Chapter 6

1. Chapter 6 Factor Endowments and Trade II: The Heckscher-Ohlin Model

2. Heckscher-Ohlin Theorem Factor Price Equalization Theorem Stolper-Samuelson Theorem Rybczynski Theorem Factor Price Insensitivity Lemma Factor Intensity Reversal Contents

3. Diagram Analysis Mathematical Proof Empirical Analysis Methodology

4. Labor and capital are resources important for production. The amount of labor and capital varies across countries, and this variation influences productivity. The supply of labor and capital in each country is constant. Only two goods are important for production and consumption: cloth and food. Competition allows factors of production to be paid a “competitive” wage, a function of their productivities and the price of the good that it produces, and allows factors to be used in the industry that pays the highest wage/rental. Only two countries are modeled: domestic and foreign Two-Factor Heckscher-Ohlin Model

5. When there is more than one factor of production, the PPF (opportunity cost in production) is no longer a straight line. Why? Let’s expand the previous chapter’s model to include two factors of production, labor and capital. aTC = hectares of capital used to produce one m2 of cloth aLC = hours of labor used to produce one m2 of cloth aTF = hectares of capital used to produce one calorie of food aLF = hours of labor used to produce one calorie of food L = total amount of labor available for production K= total amount of capital (terrain) available for production Production Possibilities

6. Production possibilities are influenced by both capital and labor (requirements): aTFQF + aTCQC≤ K aLFQF + aLCQC≤ L Total amount of capital resources Total amount of labor resources capital required for each unit of food production Total units of food production capital required for each unit of cloth production Total units of cloth production Labor required for each unit of food production Labor required for each unit of cloth production Production Possibilities (cont.)

7. Let’s assume that each unit of cloth production uses labor intensively and each unit of food production uses capital intensively: aLC /aKC > aLF/aKF Or aLC /aLF > aKC /aKF Or, we consider the total resources used in each industry and say that cloth production is labor intensive and food production is capital intensive if LC /KC > LF /KF. This assumption influences the slope of the production possibility frontier: Production Possibilities (cont.)

8. Production Possibilities (cont.)

9. The opportunity cost of producing cloth in terms of food is not constant in this model: it’s low when the economy produces a low amount of cloth and a high amount of food it’s high when the economy produces a high amount of cloth and a low amount of food Production Possibilities (cont.)

10. The above PPF equations do not allow substitution of capital for labor in production or vice versa. Unit factor requirements are constant along each line segment of the PPF. If we allow substitution of inputs, then the PPF becomes curved. For example, many laborers could work on a small plot of capital or a few labors could work on a large plot of capital to produce the same amount of output. Unit factor requirements are not constant at every quantity of cloth and food produced. Production Possibilities (cont.)

11. Assume home country is relatively labor-abundant country. L/K>L*/K* alcC+alfF=L; akcC+akfF=K; alcC*+alfF*=L*; akcC*+akfF*=K* Remember that techonology is assumed to be the same in both countries. Preference are identical in both countries. Assume same capital endowment in both countries, but home has 50% more labor force. A simple HO Model with rigid technology

12. Figure 6.1 Production Possibilities: Rigid Technology

13. The K-constraint line is assumed to intersect the labor-constraint line instead of lying everywhere above or below. Given clothing is relative labor-intensive, the capital-constraint line is flatter than the labor-constraint line. Point A is the only output combination for which both labor and capital are fully employed in foreign. Point S is the only output combination for which both labor and capital are fully employed at home. A simple HO Model with rigid technology

14. The relatively labor-abundant country produces relatively larger quantities of the labor-intensive commodity. The relatively labor-abundant country will tend to export the relatively labor-intensive commodity. Two conclusions of a simple HO Model

15. Factor requirements: alc=3, alf=1; akc=1, akf=2 Factors Market clear condition for foreign: Labor: 3C*+F*=200 Capital: C*+2F*=200 Question: how do goods’ price changes alter the distribution of income? Suppose food’s price doesn’t change before and after trade, 10 Clothing price differs in both countries before trade, but equals 10 after trade (assumed free trade) A Numerical Example

16. Unit-cost equilibrium conditions: At home 3w+r=8 (clothing) At home w+2r=10 (food) At foreign 3w*+r*=12 (clothing) At foreign w*+2r*=10 (food) Autarky Solution: at home: w=6/5; r=22/5 Abroad: w*=14/5; r*=16/5. Clothing is more expensive abroad at autarky Price changes alter the distribution of income?

