Capital-Intensity Hypothesis and Factor Price Equalization Theorem:
Intriguing Relationship?
By Hiroshi Ohta,
SIPEC, Aoyama Gakuin University
Prepared for RSIJ Annual Conference atTokushima University, October 14, 2013
ABSTRACT
Predicated upon a 2x2x2 model of general equilibrium, this paper shows conditions under which
the so-called factor price equalization theorem may not hold. Consider a developing nation witha strong propensity to save and accumulate capital on one hand and a developed country that canafford specializing in consumption on the other hand. If the consumption good sector is more
capital-intensive than the investment sector, then free trade can lower the developing nation’s
wage rate while increasing the developed nation’s wage rate. The assumed conditions are all
empirically plausible. And if the outcome sounds surprising, it deserves theoretical scrutiny.
Key Words:
2x2x2 general equilibrium, capital intensity, factor price equalization, trade, capital-rich versus-poor countries

Correspondences to:ohta@sipeb.aoyama.ac.jp0Capital-Intensity Hypothesis and Factor Price Equalization Theorem:
Intriguing Relationship?
Introduction
The so-called factor price equalization theorem states that real factor incomes such as wage rates
tend to equalize among nations after trade, if not before trade. This well-known theorem in trade
theory may not hold water if the less well-known hypothesis on certain particular technologicalconditions holds true. This latter hypo is called in macro growth theory the capital-intensity
hypothesis. (E. g., R.M. Solow, 1956; Y Shinkai, 1960.) It assumes two sectors of production,and states that stable economic growth requires, though not necessarily, the consumption good
sector to be more capital intensive than the investment good sector. This condition has recently
been confirmed empirically by H. Takahashi, et. al. (2012) utilizing data from the IO tables of
the OECD countries, H. Kawano, et. al. (2009, 2012) within the confines of the 2-sector, 2-factor
model of applied general equilibrium.
This paper challenges the well-known factor price equalization theorem on the basis ofan empirically plausible condition, albeit less known, on capital intensities in consumption andinvestment sectors. To be shown in particular is that if a rich developed nation endowed withlarge capital and a poor developing country endowed with small capital trade their products, then
their real factor prices may tend to diverge rather than converge.
The crucial conditions required for such a startling outcome other than thecapital-intensity hypothesis aforementioned are that the developing nation being capital-poor has
a strong taste for investment goods, and the developed capital-rich nation happily specializes in
consumption. The poor stay hungry, and the rich foolish. Isn’t it cool and realistic?
Background
Almost a decade ago a trilateral round of international trade conferences was inaugurated inTokyo in March 2004, followed by the subsequent ones in Hong Kong and Taipei consecutively.
Since then I have kept revisiting my past contributions to this international venture of trilateralmonopoly in effect. In order to reveal certain moral scientific nature of the well-known
Stolper-Samuelson theorem and the related less well-known proposal to ‘bribe’ for free trade, myinitial paper assumed two identical countries, identically endowed with homogeneous labor andcapital (two factors) but with internationally different tastes. Pursuant to these basic assumptions
I presented a simple account of the Stolper-Samuelson theory in a simple 2x2x2 generalequilibrium framework. The next paper presented in Hong Kong in 2005 examined the orthodox1

