2. 1 BA 187 – International Trade Hecksher-Ohlin Model & Relative Factor Endowments

3. 2 Hecksher-Ohlin Model Two countries, two goods, X and Y, and two factors of prod’n, labor, L and capital, K. (2 x 2 x 2 model) Technology identical between countries. Production functions for both goods exhibit constant returns to scale. factor intensity Each commodity has a different factor intensity, which are not affected by relative factor prices. Tastes and preferences identical between countries. Perfect competition in both industries and both countries. Factors are perfectly mobile within countries but perfectly immobile between countries. No transportation costs or tariffs or other barriers to trade.

4. 3 Production Functions, Isoquants, and Relative Factor Prices

5. 4 Production Theory Production Function Production Function – Q = F(K, L) –Shows amount of output produced for given inputs of capital & labor. –Assume exhibits constant returns to scale (CRS), diminishing marg. returns. Production Isoquant Production Isoquant – Q 0 = F(K, L) –Shows the various combination of capital & labor that can be used to produce a chosen level of output, Q 0. –Bowed shape result of diminishing marginal returns as substitute capital for labor to keep production level constant. Isocost Line & Production Equilibrium –Combination of K & L choose to produce any given level output Q depends on relative prices of capital and labor, i.e. w/r, the relative wage. –Isocost line shows all comb. of K & L with same total cost given w and r. –Firm will choose production point (K & L) which minimizes total cost for any desired level of output Q 0. With CRS prod’n function, these points fall on a straight line from origin. Slope of this line depends on relative wage vs. return on capital.

6. 5 Isoquants, Isocosts & Production Given (w/r) Labor, L Capital, K [K/L] Y labor-intensive 1. Good X is “ labor-intensive”. capital-intensive 2. Good Y is “ capital-intensive”. Relative Factor Price, (w/r) 0 Isocost line Isocost line shows all combinations of K & L with same cost given w and r. –Slope is relative factor price, w/r. 2X 0 X0X0 Isoquants Isoquants show all combinations of K & L that produce certain amount of Good X. [K/L] X Prod’n Points for Good X Prod’n Points for Good X where Isoquant tangent to Isocost Line. Assuming CRS so these points are on ray from origin. 2Y 0 Y0Y0 Can do same exercise for Good Y. Note that Labor- or Capital-intensity of a good is Determined by shape of Isoquants, i.e. prod’n.

7. 6 Factor Endowments and Factor Intensities

8. 7 Factor Intensities & Factor Abundance Factor Intensities Factor Intensities: (A property of production technologies) capital-intensive (K/L) Y > (K/L) X –A Good Y is said to be capital-intensive if the ratio of capital-labor in its production is higher than the ratio of that used to produce Good X, at any relative factor price ratio. i.e. (K/L) Y > (K/L) X. labor-intensive –In a two good world, if Good Y is capital-intensive then Good X will be labor-intensive, at any relative factor price ratio. Factor Abundance Factor Abundance: (A property of factor endowments) capital-abundant K/Llarger –Physical Units definition: A nation is capital-abundant if its capital/labor ratio (K/L) is larger than that of the other nation. capital-abundant w/rlarger –Relative Factor Price definition: A nation is capital-abundant if its ratio of wage rate for labor to rental price of capital (w/r) is larger than that of the other nation. –We assume these two def’ns are equivalent (although they aren’t exactly). H-O model combines both factor intensities of goods and relative factor abundance of nations to determine trade patterns.

9. 8 Relative Factor Costs & Intensities Relative Factor Price, (w/r) high low Given (w/r) “low” Labor, L Capital, K 2X 0 2Y 0 Y0Y0 X0X0 Relative Factor Price, (w/r) low [K/L] low Y [K/L] low X X0X0 2X 0 [K/L] high X 2Y 0 Y0Y0 [K/L] high Y labor-intensive 1. Good X is “ labor-intensive”. capital-intensive 2. Good Y is “ capital-intensive”. Labor, L Capital, K high Given (w/r) “high”

