1 BA 187 – International Trade Specific Factors & Differential Gains from Trade

2 Specific Factors & Production F Two countries, two goods (X and Y), and two factors of prod’n, (labor, L & capital, K). F Labor can be used in producing X or Y (i.e. mobile factor) F Capital is specific to prod’n of one good, K X is capital useful for producing X only. (i.e. specific or fixed factor) F Technology: X = F X (K X, L X ) and Y = F Y (K Y, L Y ) Subject to: L = L X + L Y, K X = K 0 X, K Y = K 0 Y F Returns: w = wage rate, r X = return to K X, r Y = return to K Y, p X = P X /P Y = relative price of Good X in terms of Y

3 Factor Endowments of Leading Industrial Countries, % of World Total 1980 Country Physical 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 Germany France U.K Canada ROW % Source: Mutti & Morici, Changing Patterns in US Industrial Activity & Comparative Advantage (1983)

4 Production Function X = Q X (K X, L X ) MPL X Labor Input L X Output, X Labor Input L X MP of Labor, MP LX

5 Constructing Nation’s PPF F 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. F Prod’n function for each good: –depends on fixed amount of its specific capital combined with varying quantity of labor. F 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.

6 PPF L L QYQY QXQX 1 X LXLX LYLY X = Q X (K X, L X ) Y Y = Q Y (K Y, L Y ) 3 2 Labor in Good X, L X Labor in Good Y, L Y Specific Factors & A Country’s PPF

7 Pattern of Trade F RESULT: F 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. F Straightforward to demonstrate this result using the diagram on the previous slide. –Increase specific capital K X in Good X. –Prod’n function Q X () shifts up. –More X produced with any given L X. –New PPF is skewed towards X, i.e. Nation should export X. F Can get same result by assuming nation possesses superior technology for producing Good X with any level of labor. F Prod’n at point tangent to terms of trade line.

8 Patterns of Trade Export/Import Ratios in Leading Industrial Countries (1979) ProductU.S.JapanGermanyFranceU.K.Canada Technology Intensive Services Standardized Labor Intensive Primary Products Source: Mutti & Morici, Changing Patterns in US Industrial Activity & Comparative Advantage (1983)

9 Equilibrium in the Specific Factor Model

10 Determining Prod’n Equilibrium F Equilibrium concentrates on mobile factor, Labor. F Under perfect competition, labor earns its value marginal product: w i = VMP i = P i MP L,i w i = VMP i = P i MP L,i i = industry i F Labor can move to its highest value industry, so in equilibrium must have: w X = P X MP L,X = P Y MP L,Y = w Y F Labor in both industries must equal labor endowment. L X + L Y = L F Combine VMP’s and total labor constraint on one diagram to find equilibrium production.

11 Equilibrium for Mobile Factor Wage Rate, w X Wage Rate, w Y L P X MP l,X OXOX P Y MP l,Y OYOY w LYLY LXLX

12 Properties of Equilibrium F Mobile factor: Labor –Wage rate equal in both industries, given relative prices. P X MP L,X = P Y MP L,Y = w -MP L,X /MP L,Y = -P Y /P X –Implies that prod’n point will be point on PPF tangent to relative price line. -MP L,X /MP L,Y = -P Y /P X F Specific Factors: Capital K X, K Y –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.

13 Price Changes & Gains from Trade in the Specific Factor Model

14 Price Changes & Equilibrium F Concerned with changes in prices of X and Y. –Any effects on equilibrium happen through adjustments in market for labor, the mobile factor. F Equal Proportional Change F Equal Proportional Change in Both P X and P Y. –Prices rise by same %, leads wages to rise same %. –No change relative prices or labor across industries F Relative Change F Relative Change in P x and P y. –Price of X alone rises by given %. Shifts VMP L,X up. Wage rate up by smaller %. Real wage may rise or fall. –Increase amount of labor in X, increases return to K X. –Decrease amount of labor in Y, decreases return to K Y.

15 Effect of an Increase in Price Level Wage Rate, w VMP X VMP Y VMP’ Y VMP’ X w w’ Equal % Change in both prices implies no effect on real variables.

16 Effect of a Change in Relative Price Wage Rate, w P X MP LX P Y MP LY LXLX P’ X MP LX w’ w LYLY L’ X 1. L X up, implies return to K X up. L’ Y 2. L Y down, implies return to K Y down. 3. w up but less than P X while P Y constant. Effect on real wage thus uncertain.

17 Commodity & Factor Prices F RESULT: F 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. F This result has implications for who gains and loses from opening trade. increases the export good’s relative price compared to that in autarky F 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.

18 Relative Demand & Supply F Assuming identical tastes in both countries. –Implies Relative Demand curve is the same for each. F Assuming differences in specific factor endowments. – Home Country has more K X per worker than Foreign, while Foreign has more K Y per worker than Home. larger –Relative Supply, Q X /Q Y, at any given relative price P X /P Y is thus larger in Home than in Foreign. –In autarky, result is relative price of X higher in Foreign than Home. F 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.

19 Relative Supply & Specific Factors RD World RS World (P X /P Y ) World (q X + q* X )/(q Y + q* Y ) Relative Quantity of X P X /P Y Relative Price of X (P X /P Y ) F RS Foreign RS Home (P X /P Y ) H

20 Growth in Factor Endowments Country % Change United States Capital$785,933$1,020, % Labor76,595107, Land , Japan Capital$165,976$438, Labor49,41958, Land----31, Mexico Capital$21,639$72, Labor12,84422, Land , Source: Various World Bank, ILO pubs. Capital in millions 1966$, Labor in ’000’s of persons, Land in ‘000’s hectares

21 Effects of Growth in a Specific Factor

22 L L QYQY QXQX 1 X LXLX LYLY PPF 0 X = Q 0 X (K 0 X, L X ) Y Y = Q Y (K Y, L Y ) Labor in Good X, L X Labor in Good Y, L Y Growth in Specific Factor & PPF PPF 1 X = Q 1 X (K 1 X, L X )

23 Growth in Good X Specific Capital Wage Rate, w VMP X VMP Y w VMP’ X w’ L’ X LXLX

24 Effects of Growth in the Mobile Factor

25 L L QYQY QXQX 1 X LXLX LYLY PPF 0 X = Q X (K 0, L X ) Y Y = Q Y (K Y, L Y ) Labor in Good X, L X Labor in Good Y, L Y Growth in Mobile Factor & PPF PPF 1

26 Growth in Mobile Factor, Labor Wage Rate, w VMP X Wage Rate, w VMP Y w w’

27 Growth in Specific Factor Model F RESULT 1: F 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. F RESULT 2: F 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. F 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.