shape of the
long-run average cost curve unchanged, it merely results in lower
costs at each level of output. Under these circumstances, if plant
size were measured by labor or capital, the survivor technique would
show smaller plants surviving because of the shift of the isoquants
towards the origin (A% less labor and capital are needed to produce
the same level of output), while on an output basis, the optimal (or
minimum efficient) plant size would be unchanged. If, instead, the
technological change had been labor-saving, then the apparent reduc-
tion in the size of the optimal plant would be greater if size is
measured by employment rather than by capital and vice versa if the
technological change were capital-saving. These scenarios are shown
in Figure 2. We have elected to use value-added as a measure of plant
size.

Figure 2

The survivor technique implications for an optimal range of plant
sizes (classified by value-added) over the 1850, 1860 and 1870 samples

from the manuscript censuses of manufacturers for the 24 industries in

12

Table 1 are shown in Table 3. The results generally reveal a wide

Figure 2

Effect of Neutral, Labor-Saving, or Capital-Saving Technological Change on Various

Measures of Plant Size.

A. Neutral Technological Change:

Capital

Ql

= Ql'

OK

= OK

OL

OL

KK'
OK

- LL
OL

1/ L

Labor

B. Labor-Saving Technological Change:

Capital

K
K'

Ql = Ql

OK < OK/
OL OL'

KK" < LL'

OK OL

Labor

C. Capital-Saving Technological Change:

Capital

K
K'

Ql = *i

OK > OK'
OL OL'

KK' > LL'

OK OL

L' L

Labor

-19-

Table 3

range of optimally-sized plants in almost every industry and suggest
that a considerable portion of the long-run average cost curve may have
been flat. This finding is consistent with the twentieth century cost
function studies reported in Walters (1963), the survivor technique
results reported by Saving (1961) and production function estimates for
the nineteenth century (Atack, 1976; Atack, 1977; Sokoloff, 1981;
James, 1982). There were five industries, flour-milling, bread and
bakery products, tobacco manufacture, saw and planning mills, and brick
works, in which the range of surviving plants embraced less than
$16,000 value-added. All were locally produced and traded goods.
Plants producing these goods typically supplied markets limited by pro-
duct perishability, by localized brand loyalties, or by a low value-to-
weight ratio in the presence of high transport costs.

Estimates of the minimum efficient scale of operation are also
given in Table 3. The minimum efficient scale of plant is the
smallest size of plant which increased its share of total industry
value-added over the period. In industries suspected of not being
perfectly competitive, this measure is to be preferred to the range of
optimal plant sizes because long-run equilibrium is reached at some
output less than that which minimizes long-run average cost (Weiss,
1964). The minimum efficient scale in many industries was often quite

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-21-

13
small. In flour milling, for example, firms producing as little as

S100 (1860 dollars) value-added in 1870 could still be efficient. At
the opposite end of the scale, the minimum efficient scale in cotton
textiles was apparently $128,000. Small textile mills could not sur-
vive.

The ratio of value-added in 1870 produced in optimally sized
plants to the value-added produced in those plants in 1850 (expressed
in constant 1860 dollars) shown in Table 3 is an attempt to capture
the movement towards the concentration of value-added in optimally
sized plants over the period. In most cases, the increase in the pro-
portion of output produced in optimally sized plants was quite large;
in 17 of the 24 cases, there was better than a 50 percent increase.
Moreover, in all but seven cases more than half of 18 70 value-added
originated in optimally sized plants. In some cases the increase was
exceptionally dramatic. In 1850, no farm machinery manufacturer pro-
duced more than $32,000 value-added, but by 1370, two-thirds of
industry output was produced by plants larger than that; among them
would number firms such as McCormick ($407,000 (1360 dollars) value-
added in 1870) and Case ($283,000 value-added).

With only two exceptions the range of plant sizes with costs
within 10 percent of the minimum average costs given in Table 2
overlap the range of optimal plant sizes in Table 3. In some cases
the overlap was quite extensive. In the meat packing industry, the
range of surviving plants, 532,000-64,000, compares favorably with the
range of meat packing plant sizes with costs within 10 percent of the
minimum, 314,700-63,600. In other cases, the intersection of the two

-22-

was much less. In the boot and shoe industry, for example, the ranges
were $16,000-256,000 and $0-49,200 respectively. The range of sur-
viving plants did not intersect with the lower portions of the esti-
mated average cost curve in sawmilling and in pig iron production.

In the former case, surviving plants were "too small," though even
today sawmilling is classified as a local monopoly protected by
transport costs, while in the latter case, surviving plants were "too
large." The iron industry was one of the few industries which under-
went rapid technological change between 1850 and 1870 with hard
driving, improved heat recovery in the blast furnace and the introduc-
tion of the Bessemer process in the 1860s. The survivor techniques

correctly identifies integrated blast furnaces and Bessemer plants as

, . 14
surviving.