HO model with the H.O. (H. Ohta’s, 2005) heretical ideas on taste differentials in addition toHO’s ideas on different endowments. The 2005 workshop in Hong Kong in turn inspired Ohta toponder on Ronald Jones and Roy Ruffin (2005; Ruffin & Jones, 2007) discussing their“technology transfer paradox” along with some other seeming paradoxes in trade theory in a
subsequent workshop in Taipei in 2006. Part of it has been further elaborated with Hiro
Nakagawa (2008). The more recent H. O. papers (2009, 2011, 2012) are getting increasingly
more directly focused on a bitter maxim of free trade that the Stolper-Samuelson theorem
revealed.
With these prior inquiries in the background the present paper goes beyond the static
model of general equilibrium of production and exchange by incorporating in it capital formationand economic growth. It shows conditions under which how factor prices, product prices, andsectoral factor intensities may be related to the stages of capital accumulation or economic
development. Given that the bitter maxim of free trade is an inconvenient truth despite the factor
price equalization theorem, we may have to reluctantly admit that the bitterness intensifies all themore if and when the rosy theorem is reversed.
In what follows Section 1 reviews the basic 2x2 general equilibrium model of twoclone nations with no growth, nor trade. The model for a representative clone country ispresented using just one CD parameter to represent both technology and taste. Section 2 in turnpresents a 2x2x2 by 1 CD parameter model of two contrasting nations with asymmetric national
tastes before and after trade to examine what impact free trade may have on factor prices as wellas commodity prices. We confirm the orthodox outcomes of free trade and the related
factor-price equalization theorem. Section 3 then introduces growth, asymmetric growth inparticular, to see what happens to factor prices between the trading nations. The question is if
factor price equalization will be achieved. The answer is no, we find. Moreover, we show thatfactor prices that may be equal before trade will necessarily diverge after trade. Section 4
concludes. Appendix replaces the CD with CES production functions to revisit previous analysis
of growth impact on factor prices, with a passing note on the present pension program.
Section 1. The 2x2 GE Model of Clone Economies before Asymmetric Growth and Trade
Consider an autarky economy endowed with fixed amounts of two factors, say, labor and capital.
For simplicity we further assume the same numbers of clone workers and capitalists who own
identical units of capital individually. Both capital and labor are normalized to be unity. These
factors of production are used to produce consumption goods and investment goods underconditions of constant returns to scale. For simplicity, though not needed, the production2

functions are assumed to be of Cobb-Douglas type:
The Consumption Good Sector: C = f(KC, LC) = KC LC(1)The Investment Good Sector: I = g(KI, LI) = KI(1)LI
where I stands for investment, C for consumption, and f( ), g( ) are production functions for C
and I, which are functions of capital and labor in Sectors C and I respectively. It is important tonote that  above represents ‘output elasticity’ of capital in the C sector and also ‘output
elasticity’ of labor in the sector I. This is a deliberate contrivance for analytical simplicity todifferentiate the two sectors’ methods of production by a single parameter , to be more fully
explained later.
Pursuant to these assumptions the following optimization problems and equilibrium
conditions are to be introduced.
Consumptive Optimum:
U1 (I, C)/p = U2(I, C)(1)

where U1 is one’s MU of the first good or investment I, U2 MU of the second good or
consumption, and p is the relative price of investment goods in terms of consumption goods
assumed as numeraire.
Individual Budget Constraints:
w = pIL + CL
r = pIK + CK,(2), (3)Productive Optimum:
w/r = f2/f1= g2/g1,(4), (5)where w is wage rate, r rent on capital, respectively in terms of consumption goods, f1 (or g1) ismarginal product of capital in the C sector (or I sector), f2 (= f(kI, 1)  kIf1(kI, 1)) = (kI) is
marginal product of labor in the I sector, which is a function of capital/labor ratio or capitalintensity in the I sector, and g2 (= g(kC, 1) – kCg1(kC, 1)) = (kC) is marginal product of labor in
the C sector, which is a function of capital/labor ratio or capital intensity in the C sector.
Factor Market Equilibrium:
KI + KC = 1(6)

LI + LC = 1(7)

Product Market Equilibrium:
I = f(KI, LI)(8)

C = g(KC, LC)(9)Walras’ Law:
pI + C = w + r(10)3

The following observations on the properties of the production functions are important.
1) When  = 1/2: The two production functions are identical.
2) When  > 1/2 ( < 1/2): The consumption sector C is capital intensive, and theinvestment sector I is labor intensive. (The I sector is capital intensive, and the C
sector is labor intensive.)3) The larger the parameter  (exceeding 1/2), the higher the capital intensity of thecapital-intensive C sector is, and the higher the labor intensity of the I sector bycomparison, and vice versa. [That is: The lower the  (below 1/2), the higher thelabor intensity of the labor-intensive C sector.]
Equi-MRTS (of L for K) for Optimal Resource Allocation
Focusing on autarky, the following optimization conditions are to be observed along a contract
curve, which is concave (when > 1/2) or convex (when  < 1/2).
(dKI/dLI) = ((1)/)(KI/LI) = (dKC/dLC) = (/(1))(KC/LC)
This combined with the conditions of a given endowment of L and K, which areassumed both to be unity, yields a unique relation between KC and LC (or KI and LI).