17. After trade, At home 3w+r=10 (clothing) At home w+2r=10 (food) At foreign 3w*+r*=10 (clothing) At foreign w*+2r*=10 (food) Solution: w=2; r=4 (for both countries) Free trade benefits the abundant factor of production and harms the relatively scarce factor of production. Stopler-Samuelson Theorem Two Important Results

18. Trading countries’ factor prices should equalize after trade if they satisfy: (1) Both products are produced in both countries (2) Common technology (3) Free Trade (4) No Factor Intensity Reversal (FIR) Factor Price Equalization

19. Figure 6.2 Factor-Intensity Comparison

20. When technology is flexible, one can use iso-quant to denote. When costs are minimized in each, clothing is relatively labor intensive. Food is presumed to be produced by capital-intensive techniques compared with clothing. When both industries face the same set of factor prices, the least-cost K/L ratio for food (at A) exceeds that chosen for clothing (at B) Factor-Intensity Comparison

21. Figure 6.3 Factor Intensities and Factor Endowments

22. If the K/L ratio at home is k, the w/r ratio must lie in the range BC. Why? If the w/r is higher than point c, too much demand for capital, which exceeds its maximum. If the capital-abundant foreign country has the endowment ratio k*, there is an overlap of possible w/r ratio in the two countries, DC. Free trade may equalize factor prices. If the foreign endowment ratio be at the higher value k**, the relative wage rate abroad must be higher than at home. Factor Intensities and Factor Endowments

23. Production Possibilities (cont.)

24. In the production of each unit of food, unit factor requirements of capital and labor are not constant in the Heckscher-Ohlin model Input Possibilities

25. The production possibility frontier describes what an economy can produce, but to determine what the economy does produce, we must determine the prices of goods. In general, the economy should produce at the point that maximizes the value of production, V: V = PCQC + PFQF where PC is the price of cloth and PF is the price of food. Production and Prices

26. Define an iso-value line as a line representing a constant value of production. V = PCQC + PFQF PFQF = V – PCQC QF = V/PF – (PC /PF)QC The slope of an iso-value line is – (PC /PF) Production and Prices (cont.)

27. Production and Prices (cont.)

28. Given prices of output, one iso-value line represents the maximum value of production, say at a point Q. At that point, the slope of the PPF equals – (PC /PF), so the opportunity cost of cloth equals the relative price of cloth. Production and Prices (cont.)

29. Producers may choose different amounts of factors of production used to make cloth or food. Their choice depends on the wage rate, w, and the (opportunity) cost of using capital, the rental rate r. As the wage rate increases relative to the rental rate, producers are willing to use more capital and less labor in the production of food and cloth. Recall that food production is capital intensive and cloth production is labor intensive. Factor Prices, Goods Prices and Factor Levels

30. Factor Prices, Goods Prices and Factor Levels (cont.)

31. Under competition, the price of a good equals the cost of production, and the cost of production depends on the wage rate and the rental rate. Pc=costc=w*aCL+r*aCK The effect of the rental rate of capital on the price of cloth depends on the intensity of capital usage in cloth production. An increase in the rental rate of capital will affect the price of food more than the price of cloth. Under competition, changes in w/r are therefore directly related to changes in PC /PF. Factor Prices, Goods Prices and Factor Levels (cont.)

32. Factor Prices, Goods Prices and Factor Levels (cont.)

33. Figure 6.4 Factor Prices and Commodity Prices

34. We have a relationship among factor prices and good prices and the levels of factors used in production: Stolper-Samuelson theorem: if the relative price of a good increases, then the real wage(or rate of return of the factor) used intensively in the production of that good increases, while the real wage (or rate of return of the other factor) decreases. Pc/PF up  (K/L)C up; (K/L)F up. Note that clothing is labor intensive, therefore Lf relatively decreases. Marginal productivity of a factor increases as the level of that factor used in production decreases: L down MPL up. Under competition, the real wage/return is equal to the marginal productivity of the factor: W/Pc=MPL Pc/PF up w/Pc up, r/Pc down; W/PF up, r/PF down Factor Prices, Goods Prices and Factor Levels (cont.)

