Transcript Principles of Macroeconomics

BA 187 – International Trade
Specific Factors & Differential
Gains from Trade
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Specific Factors & Production




Two countries, two goods (X and Y), and two factors of
prod’n, (labor, L & capital, K).
Labor can be used in producing X or Y (i.e. mobile factor)
Capital is specific to prod’n of one good, KX is capital
useful for producing X only. (i.e. specific or fixed factor)
Technology:
X = FX(KX, LX) and Y = FY(KY, LY)
Subject to: L = LX + LY , KX = K0X , KY = K0Y

Returns:
w = wage rate, rX = return to KX, rY = return to KY,
pX = PX/PY = relative price of Good X in terms of Y
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Factor Endowments of Leading Industrial
Countries, % of World Total 1980
Country
Physical
R&D
Capital Scientists
Skilled
Labor
Semiskilled
Labor
Unskilled
Labor
Arable
Land
All
Resources
U.S.
33.6%
50.7%
27.7%
19.1%
0.19%
29.3%
28.6%
Japan
15.5
23.0
8.7
11.5
0.25
0.8
11.2
Germany
7.7
10.0
6.9
5.5
0.08
1.1
7.2
France
7.5
6.0
6.0
3.9
0.06
2.6
6.0
U.K.
4.5
8.5
5.1
4.9
0.09
1.0
5.1
Canada
3.9
1.8
2.9
2.1
0.03
6.1
2.6
ROW
27.3
0.0
42.7
53.0
99.32
59.1
39.3
100.0%
100.0%
100.0%
100.0% 100.0%
100.0% 100.0%
Source: Mutti & Morici, Changing Patterns in US Industrial Activity & Comparative Advantage (1983)
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Production Function
MP of Labor,
MPLX
Output, X
X = QX (KX, LX )
MPLX
Labor Input LX
Labor Input LX
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Constructing Nation’s PPF

To construct nation’s PPF need to combine two
prod’n functions plus labor constraint.
– Use a “4-quadrant” diagram to relate the two prod’n
functions, the labor constraint, and the nation’s PPF.

Prod’n function for each good:
– depends on fixed amount of its specific capital
combined with varying quantity of labor.

Labor constraint is that sum of labor used by both
industries must equal total labor endowment.
– Increase labor in Good X implies equal decrease labor
in Good Y.
– Result is more Good X, less Good Y = nation’s PPF.
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Specific Factors & A Country’s PPF
Y
Y = QY(KY, LY)
3
1
QY
L
2
PPF
LY
QX
Labor in
Good Y, LY
X
LX
L
X = QX(KX, LX)
Labor in Good X, LX
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Pattern of Trade

RESULT: In the specific factors model, each country will
export the good with the absolutely abundant stock of
specific capital, assuming identical endowments of labor.
– If labor endowments differ, trade pattern depends on prod’n
functions and the relative stocks of the specific types of capital.

Straightforward to demonstrate this result using the
diagram on the previous slide.
–
–
–
–


Increase specific capital KX in Good X.
Prod’n function QX() shifts up.
More X produced with any given LX.
New PPF is skewed towards X, i.e. Nation should export X.
Can get same result by assuming nation possesses superior
technology for producing Good X with any level of labor.
Prod’n at point tangent to terms of trade line.
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Patterns of Trade
Export/Import Ratios in Leading Industrial Countries
(1979)
Product
U.S.
Japan
Germany
France
U.K.
Canada
Technology
Intensive
1.52
5.67
2.40
1.38
1.39
0.77
Services
1.47
0.73
0.80
1.32
1.19
0.50
Standardized
0.39
1.09
0.84
1.03
0.76
1.38
Labor
Intensive
0.38
1.04
0.59
0.86
0.71
0.20
Primary
Products
0.55
0.04
0.29
0.52
0.81
2.21
Source: Mutti & Morici, Changing Patterns in US Industrial Activity & Comparative Advantage (1983)
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Equilibrium in the
Specific Factor Model
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Determining Prod’n Equilibrium
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
Equilibrium concentrates on mobile factor, Labor.
Under perfect competition, labor earns its value marginal
product:
wi = VMPi = PiMPL,i i = industry i

Labor can move to its highest value industry, so in equilibrium
must have:
wX = PXMPL,X = PYMPL,Y = wY

Labor in both industries must equal labor endowment.
LX + LY = L

Combine VMP’s and total labor constraint on one diagram to
find equilibrium production.
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Equilibrium for Mobile Factor
Wage Rate, wX
Wage Rate, wY
w
PYMPl,Y
OX
PXMPl,X
LY
LX
OY
L
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Properties of Equilibrium

Mobile factor: Labor
– Wage rate equal in both industries, given relative prices.
PXMPL,X = PYMPL,Y = w
– Implies that prod’n point will be point on PPF tangent to
relative price line.
-MPL,X /MPL,Y = -PY/PX