KC 

1
1- 2
1
) 1
( -1)(
LC(K = L = 1)

C

0
C

K

C

C

P

I

K

0

L

I

L

Figure 1. Given , Arbitrary LI Determines KI, Hence

Figure 1 illustrates an autarkic equilibrium, labeled ECCA, for a clone country CC, and it isstraightforward to plot the counterpart equilibrium for another clone country CI to take place on
both the conflict curve CC on the left and the production possibilities frontier on the right hand4

side of the Figure. Before trade the country CC produce and consume more consumption goods
than the CI do. It goes without saying that the workers in the CC, before trade, are poorer thantheir capitalist neighbors. Not only are the CC workers poorer than the CC capitalists, but also
they are poorer than the workers in the CI. The workers in the CI, by comparison, are richer thannot only their domestic capitalists, but also the CC workers abroad.
These observations are made on Figure 2 below by comparing a square point with atriangular point along the concave conflict curve on the left. Note in particular that wage rate
given by factor allocation identified at the triangular point must be strictly greater than unity andhence greater that at the square point, which is required to be strictly less than unity. Associatedwith this particular wage rate of unity is a circular point at which MRTS is required to be unity.
Not only wage rate or relative factor is required to be unity at this point, but also so is relative
product price identified at a circular point on the production possibility frontier on the right.
C

0

KC

CC

CC

IC
0

LC

IC

Figure 2 Alternative Resource Allocations andUnderlying the diagram above is a more formal 2-sector, 2-factor, 2-country model ofgeneral equilibrium of production, trade, and consumption. A simple 2x2x2 CGE representationof the model is readily available subject to the basic theoretical requirements such as variable
proportions and linear homogeneity to be demonstrated below in Section 2 more fully.
Section 2. 2x2x2 GE of Clone Economies with Hetero-National Tastes before/after Trade
Suppose that the two identically endowed countries have two sectors of production to produce
consumption goods (or a basket of both nuts and bananas) and investment goods (rather thanbananas) using the same technologies assumed above, i.e.,  = 2/3. Also assume that the one
nation is addicted to consumption having an exclusive taste for consumption and little or no taste
for investment. The other nation, by comparison, loves to invest, stay hungry and live on air.

5

Commodity Prices and Factor Prices Before Trade
With no trade, under conditions of autarky, the CI is unable to import the investment goods theyneed for growth, which is nonexistent abroad. The CC produces little or no investment goods forpossible export. Each country specializes in production (and consumption) of a single kind they
are addicted to. The upshot: the workers in the investment-addicted country CI become strictly
richer than in the consumption-addicted country CC. Figure 3 below illustrates these relations.
Compare points ECIA and ECCA, which show (w/r) in CI strictly higher than (w/r) in CC underautarky.1 To be more precise the following relations are to be observed: (w/r)CIA > 1 > (w/r)CIA.
k