Seven of the 11 estimates of the size of plant which minimized
average costs in Table 2 also fall within the range of optimally sized
plants in Table 3. In two of the "failures," distilled liquors and
sawmills, the cost minimizing plants in Table 2 were larger than the
optimal range, while the cost minimizing plants in the boots and shoe
industry and iron manufacture were smaller than the range of surviving
plants.

From what has been said already, inconsistencies such as these
between the production function approach to identify long-run
equilibrium plant size and the survivor technique are to be expected.
On the one hand, transport costs for a relatively homogeneous product
which is as easily and cheaply produced in one location as another
would cause the cost minimizing plant to be smaller than that based

-23-

purely upoa production factors. On the other hand, mass distribution
lowering unit distribution costs for larger producers would cause the
cost minimizing scale of plant to be larger than that determined
solely by production consideration. The survivor technique takes both
production and marketing distribution costs into account; production
function analysis doesn't.

IV. 1870 Optimal Plants and Industrial Structure 1370-1900

We have used the range of optimal plant sizes from Table 3 as the
basis for estimating the number of optimal plants which industry value-
added could have sustained with no changes in technology, externalities
or the costs of transport between 1870 and 1900. These estimates are
shown in Table 4. The figures indicate the number of plants that would

Table 4

have been in the industry if all plants had been the same size as
either the minimum efficient scale of plant in 1870 or the largest sur-
viving plants in 1870.

In 1870 the number of plants in more than half of selected
industries; meat packing, flour milling, bread and bakery products,
tobacco, lumber milling, millwork, printing and publishing, saddlery
and harness, brick, pig iron, iron castings, and steam engine and
machinery industries fell within the range defined by the surviving
plants. The distribution of plants could, therefore, be consistent
with the majority of plants having adjusted their scale of operation
into the optimal range. However, a glance at Table 3, which shows the

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-25-

percentage of value-added originating in optimal plants in 1870, shows
that this is not necessarily the case; a combination of plants that
were "too small" and "too large" could produce a total value-added and
number of plants consistent with an optimal range. In a number of
other industries (malt and distilled liquors, cotton and wool tex-
tiles, clothing, millinery, wooden furniture, leather tanning, boots
and shoes, farm machinery and carriages and wagons) the number of
establishments in 1870 was greater than the number of minimum effi-
cient scale plants, suggesting that relatively few establishments in
those industries had achieved an efficient scale in 1870. Except for
textiles, these industries in 1870 were still dominated by small-scale
artisan shops. Most agricultural implements manufacturers, for
example, were little more than village blacksmiths and handmade shoes
still had not been displaced by the mass produced factory product.

By 1900, the number of establishments and the distribution of value-
added had changed so that only in millinery, wooden household fur-
niture, and wagons and carriages was the number of establishments in
an industry greater than the predicted range. In four industries
there were fewer establishments in the industry than predicted: Three
of these were ones in which there had been rapid technological change;
meat packing, tobacco, and blast furnaces. The other industry, brick-
making, is one of the lowest value-to-weight products and, hence, one
on which cheaper transportation is most likely to have the greatest
effect.

The nature, timing and extent of technological change influences
how the hypothetical number of 1870 optimal plants compared with the

-26-

number of plants actually in an industry at any moment. Consider the
case of meat packing. In 1870 and 1880, the number of plants in the
industry lay within the range of the numbers of optimal 1870 plants,
but, by 1390, there were fewer plants in the industry than we predict
on the basis of no changes in technology or externalities from 1870.
Yet this is precisely when the industry was revolutionized by the
introduction of the refrigerator car with a nationwide distribution
network and the conversion of meat-packing to a high volume, con-
tinuous disassembly process making full use of by-products. Firms
such as Swift and Company, P. D. Armour and the Cudahy Packing Company
drove smaller firms out of business as they integrated vertically and
spread out horizontally into cities other than Chicago (Swift and
Armour) or Omaha (Cudahy) (Chandler, 1977, pp. 300-301; Yeager, 1981).

A similar story can be told for the tobacco industry which was
revolutionized by Duke's adoption of Bonsack's continuous-process
cigarette-making machine in 1885 and his national advertising campaign
to promote the product (Chandler, 1977, pp. 290-291; Tennant, 1950).
As a result, in 1890, the number of tobacco plants was closer to the
lower-bound number of optimally-sized 1870 plants than had been the
case in 1880. By 1900, with the American Tobacco Company dominating
the industry by merger and predatory practices, the industry had been
transformed to one with fewer plants than we would have predicted had
those changes not taken place since 1870.

