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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:Technology:X = FX(KX, LX) and Y = FY(KY, LY)

Subject to: L = LX + LY , KX = K0X , KY = K0

Y

Returns: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

CountryPhysical Capital

R&D Scientists

Skilled Labor

Semi-skilled 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

X = QX (KX, LX )

MPLX

Labor Input LX

Output, X

Labor Input LX

MP of Labor, MPLX

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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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PPF

L

L

QY

QX

1

X

LX

LY

X = QX(KX, LX)

YY = QY(KY, LY)3

2

Labor in Good X, LX

Labor inGood Y, LY

Specific Factors & A Country’s PPF

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Pattern of Trade RESULT: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

Intensive1.521.52 5.675.67 2.402.40 1.381.38 1.391.39 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

0.380.38 1.04 0.59 0.86 0.710.71 0.200.20

Primary Products

0.55 0.040.04 0.290.29 0.520.52 0.81 2.212.21

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

Equilibrium concentrates on mobile factor, Labor. Under perfect competition, labor earns its value marginal

product:

wwii = VMP = VMPii = P = PiiMPMPL,iL,i i = industry i

Labor can move to its highest value industry, so in equilibrium must have:

wwXX = P = PXXMPMPL,XL,X = P = PYYMPMPL,YL,Y = w = wYY

Labor in both industries must equal labor endowment.

LLXX + L + LYY = L = 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

L

PXMPl,X

OX

PYMPl,Y

OY

w

LYLX

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Properties of Equilibrium Mobile factor: LaborMobile factor: Labor

– Wage rate equal in both industries, given relative prices.

PPXXMPMPL,XL,X = P = PYYMPMPL,YL,Y = w = w

– Implies that prod’n point will be point on PPF tangent to relative price line. --MPMPL,XL,X /MP /MPL,YL,Y = -P = -PYY//PPXX

Specific Factors: Capital KSpecific Factors: Capital KXX, K, KYY – 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.

Equal Proportional ChangeEqual 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 ChangeRelative 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

VMPXVMPY

VMP’Y VMP’X

w

w’

Equal % Change in both prices impliesno effect on real variables.

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Effect of a Change in Relative Price

Wage Rate, w Wage Rate, w

PXMPLX

PYMPLY

LX

P’XMPLX

w’w

LY

L’X

1. LX up, implies return to KX up.

L’Y

2. LY down, implies return to KY down.3. w up but less than PX while PY constant. Effect on real wage thus uncertain .

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Commodity & Factor Prices RESULT: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 increases the export good’s relative price compared to that in autarkyrelative 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

largerlarger 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

RDWorld

RSWorld

(PX/PY)World

(qX+ q*X)/(qY + q*Y)Relative Quantity of X

PX/PY

Relative Price of X

(PX/PY)F

RSForeign

RSHome

(PX/PY)H

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Growth in Factor EndowmentsCountry 1966 1985 % Change

United StatesUnited States

Capital $785,933 $1,020,600 29.9%

Labor 76,595 107,150 39.9

Land ---- 742,500 ----

JapanJapan

Capital $165,976 $438,631 164.3

Labor 49,419 58,070 17.5

Land ---- 31,396 ----

MexicoMexico

Capital $21,639 $72,753 236.2

Labor 12,844 22,066 71.8

Land ---- 176,100 ----

Source: Various World Bank, ILO pubs.

Capital in millions 1966$, Labor in ’000’s of persons, Land in ‘000’s hectares

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Effects of Growth in a Specific Factor

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L

L

QY

QX

1

X

LX

LY

PPF0

X = Q0

X(K0X, LX)

YY = QY(KY , LY)

Labor in Good X, LX

Labor inGood Y, LY

Growth in Specific Factor & PPF

PPF1

X = Q1

X(K1X, LX)

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Growth in Good X Specific Capital

Wage Rate, w Wage Rate, w

VMPX

VMPY

w

VMP’X

w’

L’X

LX

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Effects of Growth in the Mobile Factor

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L

L

QY

QX

1

X

LX

LY

PPF0

X = QX(K0, LX)

YY = QY(KY, LY)

Labor in Good X, LX

Labor inGood Y, LY

Growth in Mobile Factor & PPF

PPF1

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Growth in Mobile Factor, Labor

Wage Rate, w

VMPX

Wage Rate, w

VMPY

VMPY

w

w’

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Growth in Specific Factor Model RESULT 1: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: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.