k

E


E
p(=pI
p

kI=1

k

kC

kC

Figure 3. CP, FP, Sectoral Capital

Commodity Prices and Factor Prices after Trade
Figure 4, in turn, illustrates how factor prices equalize with free trade in the short run. The
vertical axis of the back-to-back diagram measures the relative factor prices FP = w/r, thehorizontal axis is partitioned to represent the relative commodity prices CP = pI/pC on the left
hand side and the capital intensities, either sectoral ki or aggregate k, on the right. Pursuant to theassumed extreme differences in national tastes, the 2-country autarky equilibrium points are
given as EI0 and EC0, respectively, at intersections of a vertical line on k = 1 and two lines kI andkC, representing sectoral MRTS as a function of sectoral capital intensity ki (i = I, C). Note thatthe line kC is flatter than kI by assumption A2-5. Some related notes are warranted below.
1) The country CC specializing in consumption allocates almost all resources to the
production of consumption goods. Hence their kI approaches kI=k=1. Their autarky equilibrium
point is accordingly given at EC0. Related to this is their low commodity prices CPs = pI/pC (or1Moreover, the workers of the investment-addicted CI are strictly richer than their capitalist
citizens while the capitalists of the consumption-addicted CC are richer than their workers.
6

high pC/pI) identified on a CPFP curve in the second quadrant, Figure 4.
2) The CI, by comparison, specializing in investment with little consumption finds its
autarky equilibrium at EI0, pointing to strictly higher FP (= w/r), and related CP (= pI/pC).
3) Both countries are endowed with the same identical amount of aggregate capital k =1. Nevertheless CI specializing in investment (labor-intensive sector) while CC in consumption(capital-intensive sector), the weighted average of capital intensities in CC must be strictly
higher than that in CI. The upshot differences in factor prices are reflected on the first quadrantby EI0 > EC0, and the second-quadrant commodity prices correspondingly by (pI/pC)I > (pI/pC)C.
Note that the obvious differences in CPs in the two countries provide apparent
incentives for them to trade. The question then is what happens to prices CPs and FPs. Given k =1, in the short run, trade will tend to equalize them all, as illustrated by two dotted arrows along
which the high prices before trade must fall and the low prices rise after trade.
k

=

k

 =

E

w



EC
p(=pI
p

kI=1

k

kC

kC

Figure 4. What Factor-Price Equalization after

Note as Figure 4 illustrates how factor prices tend to be equalized, nevertheless the richworkers in the investment-addicted country CI become poorer and the poor workers in the
consumption-specialized country CC richer after trade than before trade. See Ohta (2012). Thus
both the bitter part of the Stolper-Samuelson outcome of free trade and the factor priceequalization theorem are confirmed, … so far. We are now in position to proceed to the next
section to probe dynamic (or comparative static) conditions under which this seemingly robust
theorem on factor price equalization may collapse.
Section 3. Impact of Trade under Asymmetric Growth and Tastes upon Factor Prices
Despite the bitter outcomes of trade both nationals each as a nation are richer after trade, and the7CC can consume more consumption goods while the CI can invest more than they could before
trade. This implies that while the factor endowment in CC remains the same regardless of trade
the capital endowment in CI tends to increase over time, all the more after trade. As the CI
grows to be a developed economy, it can afford turning itself into a country specializing in
consumption. The ex-CI is now a developed country DCC. The ex-CC realizing no growth, bycomparison, may learn from the ex-CI to turn itself to a new developing country DCI.
What then would happen to factor prices if trade took place between these countries?
Would they tend to equalize between DCC and DCI? To answer this particular question we
restate formally the following basic assumptions/conditions of our requisite analysis.
A1) Two clone countries exist with divergent national tastes: the one addicted toconsumption, called DCC, and the other to saving and investment, called DCI.
A2) Each country is endowed with two factors of production, capital K and labor L, toproduce two kinds of goods, one for consumption and the other for investment: C and I.
A3) In both countries labor is owned by a given number of workers L, and capitalowned by a given number of capitalists K, in the same number. So, L=K=1. This, however, isbefore asymmetric growth. As ex-CI grows capital accumulated K* becomes distinctively higher
than in the ex-CC so that K* > K = 1 in the long run or asymmetric growth.
A4) Each country has two sectors of production: one for producing consumption goods
and the other investment goods. (Though not needed, the sectors of production are characterized
by the Cobb-Douglas technologies such that in the one sector, say consumption goods, output
elasticity of capital is , and that of labor (1–), while in the other sector the counterpart
elasticity are (1–) and , respectively, so that constant returns to scale prevail in all the sectors.)
A5) The consumption good sector is more capital-intensive than the investment good
sector. (This requires  > 1/2 in terms of the CD parameter assumed above.)
A6) The developing country is investment-oriented: producing investment goods
extensively with little consumption goods, therefore living on thin air. The poor stay hungry.
A7) The developed country, by comparison, having developed, is more consumptionthan investment-oriented. They specialize in consumption taking advantage of the accumulated
capital while producing little investment goods. The rich can afford staying foolish; they canafford specializing in consumption.
Further specify, for simplicity, the basic assumptions above A3) and A5) as follows.
A3)* The ex-CC’s capital outstanding remains to be Kx-CC = 1, while the ex-CI’scapital outstanding after accumulation is K*x-CI = 4.
A5)* Output elasticity of capital in the consumption sector  = 2/3.
8

