Tariffs and the Distribution of Income: The Importance of Factor Specificity,
Substitutability, and Intensity in the Short and Long Run
Author(s): Michael Mussa
Source: Journal of Political Economy, Vol. 82, No. 6 (Nov. - Dec., 1974), pp. 1191-1203
Published by: The University of Chicago Press
Stable URL: http://www.jstor.org/stable/1830668
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Tariffs and the Distribution of Income:
The Importance of Factor Specificity,
Substitutability, and Intensity in the
Short and Long Run
Michael Mussa
University of Rochester
This paper analyzes the effects of changes in relative commodity prices on
the distribution of income among factors of production in the context of
two models of a simple, two-good economy. In the first model capital is
treated as a specific factor in each industry, with labor mobile between
industries. The assumption of specificity determines the direction of factor
income changes, with magnitudes depending on substitutability between
factors and on intensities of factor use within the two industries. In the
second model, capital is viewed as a quasi-fixed factor. For the short
run, this model is identical to the model first considered. For the long
run, this model is identical to the Stolper-Samuelson model in which
the direction and magnitude of factor income changes depend solely on
relative factor intensities. The difference between the short-run and
long-run determinants of changes in factor incomes gives rise to a
conflict between factor owners' short-run and long-run interests.
Introduction
A primary effect and principal objective of commercial policy is frequently
to protect or enhance the incomes of specially favored groups. The modern
theory of the effects of commercial policy on the distribution of income,
the Stolper-Samuelson theory, however, is not adequate for analyzing
much of the clamor for protection. This theory envisions an economy in
which factors of production are costlessly and instantaneously mobile
between productive activities and emphasizes the effects of differences
in relative factor intensities. The theory suggests that if automobile
I would like to acknowledge the many useful comments and suggestions which were
made by my colleagues Rudiger Dornbusch, Ronald Jones, and Sherwin Rosen. I would
also like to acknowledge the financial support for this research which was provided by
the National Science Foundation through the MSSB Summer Workshop on the Application
of General Equilibrium Models to Economic History.
[Journal of Political Economy, 1974, vol. 82, no. 6]
?) 1974 by The University of Chicago. All rights reserved.
I 191
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I I92 JOURNAL OF POLITICAL ECONOMY
manufacturing is capital intensive, then General Motors will favor
increases in the tariff on automobiles and the United Auto Workers will
oppose such increases; and, if textile manufacturing is labor intensive,
then textile workers will favor quotas on textile imports, and domestic
textile manufacturers will oppose them. What the theory neglects is that,
in the short run, at least, factors tend to be specific to particular uses.1
The stamping machines and assembly lines of automobile manufacturers
are not costlessly transformable into the looms and weaving mills of textile
manufacturers. The skills of a tool-and-die maker in Detroit are not
instantaneously interchangeable with those of a master weaver in North
Carolina.
The objective of this paper, however, is not to criticize the StolperSamuelson
theory, but rather to integrate it with an earlier "Marshallian"
approach. An integration of the two approaches is desirable because
each lays emphasis on a different set of important phenomena. The
"Marshallian" approach emphasizes the distinction between the short
run and the long run.2 For the short run, it focuses on specific factors
and on the degree of substitutability between these factors and highly
mobile factors. For the long run, it recognizes that factors that are specific
in the short run often can be moved to alternative uses. The analysis of
the long run is complemented by the Stolper-Samuelson theory, which
assumes complete mobility of factors and focuses on general equilibrium
interactions between factor endowments and the factor intensities of
different productive processes.
The two approaches will be integrated within the context of two
related models of a simple, two-good economy.3 In the first model,
capital will be treated as a fixed factor that is specific to the industry in
which it is used, while labor will be assumed to be free to move between
industries. These assumptions about factor mobility will suffice to determine
the direction of changes in factor incomes in response to changes
in output prices: the income of capital in each industry rises more than
proportionately with increases in the price of its own output and falls
with increases in the price of the other output; the income of labor rises
less than proportionately with increases in either output price. The
magnitude of factor income changes, however, will be shown to depend
on the substitutability between labor and capital in each industry and
on the factor intensities of the two industries.
The second model will preserve the structure of the first, except that
I In the introduction to their classic article, Stolper and Samuelson (1941) take note
of the potential importance of specific factors, but do not integrate such factors into their
formal analysis. In the more recent literature, specific factors have received relatively
little attention. A notable exception is Jones (1971).
