1. BA 187 International Trade
Problem Set #3:
Specific Factor & Hecksher-Ohlin Models of Trade

2. Q 1. - Labor as the Specific Factor
Assume two goods, X and Y. Capital, K, can be used to produce either good, so Capital is the Mobile Factor. Require KX + KY = K0
Labor comes in two varieties, skilled labor LX, and unskilled labor LY. Endowment of each is fixed at L0X and L0Y. Labor is specific factor.
Prod’n function for each good is X = FX(KX, LX) and Y = FY(KY, LY)
Fig. 1.1 illustrates how the constraint on capital and the two prod’n functions along with the endowment of each type of labor determines the PPF for the country.
Fig 1.2 shows how capital is allocated between the two goods.
Fig. 1.2 also shows the effects of opening up trade:
Assume X is the export good, then PX rises with opening of trade.
Shifts out VMPK,X which raises return on capital.
More capital in Good X, less capital in Good Y.
Wage for skilled labor LX rises, wage for unskilled labor LY falls, change in real return on capital K uncertain.

3. Fig. 1.1 – Prod’n Functions & the PPFY
Y = QY(KY , L0Y) QY
PPF0 KY K QX
Capital in
Good Y, KY X KX K
X =
Q0X(KX, L0X)
Capital in Good X, KX

4. Fig. 1.2 – Effects of Trade r’ r Return on Capital, r
P’XMPK X
PXMPK X r’
K’X r
VMPK Y
Capital KX

5. Analysis on previous slides makes the following results clear:
1. Which Workers of the World Unite? “Free trade makes allies of skilled labor in developed countries and unskilled labor in developing countries. Free trade also makes allies of unskilled labor in developed countries and skilled labor in developing countries.”
Analysis on previous slides makes the following results clear:
Opening up trade raises relative price of export good, X, in the Home country. Raises relative price of good Y in Foreign. (both relative to initial autarky relative prices).
Wage for Skilled labor LHX in Home rise and wages of Unskilled labor LFY in Foreign rise relative to autarky.
Wage for Unskilled labor LHY in Home fall and wages of Skilled labor LFX in Foreign fall relative to autarky.
Effect on return to capital in both Home and Foreign is uncertain relative to autarky.
Thus LHX and LFY are allies united in favor of free trade while LHY and LFX are allies in favor united against free trade. Capital is likely indifferent in both countries.

6. Opening economies up to trade equalizes relative prices.
2. Strange Bedfellows or the End of History? “Free trade makes allies of capitalists in developed countries and labor in developing countries. Free trade also makes allies of labor in developed countries and capital in developing countries.”
This is a straight-forward application of the results we developed in class. See Fig. 2.1 & 2.2 which follow.
Opening economies up to trade equalizes relative prices.
Developing Country (Labor Abundant)
Relative price of X rises which leads to rise in (w/r) over autarky.
Labor gains from free trade, capital loses
Developed Country (Capital Abundant)
Relative price of X falls which leads to fall in (w/r) over autarky.
Labor loses from free trade, capital gains.
The statement is true but it is neither the end of history nor strange bedfellows. Free trade simply benefits the abundant factor and harms the scarce factor.

7. Fig. 2.1 – Trade & Relative Prices
Relative Price of X
(PX/PY)F
RSForeign
PX/PY
RSWorld
(PX/PY)World
RSHome
(PX/PY)H
RDWorld
Relative Quantity of X
(qX+ q*X)/(qY + q*Y)

8. Fig. 2.2 - Relative Factor & Product Prices
Wage-rental ratio,
w/r
Good X
Stolper-
Samuelson SS
Good Y
PX/ PY
K/L

9. 3. And Speaking of Exploitation… “Trade exploits a country and makes it worse off if its workers receive much lower wages than workers in other countries.”
The Stolper-Samuelson result demonstrates the double fallacy behind this statement.
Opening up to trade results in a mutual gain to both countries so no “exploitation” is occurring at all.
In addition, labor-abundant countries begin with lower wages than capital-abundant countries. Stolper-Samuelson argues that free trade should actually increase the wages of workers in labor-abundant countries.
Hence the statement is incorrect on two counts. Free trade is actually abundant labor’s ally in achieving higher wages.

10. In H-O model this statement is true.
4. Free Trade as an Immigration Policy Too? “Trade in goods and services makes movements in factors of production unnecessary.”
In H-O model this statement is true.
Differences in relative factor endowments, combined with goods with different factor intensities, produce PPF’s that provide mutual gains from trade.
Trade equalizes relative prices of goods, which in turn equalizes relative factor prices across countries.
If instead factors of production move to equalize relative factor prices, the result will be equal relative factor endowments across countries, which produces equivalent PPF’s.
Trade is irrelevant because equivalent PPF’s produce identical relative goods prices in autarky under the H-O assumptions.