Specific Factors: Capital KX, KY
– Return to specific capital in each good equals its VMP.
– VMP not equalized across specific capital types because of
lack of mobility between industries.
– Within an industry, the more labor employed, the higher
will be the MP of specific capital, and hence its return.
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Price Changes & Gains from Trade
in the Specific Factor Model
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Price Changes & Equilibrium

Concerned with changes in prices of X and Y.
– Any effects on equilibrium happen through adjustments in
market for labor, the mobile factor.
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Equal Proportional Change in Both PX and PY.
– Prices rise by same %, leads wages to rise same %.
– No change relative prices or labor across industries

Relative Change in Px and Py.
– Price of X alone rises by given %. Shifts VMPL,X up. Wage
rate up by smaller %. Real wage may rise or fall.
– Increase amount of labor in X, increases return to KX.
– Decrease amount of labor in Y, decreases return to KY.
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Effect of an Increase in Price Level
Wage Rate, w
Wage Rate, w
Equal % Change in both prices implies
no effect on real variables.
w’
VMP’Y
VMP’X
w
VMPY
VMPX
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Effect of a Change in Relative Price
1. LX up, implies return to KX up.
2. LY down, implies return to KY down.
3. w up but less than PX while PY constant.
Effect on real wage thus uncertain .
Wage Rate, w
Wage Rate, w
P’XMPLX
PXMPLX
w’
w
L’Y
PYMPLY
LY
LX
L’X
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Commodity & Factor Prices

RESULT: The increase in a good’s relative price benefits
the specific factor used in that industry, reduces the real
income of the other specific factor, and has an ambiguous
effect on the mobile factor.

This result has implications for who gains and loses from
opening trade.
Opening an economy to trade increases the export good’s
relative price compared to that in autarky.

– Export-specific capital benefits, Import-specific capital is hurt,
effect of real wage of labor is ambiguous.
– Provides a prediction of how groups will line up in political
debates regarding free trade or protectionist trade policies.
– Think steel, wood, and other primary products in the U.S.
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Relative Demand & Supply

Assuming identical tastes in both countries.
– Implies Relative Demand curve is the same for each.

Assuming differences in specific factor endowments.
– Home Country has more KX per worker than Foreign, while Foreign
has more KY per worker than Home.
– Relative Supply, QX/QY, at any given relative price PX/PY is thus
larger in Home than in Foreign.
– In autarky, result is relative price of X higher in Foreign than Home.

Opening trade between nation’s leads to World Relative
Supply Curve between RS of each nation in autarky.
– World RS curve intersects World RD curve at relative price of X
lower than Foreign but higher than Home.
– Trade equalizes relative price of X so that Home exports Good X and
Foreign exports Good Y.
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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)
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Growth in Factor Endowments
Country
1966
1985
% Change
Capital in millions 1966$, Labor in ’000’s of persons, Land in ‘000’s hectares
United States
Capital
$785,933
$1,020,600
29.9%
Labor
76,595
107,150
39.9
Land
---- 742,500 ----
Japan
Capital
$165,976
$438,631
164.3
Labor
49,419
58,070
17.5
Land
----
31,396
----
Mexico
Capital
$21,639
$72,753
236.2
Labor
12,844
22,066
71.8
Land
---- 176,100 ----
Source: Various World Bank, ILO pubs.
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Effects of Growth in a
Specific Factor
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Growth in Specific Factor & PPF
Y
Y = QY(KY , LY)
QY
1
PPF
0
L
LY
PPF
1
QX
Labor in
Good Y, LY
X
LX
L
Labor in Good X, LX
X=
Q0X(K0X, LX)
X=
Q1X(K1X, LX)
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Growth in Good X Specific Capital
Wage Rate, w
Wage Rate, w
VMP’X
VMPX
w’
w
VMPY
LX
L’X
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Effects of Growth in the
Mobile Factor
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Growth in Mobile Factor & PPF
Y
Y = QY(KY, LY)
QY
1
PPF
0
L
LY
PPF
1
QX
Labor in
Good Y, LY
X
LX
L
Labor in Good X, LX
X=
QX(K0, LX)
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Growth in Mobile Factor, Labor
Wage Rate, w
Wage Rate, w
VMPY
VMPX
VMPY
w
w’
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Growth in Specific Factor Model

RESULT 1: An increase in the endowment of a specific factor will
increase the output of the good using that factor and decrease the
output of the other good. Increases in the endowment of the mobile
factor will expand both outputs.

RESULT 2: At constant goods prices, an increase in the endowment of
a specific factor increases the returns to the mobile factor and lowers
real returns to the specific factors. An increase in the endowment of the
mobile factor will reduce its own real income and increase the real
returns to the specific factors.

These results have implications for who gains and loses from trade.
– Mobile factor, labor, will oppose easier immigration policies while owners
of specific capital will favor them.
– This should remind you of the recent debate over increasing the H-1 visa
quota for technical workers in the U.S.
– Provide predictions of how groups will line up in political debates
regarding free trade or protectionist trade policies.
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