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

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. 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.

Factor Endowments and Factor Intensities

Factor Intensities & Factor Abundance Factor Intensities: (A property of production technologies) 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 . 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: (A property of factor endowments) Physical Units definition: A nation is capital-abundant if its capital/labor ratio (K/L) is larger than that of the other nation. 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). H-O model combines both factor intensities of goods and relative factor abundance of nations to determine trade patterns.

Relative Factor Endowments Country Capital/Labor ($ per worker) Capital/Land ($ per hectare) Labor/Land (workers per hectare) Argentina $2,827.0 $101.7 .036 Australia 7,415.5 67.2 .009 Canada 10,583.1 198.0 .019 France 6,878.5 3,136.9 .456 Hong Kong 1,368.5 90,739.1 66.304 Japan 3,358.5 5,286.5 1.574 Mexico 1,684.8 122.9 .073 United Kingdom 4,359.6 5,169.8 1.186 United States 10,260.9 1,058.6 .103 Source: Bowen, Leamer, & Sveikauskaus, AER 1987

Factor Endowments & Intensities 1. Good X is “ labor-intensive” in both nations. Foreign, K/L high 2. Good Y is “ capital-intensive” in both nations. Capital, K [Implies (w/r) high] Home, K/L low Relative Factor Price, (w/r)Foreign 2Y 1Y [K/L]FY [Implies (w/r) low] Capital, K [K/L]HY 2Y 1Y 1X 2X [K/L]FX 2X [K/L]HX 1X Relative Factor Price, (w/r)Home Labor, L Labor, L

Factor Prices and Input Choices Note from previous slide: As (w/r) increases from Home to Foreign, K/L ratio used to produce Good X increases. The same is true for Good Y. Implies there is an upward-sloping relation between relative factor price w/r and K/L used in production of each good. 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. Wage-rental ratio, w/r Good X Good Y Capital-Labor Ratio K/L

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

Allocation of Factors to Goods Prod’n [K/L]HY Labor, L Capital, K OY Capital, K [K/L]HY OY Total Labor Total Capital [K/L]HY 2X 2Y 1Y 1X [K/L]HX OX Labor, L

Allocation of Factors & Nation’s PPF Y X 2. Implicit in this allocation are prod’n levels of both Y =QY(KY, LY) and X =QX(KX, LX). 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. B Capital, K LX LY OY KX KY [K/L]HX [K/L]HY OX Labor, L

Equilibrium in the Hecksher-Ohlin Model

Differing Technology/Endowments QF QH C* New equilib. consumption at C*. Each country has different prod’n ;point. Assuming identical utility function for Home & Foreign (PX/PY)* Opening trade changes relative prices PPFH PPFF Home & Foreign PPF’s differ due to differences in technology or factor endowments. Y AH AF Autarky Equilibrium at AH and AF X

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

Net Export (+) of Factor Services - 1967 Factor of Prod’n U.S. Germany Japan Mexico Philippines 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

Trade, Distribution, and Welfare in the H-O Model

Relative Product Prices & Factor Prices Relative product price (PX/PY) 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 (PX/PY) 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 (PX/PY) 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.

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

From Relative Prices to Production In the Hecksher-Ohlin Model: For a given set of factor prices, firms choose specific, but different, ratios of factor inputs (K/L) to produce each Good. A given set of relative product prices (PX/PY) 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.

Relative Factor Prices and Product Prices Good X Good Y 2. Good X is L-intensive, Good Y is K-intensive Wage-rental ratio, w/r 1. Assume Home is Labor-abundant, Foreign Capital-abundant SS (PX/ PY)F (w/r)F (K/L)XF (K/L)YF (PX/ PY)H (w/r)H (K/L)XH (K/L)YH PX/ PY K/L

Capital/Labor Ratios by Industry (For U.S. 1985) Commodity SIC Code K/L ($ per employee) Dairy Products 202 43,764.54 Grain Mill Products 204 91,328.55 Tobacco Products 21 102,560.98 Textile Mill Products 22 31,067.74 Apparel 23 5,918.62 Paper & Allied Products 26 102,355.57 Petroleum & Coal Products 29 425,090.20 Semiconductors & related devices 3674 70,183.82 Motor Vehicles & equipment 371 54,018.63 Aircraft 3721 27,481.39 Source: U.S. Dept. of Commerce, Annual Survey of Manufactures

Trade, Distribution & Welfare 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 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.

Relative Factor Prices and Product Prices Wage-rental ratio, w/r Good X Stolper- Samuelson Factor Price Equalization SS Good Y PX/ PY K/L

Convergence of Real Wages Real Hourly Wage in Manufacturing (as Percentage of U.S. Wage) Country 1959 1970 1983 1990 Japan 11 24 51 108 Italy 23 42 62 100 France 27 41 101 U.K. 29 35 53 82 Germany 56 84 118 Average 40 102 U.S. Source: IMF, OECD, and US BLS

Factor Growth in the H-O Model

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.

Factor Growth & the Rybczinski Theorem + - Good Y [K/L]HY L0X L0Y K0X K0Y O0Y L1X L1Y K1X K1Y O1Y DK + K0 [K/L]HX OX Labor, L Good X

Changes in Relative Factor Endowments Country Physical Capital R&D Scientists Skilled Labor Semiskilled Labor Unskilled Labor Arable Land U.S. 1963 41.9% 62.5% 29.4% 18.3% 0.60% 27.4% 1980 33.6 50.7 27.7 19.1 0.19 29.3 Japan 7.1 16.2 7.8 12.6 0.30 0.9 15.5 23.0 8.7 11.5 0.25 0.8 Germany 9.1 7.5 6.8 0.14 1.3 7.7 10.0 6.9 5.5 0.08 1.1 France 6.1 6.6 5.3 0.11 3.2 6.0 3.9 0.06 2.6 U.K. 5.6 7.0 6.5 1.0 4.5 8.5 5.1 4.9 0.09 Canada 3.8 1.6 2.5 1.7 1.8 2.9 2.1 0.03 ROW 25.4 0.0 39.6 48.8 98.65 59.6 27.3 42.7 53.0 99.32 59.1 Source: Mutti & Morici, Changing Patterns of U.S. Economic Activity & Comparative Advantage