These additional specifications of the Assumptions above are needed only for the sakeof yielding the initial conditions for autarky equilibrium for the two nations’ CPs and FPs underconsideration before trade as illustrated by Figure 5 below.
FP (CP

MRTS

FP

p

MRTS

 =

 =

=
CC

>1

kI

k

kC

k

Figure 5. Sectoral Capital Intensities ki’s, andNote that the differences in CPs in two countries provide apparent incentives for themto trade. The question then is what happens to prices CPs and FPs. However, remember thatgiven k = 1 for two clone countries trade tends to equalize them all, as illustrated by two dottedarrows, Figure 4 supra, along which the high prices must fall and the low prices rise after trade.
But in the long run they could diverge insofar as capital accumulation proceeds in the
CI where the workers may tend to resist opening their market in fear of their real wage declines
at least in the short run when k is fixed. But over time while the stagnant CC’s factor endowment
remains unchanged the CI’s capital tends to increase because they love to invest. Moreover, free
trade will accelerate their capital accumulation, thereby increasing their wages over time to suchan extent that their real wage will exceed the stagnant CC’s when capital accumulation proceeds
beyond k = 4, Figure 5. The growing CI’s real wages will also increase with increasing output ofinvestment goods to be exported by the stagnant CC to the growing CI, but will peak out when it
reaches  (=w/r) 2 in the figure. Thus, real wages of a growing economy can surpass those in thestagnant economy, all the more with trade, accelerating capital accumulation.
Further accumulation beyond k = 4 keeps price of investment goods increasing as theex-CI can now specialize in consumption on their production possibilities frontier that has kept
shifting outward with increasing slopes at the vertical consumption-good axis. They are now on
PPFDCC and capable of offering the entire amount of the consumption goods in exchange for the9maximum investment goods the ex-CC can produce along their PPFDCI that intersects with thehorizontal axis. The maximum wage DCImax that the DCI can earn by producing the investment
goods at EDCIP* is now strictly lower than the minimum DCCmin that the DCC earn byspecializing in consumption now at the left corner of PPFDCC with kDCI > 4. See Figure 6.
C
EDCC

PPFDCC:P*DCCmin > DCImax when
DCC

PPFDCI:EDCIP*:

I

Figure 6-1 Trade Can Cause Factor
FP (CPFP (CP

p

MRTS

MRTS



ED

ED

=
DCI

>

kI=1

kD

kI

kC

kDC

kC

Figure 6-2 Trade Can Cause Factor Price Diversions under

Underlying Figure 6 are assumptions A1) through A7) including two special-case assumptions
A3)* and A5)* imposed on A3) and A5). Figure 6-1, upper panel, depicts two contrastingproduction possibility frontiers PPFDCI and PPFDCC of the ex-developing (now developed)
country DCC and the ex-consumption-addicted (now hungry) country DCI, respectively. Noteinitially that asymmetric autarky equilibria are represented by EDCIP* and EDCCP* and related10equilibrium commodity prices of pDCC > pDCI.
Then two arrows show how trade may yield resource reallocations and relatedchanges in the commodity bundles produced and, of particular interest to the present inquiry, thefactor prices between the countries under consideration. In particular the rich DCC that now
prefers consumption to investment nevertheless had better produce less consumption goods andmore investment goods for export while the poor DCI that now prefers investment to
consumption should produce more consumption goods for export. Thus they move along theirown PPCs until when pDCC = pDCI is established. In this process toward equilibrium what
happens to factor prices within the trading countries is that they must necessarily diverge as
indicated by the dotted arrows in opposite directions.
Note also in this related vein that trade tends to lower the poor nation’s real wages
and increase, on the contrary, the wages of the rich nationals! An inconvenient truth it may be?
Or would it call for the Stolper-Samuelson proposal to ‘bribe’ for free trade, with no apology?
Section 4. Conclusions
A simple model of general equilibrium with trade by Ohta (2004, 5, 6) has been revisited toprobe the Stolper-Samuelson (SS) theorem and the related orthodoxy of the HO factor priceequalization theorem. We find that free trade may dis-equilibrate factor prices under certain
particular empirically plausible conditions of asymmetric international tastes among nations at
the outset of asymmetric growth, followed by non ad hoc reversal of national tastes upon
asymmetric growth. Taste reversal is likely to occur insofar as an ex-hungry, now rich nation canafford specializing in consumption while a stagnant nation with little prior saving realizes thatthey need to become hungry to take off for growth/development.
This conclusion, if surprising, can be readily confirmed by the departure point conditions,seemingly ad hoc but not in fact, that factor prices, say, real wages, happened to be equal in apoor developing country and a rich developed country under autarky, respectively. Within theconfines of our simple 2x2x2 GE model presented in Section 3, related Figures 4, 5, and 6, thisrequires capital stock of the developed country to be four times that of the developing country.
The assumed technological clones are represented by just one CD parameter , and moreover = 2/3. This last specification reflects our other related basic assumption that requires theconsumption sector to be more capital intensive than the investment sector.
This required condition is to be noted as crucial to our present inquiry, crucial for two
counts. First, our conclusion above crucially depends upon this seemingly unrealistic assumption.
Second, if this seemingly unrealistic assumption were in fact unrealistic, then our surprising11

conclusion must collapse. Fortunately, the seemingly unrealistic assumption is empiricallysupported, and hence crucial and relevant in the second sense. And our conclusion is valid.
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was presented at the Tokyo Workshop on  and  Topics in International Trade andFinance, March 15, 04 (Aoyama Gakuin University).
Jones, Ronald and Roy Ruffin (2005) “The Technology Transfer Paradox,” Presented
at City University of Hong Kong International Workshop on International Trade and Finance,
March 15, 2005.
Kawano, H., and H. Ohta (2012) “2×2×2 by 1 Cobb-Douglas Parameter Model ofGeneral Equilibrium with Trade” for Presentation for the KIER Workshop on Macroeconomics
and Economic Systems, Kyoto University, March 12, 2012.
Kawano, H., and H. Ohta (2008) “How Much More ‘Evil Bribery’ a la J. S.
Mill-Stolper-Samuelson Needed or ‘Prevented’ for Further Opening Trade?: Calibrating an
AGE model with Japan’s Food-Agricultural Sector,” Presented at the 45th Annual Meeting of
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SectionoftheRegional

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FutureUniversity-Hakodate.
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Mill J. S. (1825) “The Corn Laws,” Westminster Review 3, pp. 394-420. In J.M.
Robson, ed., Collected Works of John Stuart Mill, Vol. IV, “Essays on Economics andSociety,” pp. 45-70. University of Tronto Press and Routledge and Kegan Paul (1967),
London.
Ohta, H. (2012) “The Moral Scientific Nature of the Stolper-Samuelson Proposal to‘Bribe’ for Free Trade,” Positive and Normative Analysis in International Trade in Honour of
Hiroshi Ohta, Chapter 2, Palgrave Macmillan.
Ohta, H. (2011) “2x2x2 by 1 CD Model of Production, Distribution and Trade:
Revisiting the Stolper-Samuelson Theorem and Related Proposal to ‘Bribe’,” presented
at Hong Kong- Taipei-Tokyo Trade Conference, City University of Hong Kong, May 14, 2011.
Ohta, H. (2009) “Moral Scientific Aspects of the Stolper-Samuelson Proposal to‘Bribe’ for Free Trade,” presented at Tamkang University International Conference on Trade,12Industrial and Regional Economics, March 13-14, 2009, and Don-Hwa University, Departmentof Economics Seminar, March 20, 2009.
Ohta, H. and H. Nakagawa (2008) “On the ‘Technology Transfer’ Paradox and‘Worsening Terms of Trade’ Paradox,” Asia-Pacific Journal of Accounting and Economics, vol.
15, pp. 41-54.
Ohta, H. and H. Kawano (2008) “How Much Evil or Bribery a la J.S. Mill-StolperSamuelson Needed or ‘Prevented’ to Open Up?: Calibrating an AGE Model with Japan’s
Food-Agriculture Sector,” presented at Hong Kong- Taipei-Tokyo Trade Conference, City
University of Hong Kong, May 19, 2008.
Ohta, H. (2006) “On the ‘Worsening Terms of Trade’ and Related Paradoxes in Trade
Theory,” presented at Tamkang University International Workshop on International Trade andIndustrial Organization, Taipei, Taiwan, March 23, 2006
Ohta, H. (2005) “The Simplest Possible 2x2x2 CGE Diagranomics: Revisiting the HO,
S-S Othodoxies,” presented at City University Hong Kong International Workshop on
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Ohta, H. (2004) “The Stolper-Samuelson Theorem: Diagranomics Pedagogica,”
presented at the Tokyo Workshop on  and  Topics in international trade andFinance, March 15, 2004 (Aoyama Gakuin University).
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Appendix: What If Sectoral Elasticities of Substitution Are Different?
Following Jensen and Larsen (2004) we show below how different elasticity of
substitution parameters  in different production sectors are related to the convexity/concavity of
the contract curve in the factor endowment space, capital intensity k, relative factor price (=w/r), and commodity price p(=pI/pC). The Edgeworth box diagrams and back-to-back diagrams
can do the job. An interesting example case is when one sector’s  is large (>1) and the othersmall (<1). As capital accumulation proceeds with a rise in capital intensity k, we can show how
or why price in the elastic sector tends to rise initially, but followed by a decline eventually.
According as either ‘ C low and  I high’ or conversely ‘ C high and  I low’  tends to either
rise or decline as relative price changes along the PPF. Figure 7 below shows how.
I:



C>1
k
C:
k

o

kI

p(=p /pC)k

0C


k





k

I

0
Figure 7. Trade Impact on Capital Accumulation, Contract Curves, PP Sets, FPs, CPs

Figure 7 assumes C > 1, I < 1 and shows that under asymmetric capital accumulation factor
price equalization is impossible regardless of free trade.
141) Given different elasticities of substitution,  C > 1 and  I < 1, economic growth in terms ofincreasing capital endowments and related increases in capital intensity (from, say, k0 to k*
to k1) must expand the more capital-intensive sector more than does the lesscapital-intensive sector, be it the capital goods sector I or the consumption goods sector C.
2) Any particular sector, say, capital goods sector, may be capital intensive at an earlier stageof growth. But a continued growth must eventually reverse each sector’s factor intensity
insofar as the one elasticity of substitution is assumed small and the other large.
3) The relative wage rate  tends to increase monotonically with the aggregate capitalintensity, but the product prices, say, in the consumption sector C, that may also increase
with  initially (as does under the present parameter combinations:  C > 1,  I < 1) must
peak out eventually while  keeps increasing.
4) Opposite relations must hold for the other sector’s prices. Prices, say, in the capital goods
sector must decline initially as  increases, but the decreasing prices must bottom out
eventually and start rising as  keeps increasing with capital accumulation.
5) Short-Run (Given k) Results: Summary Proposition A
Wages may either rise or fall if and when any structural changes take place along a given
production possibilities frontier according as either the one sector’s elasticity is small andthe other large or oppositely large and small. Related to this is either a concave or convex
contract curve reflecting relevant differences in the method of production in two sectors.
6) Short-Run (Given k) Results: Summary Proposition B
When k is small enough a rise in real wages can be accompanied by a fall in a given
sector’s output and price, say, in the capital good sector if it is more capital intensive thanthe other sector (given  C > 1 and  I < 1).
7) Short-Run (Given k) Results: Summary Proposition C
When k becomes large enough and the consumption sector becomes more capital-intensive,given  C > 1 and  I < 1, then any further rise in relative wage rates must be accompanied
by a rise in output and price in the small elasticity of substitution sector, i.e., investment.
8) Long-Run Results A: Early Stage
Growth at an early stage requires lower real wages and higher capital good prices relative
to consumption goods in order to reallocate resources to promote the capital good sector.
9) Long-Run Results B: Intermediate Stage
Growth in terms of increasing k tends to raise consumer prices along with wage rates. The
prices that may have been decreased in the short run must start to rise as the PPF shifts out
with a particular skew, strictly steeper (and linear) than ever.
1510) Long-Run Results C: Mature Stage
However, consumer prices will eventually peak out as growth continues with rising wages,
consumer prices must start falling thereafter provided J large and I small. Otherwise, if