10. 9 Good XGood Y K/L Capital-Labor Ratio w/r Wage-rental ratio, Factor Prices and Input Choices Note from previous slide: 1. As (w/r) increases from “low” to “high”, K/L ratio used to produce Good X increases. The same is true for Good Y. 2. Implies there is an upward- sloping relation between relative factor price w/r and K/L used in production of each good. 3. Also, at any level of (w/r) Good Y always uses higher K/L in prod’n. Thus its relation is below that for Good X. (w/r) lo w (w/r) high

11. 10 Deriving a Nation’s PPF in the H-O Model

12. 11 Edgeworth Box – Joint Prod’n Labor, L Capital, K 2X 0 X0X0 [K/L] X [K/L] Y 2Y 0 Y0Y0 Labor, L Capital, K [K/L] Y 2Y 0 Y0Y0 Labor, L Capital, K [K/L] Y 2Y 0 Y0Y0 Labor, L Capital, K [K/L] Y 2Y 0 Y0Y0 Labor, L Capital, K [K/L] Y 2Y 0 Y0Y0 Labor, L Capital, K Labor, L Capital, K 2X 0 X0X0 [K/L] X

13. 12 [K/L] H Y Allocation of Factors to Goods Prod’n Labor, L 2X 2Y 1Y 1X Capital, K [K/L] H X [K/L] H Y Labor, L Capital, K OYOY OXOX [K/L] H Y OYOY Total Labor Total Capital

14. 13 Allocation of Factors & Nation’s PPF Labor, L Capital, K [K/L] H X OXOX [K/L] H Y OYOY LXLX LYLY KXKX KYKY 1. Box below shows allocation of capital and labor to each good, for a given w/r ratio. PPF 3. Varying w/r picks out different allocations and prod’n points, tracing out PPF. Y X 2. Implicit in this allocation are prod’n levels of both Y =Q Y (K Y, L Y ) and X =Q X (K X, L X ). B B

15. 14 Factor Endowments and Factor Intensities in the H-O Model of Trade

16. 15 Relative Factor Endowments Estimates for 1966 CountryCapital/Labor ($ per worker)Capital/Land ($ per hectare)Labor/Land (workers per hectare) Argentina$2,827.0$101.7.036 Australia7,415.567.2.009 Canada10,583.1198.0.019 France6,878.53,136.9.456 Hong Kong1,368.590,739.166.304 Japan3,358.55,286.51.574 Mexico1,684.8122.9.073 United Kingdom4,359.65,169.81.186 United States10,260.91,058.6.103 Source: Bowen, Leamer, & Sveikauskaus, AER 1987

17. 16 Factor Endowments & Intensities Home, Labor-Abundant K/L low & (w/r) low Labor, L Capital, K Labor, L Capital, K 2X 2Y 1Y Foreign, Capital-Abundant K/L high & (w/r) high 1X Relative Factor Price, (w/r) Home Relative Factor Price, (w/r) Foreign [K/L] H Y [K/L] H X 1X 2X [K/L] F X 2Y 1Y [K/L] F Y 1. Good X is “ labor-intensive” in both nations. 2. Good Y is “ capital-intensive” in both nations.

18. 17 Good XGood Y K/L Capital-Labor Ratio w/r Wage-rental ratio, Factor Prices and Input Choices Note from previous slide: 1. As (w/r) increases from Home to Foreign, K/L ratio used to produce Good X increases. The same is true for Good Y. 2. Implies there is an upward- sloping relation between relative factor price w/r and K/L used in production of each good. 3. Also, at any level of (w/r) Good Y always uses higher K/L in prod’n. Thus its relation is below that for Good X.