2 For an excellent summary of the "Marshallian" approach to the analysis of the effects
of commodity price changes on factor incomes, see Pigou (1906, especially pp. 55-59).
3 In a recent paper, brought to my attention by the editor of this Journal, Mayer
(1974) analyzes similar models, focusing on a slightly different set of issues.
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TARIFFS AND INCOME I I93
capital will be treated as a quasi-fixed factor that is specific to a given
industry at a moment of time, but free to move between industries in the
long run. For the short run, this model is identical to the first model.
For the long run, it is identical to the Stolper-Samuelson model. By
using known properties of the Stolper-Samuelson model, it will be shown
that the short-run and long-run determinants of the behavior of factor
incomes are very different and that these differences necessarily imply
a conflict between factor owners' short-run and long-run interests.
I. Factor Specificity and the Direction of Income Changes
Consider a two-comrnmodity, three-factor model with the following
properties. (1) There is a single mobile factor, labor, which is used in the
production of both commodities, X and Z. (2) There are two specific
factors, capital in X and capital in Z, which are used only in their respective
industries, and which are in fixed supply to those industries.
(3) The production functions for the two commodities are each linear
homogeneous in their respective inputs and have the standard neoclassical
properties of differentiability and of positive and declining marginal
physical products for each of the inputs, specifically,
X = F(LX, Kx), (1)
Z = G(LZ, KZ). (2)
(4) The total quantity of labor used in both industries is equal to the
fixed aggregate supply of labor; that is,
LX + Lz = L. (3)
Given an initial relative price of X in terms of Z (within the range of
nonspecialization), say Px, the distribution of the labor force, the level
of the wage rate, and the income of capital in X and capital in Z may
be determined with the aid of figure 1. The length of the horizontal axis
is equal to the total supply of labor, L. The vertical axes passing through
OX and OZ measure the wage of labor in terms of units of Z per unit of
labor. The curve labeled VMPLX(P') is plotted relative to the origin
Ox and shows the value of the marginal product of labor in X as a function
of Lx. The vertical position of this curve depends on the given value of
the relative price of X, Po. The curve labeled VMPLZ is plotted relative
to the origin Oz and shows the value of the marginal product of labor in
Z as a function of Lz. Its position is independent of the commodityprice
ratio. The point of intersection, (L0, w0), determines the equilibrium
distribution of the labor force and the equilibrium value of the wage
rate. The income of labor in X and the income of labor in Z are shown
by the corresponding rectangular areas under the wage line, w = w0.
The incomes of the two types of capital are shown by the corresponding
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I I94 JOURNAL OF POLITICAL ECONOMY
w w
W
VM P Lz i l VM P X(PX
O X LO Li 0
FIG. 1.-Equilibrium wage rate and allocation of the labor force
triangular regions between the wage line and the respective value of
marginal product curves.
An increase in Px, say from Po to Pk, shifts the VMPLX curve
portionately upward, resulting in a new equilibrium at (L', w1). The
increase in the wage rate (measured in terms of Z), however, is less than
the proportionate increase in the relative price of X in terms of Z. Labor,
the mobile factor, gains in terms of Z but loses in terms of X. In contrast,
capital in X gains in terms of both commodities, and capital in Z loses
in terms of both commodities.4 The loss to capital in Z is apparent
from the fact that the increase in the wage rate reduces the size of the
triangular region which corresponds to the income to capital in Z.
The gain to capital in X can be seen by considering only the units of X
which were (and still are) produced by the original amount of labor,
Lo. The value of these units of X rises proportionately with the increase
in PX. The cost of the labor employed in producing these units rises,
'Marshall (1961, p. 664), summarizes these results in the following words: "The
employer stands as a buffer between the buyer of goods and all the various classes of
labor by which they are made. He receives the whole price of the one and pays the whole
price of the others. Fluctuations of his profits go with fluctuations of the prices of the
things he sells, and are more extensive: while those of wages of his employees are less
extensive."
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TARIFFS AND INCOME I I95
but by less, proportionately, than the increase in PX. Hence, the return
to capital, on just these original units, must rise by more, proportionately,
than the increase in PX. Since capital in X also earns a positive amount
on the additional units which are produced, it follows that capital in
X must gain in terms of both goods.