J small and I large, investment prices must start falling as wages increase, all the more if
production of consumption goods increases along the PPF. If preference for consumption isstrong enough, as in the Nuts Country in our example above, then capital accumulation
could come to a halt. This could be one underlying reason for the so-called capital intensity
hypothesis, which states that stable economic growth requires the consumption sector to be
more capital intensive.
We have seen above that commodity market equilibrium requires not only the rich national’s real
wages to decline, but also the poor wages to decline with free trade. This may appear as aresurging stumbling block to free trade, which could have engineered the world-wide sentiment
against the so-called irrational exuberance starting from stock-market, housing-market,
auto-market, and everything else, say, on American over-consumption?
If free trade is to be maintained should the poor workers adversely affected from free
trade in both countries be ‘bribed’ for Pareto improvement? But in this example, it would notequalize international wage gaps.
Note in this connection that we assumed identical workers equally endowed in bothcountries. If free trade of factors were introduced along with commodities, then factor prices
would surely equalize internationally. But they are likely to provoke the rich country’s richworkers to cry against free trade of not only commodities but also factors, lest workers fromabroad enter their labor market while the poor country’s rich capitalists would have incentives
for blocking capital inflow from abroad. Genuine factor price equalization for homogeneous
factors would then require free trade of both commodities and factors, and without bribing thatwould keep genuine factor price equalization from being fully achieved. Moreover, given even if
asymmetric tastes are assumed, capital accumulation thanks to the thrift country will enable bothnations welfare to increase over time. Furthermore welfare must increase with no gap ininternational factor prices inasmuch as there will be a single international capital/labor ratio thatwill keep increasing over time.
In a stationary economy the original capitalists may own capital and nothing else. The
original workers, by comparison, own labor and nothing else. As the economy starts to grow theoriginal capitalists remain to be capitalists, own capital, and nothing else. The original workers,
by comparison, now own both labor and capital insofar as their wages, even if paid in16

consumption goods, are saved for investment. If trade causes rent on capital to rise and wage rate
to fall, then the original capitalists would have no reason to complain. How about the workers?
They become the working capitalists. The capitalists do not work, but the working capitalists do.
So, income distribution becomes little or no stumbling block to free trade if and insofar
as individuals were equally gifted with both factors of production. The poor young generation
with little or no capital may have his day in the future. However, the poor old generation, even if
endowed with a lot of capital, are unable to work.
In a nutshell, free trade may become a stumbling block to the rich developed nation
more than it does to the poor developing nation, all the more if their rent on capital declines.
Diminishing income should be hard to those unable to work. Here lies, it seems to me, the raisond’etre for the present pay-as-you-go pension program, even if it is characterized as the so-called
2x4x8 rule, thus allegedly unfair or imposing unbearable burden to the future generation.

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