19. 18 Differences in PPF’s across Nations in the H-O Model

20. 19 Labor-Abundant Nation’s PPF Labor, L Capital, K [K/L] H X OXOX [K/L] H Y OYOY LXLX LYLY KXKX KYKY 1. Box below shows allocation of capital and labor to each good, for a given w/r ratio. PPF Home 3. Varying w/r picks out different allocations and prod’n points, tracing out PPF. Y X 2. Implicit in this allocation are prod’n levels of both Y =Q Y (K Y, L Y ) and X =Q X (K X, L X ). B B

21. 20 Capital -Abundant Nation’s PPF Labor, L Capital, K OXOX LXLX LYLY KXKX KYKY 1. Assume Foreign has more capital than labor. PPF Foreig n Y X [K/L] H X [K/L] H Y OYOY B B PPF Home

22. 21 Equilibrium in the Hecksher-Ohlin Model

23. 22 (P X /P Y ) * Opening trade changes relative prices Assuming identical utility function for Home & Foreign PPF H PPF F Home & Foreign PPF’s differ due to differences in technology or factor endowments. Differing Technology/Endowments Y X AHAH AFAF Autarky Equilibrium at A H and A F QFQF QHQH C*C* New equilib. consumption at C *. Each country has different prod’n ;point.

24. 23 Hecksher-Ohlin Theorem Countries will export goods that use their abundant factors intensively and import those goods that use their scarce resources intensively. Countries will export goods that use their abundant factors intensively and import those goods that use their scarce resources intensively. –Previous slides showed how factor endowments determine shape of each nation’s PPF. –Assuming identical utilities, then Hecksher-Ohlin theorem result arises for the pattern of trade. Effects of trade: Effects of trade: 1.Trade results in mutual gains. 2.Countries reallocate factors to increase specialization in goods that use their abundant factors intensively. 3.Relative commodity prices are equalized across nations after trade. (This will have implications for relative factor prices across nations also.)

25. 24 Net Export (+) of Factor Services - 1967 Factor of Prod’n U.S.GermanyJapanMexicoPhilippines Capital Stock +---- Total Labor Force --++- Professional/technical labor ++++- Managerial Labor -+++- Clerical workers -+++- Sales workers ---++ Service workers ---++ Agricultural workers +--++ Production workers -++-- Arable Land +--++ Forest Land ---+- Pasture Land ---+- Source: Bowen, Leamer, & Sveikauskaus, AER 1987

26. 25 Trade, Distribution, and Welfare in the H-O Model

27. 26 Relative Product Prices & Factor Prices Relative product price (P X /P Y ) is linked to relative factor returns (w/r) in the H-O model by the mobility of factors between industries within a country. Assume relative price of X rises in Home from opening trade. –Higher (P X /P Y ) leads Home producers to raise supply of X relative to Y. –Good X is labor-intensive so generates larger increase in demand for labor than labor released by fall in supply of capital-intensive Good Y. –Result is increase in demand for labor, driving up real wage, w. –Exact opposite result for capital in Home as prod’n shifts to Good X. –Higher (P X /P Y ) thus leads to higher (w/r) as a result of different factor intensities of the Goods combined with labor mobility between industries within Home. Diagram on next slide illustrates this relationship between relative product prices and relative factor prices in H-O model.

28. 27 Relative Factor Prices and Product Prices w/r Wage-rental ratio P X / P Y Relative Price of X, 1. As (P X /P Y ) increases suppliers switch production from Good Y to Good X. 2. Good Y is capital-intensive, while Good X is labor- intensive. 3. Reducing production of Y increases capital by more than that needed for X. Implies fall in return to capital, r. 4. This also increases labor by less than that needed for X. Implies rise in return to labor, w. 5. Rise in (P X /P Y ) thus results in rise in (w/r). SS

29. 28 From Relative Prices to Production In the Hecksher-Ohlin Model: 1.For a given set of factor prices, firms choose specific, but different, ratios of factor inputs (K/L) to produce each Good. (P X /P Y ) (w/r) 2.A given set of relative product prices (P X /P Y ) is associated with a given relative factor price (w/r). Combining these two results allows us to examine what capital/labor ratios are used in prod’n of each good in each nation before trade. –Provide diagrams linking the two results on next slide. Will also be able to examine the consequences of the equalization of relative product prices as result of trade for the relative factor prices and capital/labor ratios across countries.