The assumption of specific capital and mobile labor determines the
direction of factor income changes in response to commodity-price
changes. The property of "specificity," however, should not be conceived
of as a wholly technological matter. If Px is so high that all labor is
specialized in the production of X, then the income of labor will respond
in exactly the same way as the income of capital specific to X to an
increase in Px: both will increase proportionately with the increase in
Px. "Specificity" is an economic, as well as a technological, matter.
The results of the present model concerning the responses of factor
incomes to changes in commodity prices can be interpreted in terms of
the "Marshallian" concept of "rents". "Rents" are payments to factors
of production in excess of what they can earn in their best alternative
use. Since capital in each industry is specific to that industry, the incomes
of both types of capital can be thought of as rents. In a sense, the payments
to labor can also be thought of as "rents." For while the supply of labor
to each industry is not absolutely fixed, the total supply of labor to both
industries is fixed, and the supply of labor to any one industry is less than
infinitely elastic. In fact, the supply curve of labor facing the X industry
is precisely the VMPLZ curve looked at from the origin Ox. It is because
this supply curve is positively sloped that an increase in the demand for
labor in X cannot be absorbed without an increase in the wage rate.
II. Substitutability, Intensity, and the Magnitude of Income Changes
In the model of the preceding section, the direction of factor income
changes is completely determined by the assumption of specific capital
and mobile labor. The magnitudes of factor income changes, however,
depend on the substitutability between labor and capital in the two industries
and on the intensities with which the two factors are used in the
two industries. In this section, we will examine the magnitude of the
factor income change, first for labor, then for the two specific types of
capital, and finally for capital as a whole.
A. The Income of Labor
A formal expression for the change in the equilibrium wage rate may
be obtained by using the labor-market equilibrium condition5
Lk(wIPx, Kx) + L' (w, Kz) = L, (4)
5 An alternative approach to deriving a number of the results discussed in this section
is given inJones (1971).
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II96 JOURNAL OF POLITICAL ECONOMY
where Ldk and Ld are the labor-demand functions for the two industries
(the inverse of the VMPL functions). Differentiating equation (4),
holding Kx and Kz constant, we obtain
W = LXSX x (5)
XLX4X + ALZ4Z
where w dw/w, Px dPx!Px,6 and XLi is the fraction of the labor
force employed in industry i, and (i is the elasticity of demand for labor
in industry i. The magnitude ij, which is defined in (5), is the elasticity
of the wage rate with respect to the relative price of X. By making use
of the fact that the elasticity of demand for labor in each industry can
be written as
(6)
- 0Li
where a, is the elasticity of substitution betwee
industry i, and OLi is the distributive share of labor in the value of output
in industry i, the elasticity q may be rewritten as7
XLX ( OLX( X (7)
LX ( ax) + ;tLZ (1 )
The result (6) shows the importance of factor substitution and factor
intensity (as measured by distributional shares) for the responsiveness of
the wage rate to changes in Px. Holding the A's and 0's constant, when
ax is large and az is small, the behavior of the wage rate follows very
closely the behavior of Px. Geometrically, the reason for this is that the
VMPLX curve is very flat, while the VMPLz curve is very steep; vertical
shifts in the VMPLX curve, therefore, result in virtually equal changes
in the equilibrium wage rate. The same result obtains when OLX is large
and OLZ is small, and for the same reason. Factor substitutability and
factor intensity affect the responsiveness of the wage rate in the same way
because both have similar effects on the elasticities of demand for labor
in the two industries. From equation (5) it is apparent that these
elasticities are the determinants of the elasticity of the wage rate with
respect to Px.
6 We will use a caret to indicate the operation of taking a percentage change.
7 I am indebted to Carlos Rodriguez for suggesting the rewriting of eq. (5) in the form
of eq. (7).
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TARIFFS AND INCOME II97
B. The Income of Specific Capital
The income of capital in each industry is determined as a residual after
payments to labor:
YKX = PxX - wLx; YKZ = Z - wLZ. (8)
By differentiating these equations, making use of the fact that the wage
rate is equal to the value of the marginal product of labor in each industry,
and expressing the results in elasticity form, it follows that
YKX = (1 - OLXn)PX) (9)
YKZ K (OLZ).PX (1 0)
where OKX YKX/PXX = 1
slight asymmetry between (9) and (10) arises because Z has been taken
as the numeraire.