35. Factor Prices, Goods Prices and Factor Levels (cont.)

36. We have a theory that predicts changes in the distribution of income when the relative price of goods changes, say because of trade. An increase in the relative price of cloth, PC /PF , will: raise income of workers relative to that of capitalowners, w/r. raise the ratio of capital to labor, K/L, in both industries and raise the marginal product of labor in both industries and lower the marginal product of capital in both industries. raise the real income of workers and lower the real income of capital owners. Factor Prices, Goods Prices and Factor Levels (cont.)

37. The allocation of factors used in production determine the level of output at the economy’s PPF. We summarize the relationship between the levels of factors used in production and output levels, using the following diagram: Factor Prices, Goods Prices, Factor Levels and Output Levels

38. Factor Prices, Goods Prices, Factor Levels and Output Levels (cont.)

39. How do output levels change when the economy’s resources change? If we hold output prices constant as a factor of production increases, then the supply of the good that uses this factor intensively increases and the supply of the other good decreases. This proposition is called the Rybczynski theorem. Factor Prices, Goods Prices, Factor Levels and Output Levels (cont.)

40. Factor Prices, Goods Prices, Factor Levels and Output Levels (cont.)

41. Factor Prices, Goods Prices, Factor Levels and Output Levels (cont.)

42. An economy with a high ratio of capital to labor is predicted to have a high output of food relative to cloth and a low price of food relative to cloth. It will be relatively efficient at (have a comparative advantage in) producing food. The relative supply of food shifts to the right. An economy will be relatively efficient at producing goods that are intensive in the factors of production in which the country is relatively well endowed. Factor Prices, Goods Prices, Factor Levels and Output Levels (cont.)

43. Suppose that the domestic country has an abundant amount of labor relative to the amount of capital. The domestic country is abundant in labor and the foreign country is abundant in capital: L/T > L*/ K* Likewise, the domestic country is scarce in capital and the foreign country is scarce in labor. However, the countries are assumed to have the same technology and same consumer tastes. Because the domestic country is abundant in labor, it will be relatively efficient at producing cloth because cloth is labor intensive. Trade in the Heckscher-Ohlin Model

44. Since cloth is a labor intensive good, the domestic country’s PPF will allow a higher ratio of cloth to food relative to the foreign county’s PPF. At each relative price, the domestic country will produce a higher ratio of cloth to food than the foreign country. The domestic country will have a higher relative supply of cloth than the foreign country. Trade in the Heckscher-Ohlin Model (cont.)

45. Trade in the Heckscher-Ohlin Model (cont.)

46. Like the Ricardian model, the Heckscher-Ohlin model predicts a convergence of relative prices with trade. With trade, the relative price of cloth will rise in the domestic country and fall in the foreign country. In the domestic country, the rise in the relative price of cloth leads to a rise in the relative production of cloth and a fall in relative consumption of cloth; the domestic country becomes an exporter of cloth and an importer of food. The decline in the relative price of cloth in the foreign country leads it to become an importer of cloth and an exporter of food. Trade in the Heckscher-Ohlin Model (cont.)

47. An economy will be relatively efficient at (have a comparative advantage in) producing goods that are intensive in its abundant factors of production. An economy will export goods that are intensive in its abundant factors of production and import goods that are intensive in its scarce factors of production. This proposition is called the Heckscher-Ohlin theorem Trade in the Heckscher-Ohlin Model (cont.)

48. Over time, the value of goods consumed is constrained to equal the value of goods produced for each country. PCDC + PFDF = PCQC + PFQF where DCrepresents domestic consumption demand for cloth and DFrepresents domestic consumption demand for food (DF – QF) = (PC /PF)(QC – DC) Quantity of exports Price of exports relative to imports Quantity of imports Trade in the Heckscher-Ohlin Model (cont.)

49. (DF – QF) = (PC /PF)(QC – DC) This equation is the budget constraint for an economy, and it has a slope of – (PC /PF) (DF – QF) – (PC /PF)(QC – DC) = 0 Trade in the Heckscher-Ohlin Model (cont.)

50. Trade in the Heckscher-Ohlin Model (cont.)