This pattern is repeated in industry after industry although in
some industries, such as agricultural implements, it is difficult to

-27-

point to specific innovations other than the adoption of factory pro-
duction, superior machine tools and more reliable supplies of low cost
metals to account for the marked change in the number and size of
plants. The data in Table 5 reveal the magnitude of industry

Table 5

adjustment towards optimal plant sizes by 1900. They do not, however,
necessarily measure the extent, degree and significance of tech-
nological progress. Some changes came about because of widespread
adoption of factory production to take advantage of improvements in
transportation and distribution but using pre-Civil War technology.
The most rapid relative adjustment was in the boot and shoe industry
in which the artisan producer was virtually driven out of business,
except in the repair of shoes, in favor of factory-made products
(Hazard, 1921; Clark, 1929). One would add in passing that the switch
to mass-produced shoes was accompanied not only by a decline in price
but by improvements in fit and durability (Keir, 1920). Leather
tanning also underwent a marked change as a result of improvements in
the chemical industry and the effects of concentration in the meat-
packing industry which confer a degree of monopoly power on the
packers. In the brewing industry, brewmasters, led by Pabst, estab-
lished vertically integrated plants to supply far-flung markets via
temperature-controlled tank cars. The clothing industry, revolu-
tionized by the sewing machine and the adoption of standard sizes,
underwent the fourth most rapid transition. The agricultural machinery
industry which experienced the fifth most dramatic relative change

-28-

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-29-

finally broke with its blacksraithing origins to become a mass-produced,
factory product. At the opposite end of the scale, industries such as
brick making, sheet metal and printing underwent remarkably little
change by way of transforming the industry. Nor is there evidence of
revolutionary change in the flour milling industry; despite the adop-
tion of reduction milling and the development of national brands such
as Pillsbury and Gold Medal, the small flour mill continued in
existence. Other "laggard" industries such as wagons and carriages or
saddlery and harness, are less surprising as these underwent no tech-
nological change nor probably did they benefit from the development of
a national market.

Conclusion

In aggregate terms, few industries showed a dramatically different
structure in 1900 than had been present in 1870. Some of the most
pronounced changes were in those industries which had successfully
moved from the workshop or small factory serving local needs to fac-
tories serving a wider clientele; industries such as boots and shoes,
leather tanning, brewing, clothing and agricultural implements. With
few exceptions, these were not the industries undergoing rapid tech-
nological change after the Civil War. For the most part they were
taking advantage of pre-Civil War technology and the post-War revolu-
tion in transportation and distribution. The typical plant in these
industries in 1900 was no larger than an efficient plant in 1870 would
have been.

-30-

In some industries, however, the average scale of operation by
1900 was much larger than that of an efficient plant of 1870. These
were generally industries which had experienced technological change
permitting high-speed, continuous-production processes and had also
taken advantage of mass marketing and distribution for their product.
However, only a few establishments in each industry took advantage of
these opportunities. Their output level was often many times greater
than that of even the largest 1870 efficient plants and, for the most
part, they survived. The rest of the plants in these industries
remained small. They were the typical producing units but they are
generally ignored. Certainly, they do not appear in Chandler's model,
Bigness is better documented; more heroic and although big firms made
their mark, the successful coexistence of small producers is at least
as deserving of study. Their survival seems to stem from the rapid
exhaustion of production economies in many activities and the ability
of the small firm to carve out a niche catering to local tastes and
needs not met by a mass-marketed, homogenized product.

-31-

Footnotes

*I wish to thank Fred Bateraan and Larry Neal for their helpful
comments and suggestions on this version of the paper. Earlier work
from which this paper was derived benefitted from the advice and com-
ments of Richard Arnould, Barry Baysinger, Jan Brueckner, Larry
Davidson, Wayne Lee, Julian Simon and George Stigler.

The difficulties of raising impersonal capital were a frequent
lament of nineteenth century industrialists, particularly in the South
and West. The issues are discussed in Livermore (1935). Various stu-
dies have been made of the progress of limited liability and the
granting of corporate charters to business. None, however, is compre-
hensive. See, for example, Evans (1948), Kuehnl (1959), Wilson (1964)
and Wolfe (1965).

2

Daniel Pratt, for example, raised the $110,000 for his Prattville

Manufacturing Company No. 1 from personal resources, friends and rela-
tives (Miller, 1972, p. 17). The large New England textile mills
were, however, able to attract institutional funds for operating capi-
tal and expansion, and sell equity to finance the initial construction
(Davis, 1957; Davis, 1958; Davis, 1960).