The results in equations (9) and (10) demonstrate the importance of
factor intensities and, indirectly, of factor substitutability for the magnitudes
of YKX and YKZ. The degree of substitutability between labor and
capital in the two industries affects these results through its influence on
q. From (7) it follows that an increase in ax or a decrease in az will
decrease the absolute value 5Kx and increase the absolute value of YKZ'
The essential symmetry of this result may be seen more clearly when it
is restated as follows: the greater the elasticity of substitution between
labor and capital in a given industry, relative to what it is in the other
industry, the more closely the income of labor and the income of capital
in that industry mirror the behavior of the price of that industry's output.
When ax is relatively large, both w/Px and YKXA!X tend to be close to
unity.
The value of il can be thought of as determining the degree of "effective
protection" which is afforded to the two types of specific capital.
From the viewpoint of the owners of capital, labor is purchased input,
just as material inputs would be purchased inputs if intermediate goods
were used in production. If the price of the purchased input (i.e., the
wage rate) were to remain constant when Px rises, then the degree of
"effective protection" afforded to capital in X (as measured by YKX)
would equal PX/OKX. The fact that the wage rate rises when P. rises
means that the degree of "effective protection" which is afforded to
capital in X is smaller than PX/OKX by the amount (OLX/OKX)W. Fro
the standpoint of the owners of capital in Z, the increase in the wage
rate which is induced by an increase in Px means that capital in Z
suffers from "negative effective protection" to the extent of (OLZ/OKZ) iW
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I i98 JOURNAL OF POLITICAL ECONOMY
The importance of factor intensities is also apparent in equations (9)
and (10). The inverse of capital's share in each industry determines the
"leverage" of that type of capital with respect to changes in relative
commodity prices. When capital's share is unity, the income of capital
moves in proportion with the price of its output. As capital's share
decreases, the percentage change in the income of capital increases with
the inverse of capital's share.
Formally, differentiating (9) and (10) with respect to OKx and OZ
holding tj constant, we obtain
dYKx = -( I (11)
dOKX (OKX)2
dif~~z IUP. (12)
dOKZ (O xZ) 2
It follows that the greater the intensity of capital in an industry, the more
closely the income of that capital mirrors the price of its output (e.g.,
the greater OtKX the closer is YKXiPX to unity). On the other hand, th
leverage effect says that the smaller the intensity of capital in a particular
industry, the more strongly the income of that capital responds the
price of its output (e.g., the smaller OKX' the larger is -kKx/Px). Howev
both of these conclusions may be reversed if the indirect effects of changes
in factor intensities on the value of tj (holding ax and uz constant) are
incorporated into the results (11) and (12).
C. The Income of Capital as a Whole
The question of what happens to the income of capital as a whole when
Px rises is likely to be interesting if ownership of the two types of cap
is widely diversified within the capital-holding class. Diversification is
to be expected if the claims to the ownership of the two types of capital
are fairly easily marketable. In such a circumstance, the negative
correlation between the incomes of the two types of capital which will
be produced by relative price changes will provide a strong incentive to
portfolio diversification and, hence, lead the capital-holding class to be
more concerned with the income of capital as a whole rather than with
the income of either specific type of capital.
The income of capital as a whole, YK, is given by
YK = Y-wL = (PXX + Z) - wL. (13)
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TARIFFS AND INCOME I I99
If we differentiate this equation, making use of the fact that dY = XdPX,
and express the result in elasticity form, it follows that
Tk (Y OLD)
(14)
= (:x OL-1)PX)
OK
where OK YKIY, OL YL1Y, and flx PxX/Y. From equation (14)
it is apparent that the income of capital as a whole may either rise or
fall as a result of an increase in Px. A decline is likely when the aggreg
share of labor, OL, and the elasticity of the wage rate, I, are large, and
when the share of X in the value of total output is small.
The second line of equation (14) is identical to the result given in
equation (9) for the value of STKX, except that the fraction f3x has
the number 1. As in the case of YKX, the inverse of OK determines the
leverage of capital as a whole with respect to changes in PX, and the
value of t determines the degree of effective protection which is afforded
to capital as a whole. The importance of the elasticities of substitution
and distributional shares within industries for the value of 5K is apparent
from the roles which these parameters play in the determination of Ij.