30. 29 Relative Factor Prices and Product Prices w/r P X / P Y K/L Wage-rental ratio, SS (P X / P Y ) H (w/r) H (P X / P Y ) F (w/r) F (K/L) X H (K/L) Y H (K/L) X F (K/L) Y F 1. Assume Home is Labor-abundant, Foreign Capital-abundant Good X Good Y 2. Good X is L-intensive, Good Y is K-intensive

31. 30 Capital/Labor Ratios by Industry (For U.S. 1985) CommoditySIC CodeK/L ($ per employee) Dairy Products20243,764.54 Grain Mill Products20491,328.55 Tobacco Products21102,560.98 Textile Mill Products2231,067.74 Apparel235,918.62 Paper & Allied Products26102,355.57 Petroleum & Coal Products29425,090.20 Semiconductors & related devices367470,183.82 Motor Vehicles & equipment37154,018.63 Aircraft372127,481.39 Source: U.S. Dept. of Commerce, Annual Survey of Manufactures

32. 31 Trade, Distribution & Welfare Factor Price Equalization Theorem Factor Price Equalization Theorem –International trade will bring about the equalization in the relative and absolute returns to homogenous factors of production across nations. –Trade in final goods essentially substitutes for movement of factors between countries to equalize differences in relative factor returns. Stolper-Samuelson Theorem Stolper-Samuelson Theorem –Free trade will result in an increase in the reward to the abundant factor and a decrease in the reward to the scarce factor –Free trade will result in an increase in the reward to the abundant factor and a decrease in the reward to the scarce factor, i.e. the relative return earned by the abundant factor will rise with the opening of trade. –Assuming full employment before and after trade. Do not find complete factor price equalization of H-O theory. –May be barriers to adjustment: trade barriers, transportation costs, heterogeneous capital or labor, non-traded goods, imperfect competition, unemployed factors, etc.

33. 32 Relative Factor Prices and Product Prices w/r P X / P Y Good XGood Y K/L Wage-rental ratio, SS Factor Price Equalization Stolper- Samuelson

34. 33 Convergence of Real Wages Country1959197019831990 Japan112451108 Italy234262100 France274162101 U.K.29355382 Germany295684118 Average244062102 U.S.100 Real Hourly Wage in Manufacturing (as Percentage of U.S. Wage) Source: IMF, OECD, and US BLS

35. 34 Factor Growth in the H-O Model

36. 35 Rybczinski Theorem At constant product prices, an increase in the endowment of one factor will increase by a greater proportion (magnification effect) the output of the good intensive in that factor, and will reduce the output of the other good. Intuition: –Assume that the supply of capital increases. –Constant product prices imply constant relative factor returns, (w/r). –But relative factor returns can remain constant only if K/L and productivity of K and L remain constant in prod’n of both goods. –To fully employ new capital, while keeping K/L constant in both goods, requires fall in output of labor-intensive Good X to release enough labor to absorb increase in K in prod’n of Good Y. –Thus output of capital-intensive Good Y increases while output of labor-intensive Good X falls.

37. 36 Labor, L K0K0 [K/L] H X OXOX Factor Growth & the Rybczinski Theorem [K/L] H Y L0XL0X L0YL0Y K0XK0X K0YK0Y O0YO0Y L1XL1X L1YL1Y K1XK1X K1YK1Y + - - + O1YO1Y KK + Good X Good Y

38. 37 Changes in Relative Factor Endowments Country Physical Capital R&D Scientists Skilled Labor Semiskilled Labor Unskilled Labor Arable Land U.S.196341.9%62.5%29.4%18.3%0.60%27.4% 198033.650.727.719.10.1929.3 Japan19637.116.27.812.60.300.9 198015.523.08.711.50.250.8 Germany19639.17.57.16.80.141.3 19807.710.06.95.50.081.1 France19637.16.16.65.30.113.2 19807.56.0 3.90.062.6 U.K.19635.66.17.06.50.141.0 19804.58.55.14.90.091.0 Canada19633.81.62.51.70.066.5 19803.91.82.92.10.036.1 ROW196325.40.039.648.898.6559.6 198027.30.042.753.099.3259.1 Source: Mutti & Morici, Changing Patterns of U.S. Economic Activity & Comparative Advantage