3
Even in cities such as Lowell or Lawrence centered upon large

developed water rights, future expansion could only be met by improve-
ments in the use of the available water or the adoption of supplemen-
tary steam power (Atack, Bateman and Weiss, 1980). Pressure upon
existing water rights led to the pioneering research and development

-32-

work of Che Locks and Canal Company at Lowell and its chief engineer,
James B. Francis, inventor of the Francis turbine (Francis, 1868).

4
For an attempt at measuring the geographic spread of steam power

as coal became available, see Atack and Bateman (1983).

See, for example, Atack (1976; 1977) and Sokoloff (1981) for the
antebellum period and Ringstad (1974) for comparable results for
modern industry.

See, for example, Nerlove (1963); Soskice (1968); Zellner and
Revankar (1969); Ringstad (1974); Christensen, Jorgensen and Lau
(1973); Christensen and Greene (1976).

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

ln£ = constant - -y In a + In J(X;V)

" n K ~r

Z In (V ). - InA - u ■ InL. - 0 • ln(-^-)

m X X Ll,

1=1 i

2a2

2
where a is the variance of the normally and independently distributed

random error term with mean zero, n is the number of observations and

J(A;V) is the Jacobian of the monotonic transformation.

J(X;V) = Eln(l+9V.). Ordinary least squares minimizes the last term

i 1
of equation [2] for any predetermined value of 0, yielding a

conditional maximum for the likelihood function. By varying 0 and

evaluating (InA - constant) the estimate of 0,(0), follows a chi-square

distribution such that:

[2:

-33-

in£(e) - lni(e) < 1/2 x2(n)

max

where n is the confidence interval. Using n = .05 yields a value for

2
1/2 Y of 1.94. Thus ln£(e) < 1.94 in the test for the confidence
A max

interval around the value of 0, the global maximum likelihood
function can be determined.

8
The data are from the samples drawn from the manufacturing census

of 1350, 1860 and 1870 by Fred Bateraan and Tom Weiss. Sokoloff (1981)
also reports relatively slight support favoring a variable scale
elasticity production function in 1820 and 1850 data. Similar fin-
dings of increasing scale elasticity with plant size have been noted
by Sokoloff (private communication) and James (1982).

9
For analogous results for the pre-Civil War period, see Atack

(1977).

10

Manuscript census data. The higher value-added produced in

steam- powered factories as compared with that produced in water-driven

plants holds across virtually every industry, in each region and in

each of the three years exasrained: 1350, 1860 and 1870. It is also

greater than can be accounted for by the elimination of seasonality.

Steam-driven factories were larger and the machinery was probably

driven longer and harder than that in water-powered plants.

Similarly a technological change which reduces raw material
waste would increase value-added for the same level of output.

-34-

Evidence favoring substantial biased technological change over the
period 1850-1919 is given in Cain and Paterson (1981) and in James
(1982) for the period 1850-1900. The bias was generally in favor of
labor-saving technological change, and although it was not necessarily
capital-using, there is evidence of material-using and capital-using
biases. James' (1982) work suggests much of the biased technological
change occurs from 1880 onward, except in iron, leather tanning and
cotton textiles. However, 10 of the industries in this study (bread
and other baked goods; malt liquors; tobacco; millinery; millwork;
household furniture; saddlery and harness; sheet metal work; farm
machinery; and transportation equipment) are not included in James'
work.

12

The theory gives no guidance over the appropriate size cate-
gories, probably because modern studies applying the survivor tech-
nique have to rely upon census size classifications. I elected to use
a logarithmic progression of size categories; the limits of each cate-
gory are double those of the next smaller category. Because of the
large numbers of small firms in many industries I selected $0-249
value-added (1860 dollars) as the smallest category. The largest size
groups is $250,000 or more value-added (1860 dollars) and is open-
ended. An upper bound on plant value-added for plants falling in this
group is not specified. No size distribution of firms/plants was
published before 1900 (U.S. Census Office, 1902).

13

James (1982) also notes the generally small scale of optimal

size plants though his results suggest some significant increases in

size between 1860 and 1870.

-35-

14

Only one integrated blast-furnace and Bessemer plant was in the

sample and its inclusion in the $128,000-255,990 category resulted in
that size class surviving. On the other hand, there were only three
Bessemer plants in operation in 1370 (Jeans, 1880). Nevertheless,
there was a marked shift in favor of larger blast furnaces to econo-
mize on fuel and recycle heat otherwise lost in the process. See also
Allen (1967).

In these industries the only technical changes of consequence in
the production process were the McKay welting machine in boot and shoe
manufacture and the pneumatic malting process in brewing (Hazard,
1921; Chandler, 1977).

-36-

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