III. Capital as a Quasi-fixed Factor
The analysis of the last two sections can be given an added dimension by
viewing capital as a quasi-fixed factor.8 In the short run, each unit of
capital is specific to the industry in which it is engaged. The short-run
effects of a change in relative commodity prices are exactly as described
in the last two sections. Over time, however, capital can move from one
industry to another in search of its highest reward. Long-run equilibrium
requires that the distribution of the capital stock be such that the value
of the marginal product of capital is equal in the two industries.
A. The Effects of a Shift of Capital
Starting from an initial long-run equilibrium, an increase in Px leads to a
short-run equilibrium in which the value of the marginal product of
capital in X exceeds the value of the marginal product of capital in Z.
Capital moves from Z to X. To determine the effect on the wage rate
of a redistribution of the capital stock, differentiate the short-run equi-
8 For many applied problems, it is appropriate to think of labor, as well as capital, as
a quasi-fixed factor. See Oi (1962) on the subject of labor as a quasi-fixed factor.
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I200 JOURNAL OF POLITICAL ECONOMY
librium condition (4) with respect to Kx and Kz, impose dKz = - dKx,
and make use of the fact that linear homogeneity of the production
functions implies OL4/dKi = Li/Ki, to conclude that
w -= [(LxlKx) - (Lz(Kz)](dKx1L). (15)
Ax~ + AzL~K)]d~/)
Further, if we make use of (6), this result can be rewritten as
A - (OLX - OLZ)
iWffX~t- OLz) + XZ= (l - OL) (r/w) (dKx/L), (16)
where r is the rental rate on capital at the initial long-run equilibrium
(measured in terms of Z).'
Since the elasticities which appear in the denominators of equations
(15) and (16) are negative, it follows that the direction of the change in
the wage rate which results from the shift of an initial unit of capital
from Z to X depends only on the long-run relative factor intensities of
the two industries, as measured by either the factor ratios or by distributional
factor shares. As suggested by the Stolper-Samuelson theorem,
the wage rate rises if and only if X production is relatively labor intensive. 1 0
Note, however, that the magnitude of the change in the wage rate which
results from the shift of an initial unit of capital also depends on the
degree of substitutability between labor and capital in the two industries.
Geometrically, what is happening is that the shift of capital shifts both
the VMPLX curve and the VMPLz curve of figure 1 to the right. The
wage rate rises if and only if the horizontal shift of the VMPLX curve
exceeds the horizontal shift of the VMPLZ curve, at w = w1. The latter
condition is satisfied if and only if the Lk/KO is greater than LKzo."
B. Long-run Equilibrium and the Stolper-Samuelson Model
In the long run, capital is completely mobile between industries, and the
model presented in Section I reduces to the Stolper-Samuelson model in
which direction of change in factor incomes induced by an increase in
Px depends only on the (long-run) relative factor intensities of X and
9 Recall that we are considering small changes, starting at a position of initial long-run
equilibrium.
10 If X production is capital intensive in the long run, then a large increase in P
result in a short-run reversal of the relative factor proportions (which is not the same thing
as a "factor intensity reversal" in the Stolper-Samuelson model). In this event, the wage
rate will initially rise as capital begins to shift. However, once the original relationship
between factor proportions has been restored, the wage rate will start to fall and must
eventually fall below its previous long-run equilibrium value.
" From linear homogeneity of the two production functions, it follows that the
horizontal shift of the VMPL curve which results from the shift of one unit of capital
is proportional to the labor-capital ratios in the respective industries.
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TARIFFS AND INCOME I20I
The factor that is used relatively intensively in the production of X gains
in terms of both goods, and the other factor loses in terms of both goods.
Further, from Jones's results it is also known that, at least for small
increases in PX, the magnitude of factor income changes in the StolperSamuelson
model depends only on factor intensities.12
Formally, differentiating the zero-profit restrictions for the two industries
(which requires that the weighted sums of factor prices equal
the respective output prices, where the weights are the amounts of labor
and capital used to produce a unit of output) and expressing the results
in terms of percentage changes, it follows that
OLXW + OKX' = Px) (17)
OLZW + OKZr = 0- (18)
Solving for wz and r yields
A = OKZ J9
OLX OLZ
A -OLZ
r= P (20)
0LX - OLZ
These results reveal great differences among the parameters that are
important for determining the direction and magnitude of factor income
changes in the long run, after redistribution of the capital stock is complete;
and those that are relevant in the short run, in which capital is
assumed to be fixed; or during the period of adjustment of the capital
stock. In the short run, the direction of factor income changes is wholly
determined by the assumption that labor is mobile while capital is immobile:
labor gains in terms of Z and loses in terms of X when Px rises, while
capital in X gains in terms of both goods and capital in Z loses in terms
of both goods. The magnitude of short-run changes in factor incomes
depends on the degree of substitutability between capital and labor in
the two industries and on the factor intensities in the two industries.
