BA 187 International Trade
Homework #4:
Specific Factor & Hecksher-Ohlin
Models of Trade
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.
Fig. 1.1 – Prod’n Functions & the PPF
Y
Y = QY(KY , L0Y)
QY
PPF
0
K
KY
QX
Capital in
Good Y, KY
X
KX
K
Capital in Good X, KX
X=
Q0X(KX, L0X)
Fig. 1.2 – Effects of Trade
Return on Capital, r
Return on Capital, r
P’XMPK X
PXMPK X
r’
r
VMPK
Y
K’X
KX
Capital
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 folloowing 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.
2. True, False, or Uncertain?
“Import-oriented growth in the specific factor model is an undesirable
event from the point of view of the home country because it lowers our
well-being as a nation.”
• Import-oriented growth in the specific factor model can
only mean that the factor-specific to the import good has
increased.
• Good Y is the assumed import good, so KY has increased.
– In Fig 2.1, Prod’n function for Good Y shifts upwards.
– At any LY more of Good Y produced implies PPF shifts up in
direction of more Y.
• In Fig. 2-2 PPF shift leads to inward shift in Relative
Supply, RS , as more Good Y for any level of X.
– Terms of trade increases, leads economy to produce at Q .
• Import-biased growth increases home country well-being.
• Thus statement is FALSE.
Fig 2.1 - Growth in Import-Specific Factor
Y = QY(K1Y, LY)
Y
Y = QY(K0Y, LY)
L
PPF1
PPF0
LY
Labor in
Good Y, LY
X
LX
L
Labor in Good X, LX
X = QX(KX, LX)
Fig. 2.2 - Import-Biased Growth and Trade
Y PPF1
Relative Price of X
U1
PX/PY
U0
RS1
RS0
Q1
PPF0
Q0
(PX/PY)
1
(PX/PY)
0
X
RD0
Relative Quantity of X
(qX + q*X )/(qY + q*Y )
3. 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. 3.1 which follows.
• 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.
Fig. 3.1 - Relative Factor & Product Prices
Wage-rental ratio,
w/r
StolperSamuelson
Good X
SS
Good Y
PX/ PY
K/L
4. 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.”
•
1.
2.
•
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. StolperSamuelson 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.
Relative Supply & Specific Factors
Relative Price of X
PX/PY
RSForeign
RSWorld
RSHome
(PX/PY)F
(PX/PY)World
(PX/PY)H
RDWorld
Relative Quantity of X
(qX+ q*X)/(qY + q*Y)