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BA 187 – International Trade. Specific Factors & Differential Gains from Trade. 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)

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ba 187 international trade

BA 187 – International Trade

Specific Factors & Differential Gains from Trade

specific factors production
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

factor endowments of leading industrial countries of world total 1980
Factor Endowments of Leading Industrial Countries,% of World Total 1980

Source: Mutti & Morici,Changing Patterns in US Industrial Activity & Comparative Advantage (1983)

production function
Production Function

MP of Labor,

MPLX

Output, X

X = QX (KX, LX )

MPLX

Labor Input LX

Labor Input LX

constructing nation s ppf
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.
slide6

Y = QY(KY, LY)

3

1

QY

2

PPF

LY

L

QX

LX

L

X = QX(KX, LX)

Specific Factors & A Country’s PPF

Y

Labor in

Good Y, LY

X

Labor in Good X, LX

pattern of trade
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.
patterns of trade export import ratios in leading industrial countries 1979
Patterns of TradeExport/Import Ratios in Leading Industrial Countries (1979)

Source: Mutti & Morici,Changing Patterns in US Industrial Activity & Comparative Advantage (1983)

determining prod n equilibrium
Determining Prod’n Equilibrium
  • Equilibrium concentrates on mobile factor, Labor.
  • Under perfect competition, labor earns its value marginal product:

wi = VMPi = PiMPL,ii = 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.
slide11

w

PYMPl,Y

PXMPl,X

LX

LY

OY

OX

Equilibrium for Mobile Factor

Wage Rate, wX

Wage Rate, wY

L

properties of equilibrium
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.
price changes equilibrium
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 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.
slide15

Equal % Change in both prices implies

no effect on real variables.

w’

VMP’Y

VMP’X

Effect of an Increase in Price Level

Wage Rate, w

Wage Rate, w

w

VMPY

VMPX

slide16

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 .

P’XMPLX

w’

L’Y

L’X

Effect of a Change in Relative Price

Wage Rate, w

Wage Rate, w

PXMPLX

w

PYMPLY

LY

LX

commodity factor prices
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.
relative demand supply
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.
slide19

RSForeign

RSWorld

RSHome

(PX/PY)F

(PX/PY)World

(PX/PY)H

Relative Supply & Specific Factors

Relative Price of X

PX/PY

RDWorld

Relative Quantity of X

(qX+ q*X)/(qY + q*Y)

growth in factor endowments
Growth in Factor Endowments

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

Source: Various World Bank, ILO pubs.

slide22

PPF1

X =

Q1X(K1X, LX)

Growth in Specific Factor & PPF

Y

Y = QY(KY , LY)

QY

1

PPF0

LY

L

QX

Labor in

Good Y, LY

X

LX

L

X =

Q0X(K0X, LX)

Labor in Good X, LX

slide23

VMP’X

w’

L’X

Growth in Good X Specific Capital

Wage Rate, w

Wage Rate, w

VMPX

w

VMPY

LX

slide25

PPF1

Growth in Mobile Factor & PPF

Y

Y = QY(KY, LY)

QY

1

PPF0

LY

L

QX

Labor in

Good Y, LY

X

LX

L

X =

QX(K0, LX)

Labor in Good X, LX

slide26

Wage Rate, w

VMPY

VMPY

w

w’

Growth in Mobile Factor, Labor

Wage Rate, w

VMPX

growth in specific factor model
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.