During the period of adjustment, directions of income changes depend
only on factor intensities, but magnitudes also depend on substitutability.
In the long run, the direction of factor income changes depends only on
the difference in factor intensities between the two industries, OLX - OLZ)
and the magnitudes of factor income changes are independent of the
degree of substitutability between capital and labor in either industry. 13
Further, the Stolper-Samuelson model, which is relevant for long-run
12 See Jones (1965) for a more complete explanation of the derivation of the resul
discussed in this paragraph.
13 This is apparent from the fact that the elasticities of substitution do not enter into
(19) and (20). These results are unaffected by assuming a fixed-coefficients technology
for which the elasticity of substitution in each industry is zero.
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I202 JOURNAL OF POLITICAL ECONOMY
analysis, has a "knife edge" property which has no counterpart in the
short run. From (19) and (20) it follows that for a given value of Px t
magnitude of the implied factor imcome changes becomes very large as
the factor intensities of the two industries come close together. Thus,
capital gains from an increase in Px provided that X is relatively capital
intensive, but capital gains the most when the intensity differential is the
smallest.
Conclusion: The Conflict between Short-Run and Long-Run
Interests
These differences between the determinants of short-run and long-run
changes in factor incomes imply a conflict between factor owners' shortrun
and long-run interests with respect to commodity prices. Consider
any policy which results in an increase in Px. If X production is relatively
capital intensive, then laborers gain in the short run in terms of X but
lose in the long run in terms of both goods, and the owners of capital
initially employed in Z lose in the short run in terms of both goods but
gain in the long run in terms of both goods. On the other hand, if X
production is relatively labor intensive, then, even though capital initially
employed in X gains in terms of both goods in the short run, it loses in
terms of both goods in the long run; and, even though labor loses in
terms of Xin the short-run, it gains in terms of both goods in the long run.
Hence, no matter what the factor intensities of the two industries, there
must be at least one factor whose long-run interest runs counter to its
short-run interest. Further, if the factor intensities of the two industries
are similar, then, in the long run, large changes in factor incomes will
be required to accommodate small changes in commodity prices. Not
only will some factor's short-run interest differ from its long-run interest,
but it will differ a great deal.
Appendix
Generalization of the Results of Section II to an N Commodity,
N + 1 Factor Model
The results which were obtained for the simple, two-good, three-factor model in
Section II generalize in a straightforward way to a model with N commodities,
each produced with its own specific capital and mobile labor.'4 Equilibrium in
the distribution of the labor force requires that the value of the marginal product
of labor be equated across industries. If a government policy produces a vector of
commodity price changes (dPj, dP2,..., dPN), then, differentiating the equi-
14 The results presented in this Appendix can also be applied to the case where there
are many different firms, each with its specific capital, all producing two or more
commodities.
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TARIFFS AND INCOME I203
librium condition and expressing the result in the form of percentage changes,
it follows that
N
e= ,PA, (21)
1=1
where Pi = dPi/Pi and
_ LiLi_ _ ILI(l - OLi)]ai
-Z-1 ALJCLJ Zj=1 VtLi1(1 OLj)] (j2
where ALi -ilL, OLM wL/lP1X1, CLi is the elasticity of demand for lab
industry i, ai is the elasticity of substitution between labor and capital in ind
i, and Xi is the output of good i. Further, using the same procedures as in S
II, it follows that
YKi = (O) (pi OLi)), (23)
YK = (X) ( Y SL), (24)
where 0Ki - YKiPliXi, OK -YKIY OL YL1Y = WL/Y, Y - iN=1 PiX1,
ft1i =P1X1/Y, and
N
Y = E fi1P1 (25)
Inspection reveals that all of these results are direct analogues of the results for
the two-good case and reduce to the two-good results when N = 2.
References
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Marshall, A. Principles. 9th ed. London: Macmillan, 1961.
Mayer, W. "Short-Run and Long-Run Equilibrium for a Small Open Economy."
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