International Trade Lecture 3: The Heckscher-Ohlin Model
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1 International Trade Lecture 3: The Heckscher-Ohlin Model Yiqing Xie School of Economics Fudan University July, 2016 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
2 Outline Heckscher-Ohlin Model: an Intuitive Approach Heckscher-Ohlin Theorem: a Formal Approach Factor-Price-Equalization Theorem Rybczynski Theorem Stolper-Samuelson Theorem Summary Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
3 Heckscher-Ohlin Model: Model Assumptions Two Goods: X 1 and X 2 Two Factors: V 1 and V 2, V ij is industry i s use of factor j X 1 F 1 (V 11, V 12 ) X 2 F 2 (V 21, V 22 ) V 1 V 11 + V 21 V 2 V 12 + V 22 (1) Two countries: h and f Identical Technologies V 11 V 12 > V 21 V 22 CRS and Perfect Competition Identical Homogeneous Demand and V h1 V h2 > V f 1 V f 2 (2) Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
4 Heckscher-Ohlin Model Factor Intensities and Factor Abundance Factor Intensities Characteristics of technologies Definition of factor intensities: If at a given factor-price ratio w 1 /w 2, optimal factor input ratios are V 11 V 12 > V 21 V 22 X 1 is said to be V 1 intensive and X 2 is V 2 intensive. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
5 Heckscher-Ohlin Model Factor Intensities and Factor Abundance Factor Intensities Characteristics of technologies Definition of factor intensities: If at a given factor-price ratio w 1 /w 2, optimal factor input ratios are V 11 V 12 > V 21 V 22 X 1 is said to be V 1 intensive and X 2 is V 2 intensive. Factor Abundance Characteristics of countries Let V kj give country k s endowment of factor j. Then if V h1 V h2 > V f 1 V f 2 country h is said to be V 1 abundant, f is V 2 abundant. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
6 Heckscher-Ohlin Model: Data Factor Intensities Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
7 Heckscher-Ohlin Model: Data Relative Factor Endowments Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
8 Heckscher-Ohlin Model: Data World Factor Endowments Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
9 Heckscher-Ohlin Model: Theorem Each country will export the good using intensively its abundant factor. Step 1: Comparative advantage is indirect. Differences in relative endowments between countries + Differences in relative factor intensities between goods Comparative advantage Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
10 Heckscher-Ohlin Model: Theorem Each country will export the good using intensively its abundant factor. Step 1: Comparative advantage is indirect. Differences in relative endowments between countries + Differences in relative factor intensities between goods Comparative advantage Step 2: Autarky prices reflect comparative advantage. Each country has a relatively low price for the good using intensively its abundant factor. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
11 Heckscher-Ohlin Model: Theorem Each country will export the good using intensively its abundant factor. Step 1: Comparative advantage is indirect. Differences in relative endowments between countries + Differences in relative factor intensities between goods Comparative advantage Step 2: Autarky prices reflect comparative advantage. Each country has a relatively low price for the good using intensively its abundant factor. Step 3: Free trade prices must lie between the two autarky prices. In free trade, each country exports the good using intensively its abundant factor. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
12 Heckscher-Ohlin Model: A Special Case Figure 8.1 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
13 Heckscher-Ohlin Model: A Special Case Figure 8.1 Figure 8.2 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
14 Heckscher-Ohlin Theorem: a Formal Approach Zero Profit Condition Consider a single country, c1 (w 1, w 2 ) a11 a 12 w1 c 2 (w 1, w 2 ) a 21 a 22 w 2 p1 c i : the production cost p i : the good price w j : the factor price a ij : the optimal amount of factor j used in industry i p 2 (3) Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
15 Heckscher-Ohlin Theorem: a Formal Approach Zero Profit Condition Consider a single country, c1 (w 1, w 2 ) a11 a 12 w1 c 2 (w 1, w 2 ) a 21 a 22 w 2 p1 c i : the production cost p i : the good price w j : the factor price a ij : the optimal amount of factor j used in industry i p 2 (3) c 1 a 11 w 1 + a 12 w 2 p 1 c 2 a 21 w 1 + a 22 w 2 p 2 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
16 Heckscher-Ohlin Theorem: a Formal Approach Zero Profit Condition Consider a single country, c1 (w 1, w 2 ) a11 a 12 w1 c 2 (w 1, w 2 ) a 21 a 22 w 2 p1 c i : the production cost p i : the good price w j : the factor price a ij : the optimal amount of factor j used in industry i p 2 (3) c 1 a 11 w 1 + a 12 w 2 p 1 c 2 a 21 w 1 + a 22 w 2 p 2 dc 1 a 11 dw 1 + a 12 dw 2 + w 1 da 11 + w 2 da 12 dp 1 (4) dc 2 a 21 dw 1 + a 22 dw 2 + w 1 da 21 + w 2 da 22 dp 2 The term in brackets is ZERO: a ij is optimally chosen, small changes in these values have no effect in cost. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
17 Heckscher-Ohlin Theorem: a Formal Approach Zero Profit Condition dc1 a11 a 12 dw1 dp1 dc 2 a 21 a 22 dw 2 dp 2 (5) Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
18 Heckscher-Ohlin Theorem: a Formal Approach Zero Profit Condition dc1 a11 a 12 dw1 dp1 dc 2 a 21 a 22 dw 2 dp 2 By Cramer s Rule, a22 /D a 12 /D a 21 /D a 11 /D dp1 dw1 dp 2 dw 2 (5) (6) Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
19 Heckscher-Ohlin Theorem: a Formal Approach Zero Profit Condition dc1 a11 a 12 dw1 dp1 dc 2 a 21 a 22 dw 2 dp 2 By Cramer s Rule, a22 /D a 12 /D a 21 /D a 11 /D dp1 dw1 dp 2 dw 2 (5) (6) Since X 1 is V 1 intensive, so that a 11 a 12 > a 21 a 22 a 11 a 22 > a 12 a 21 a 11 a 22 a 12 a 21 D > 0 (7) Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
20 Heckscher-Ohlin Theorem: a Formal Approach Zero Profit Condition dc1 a11 a 12 dw1 dp1 dc 2 a 21 a 22 dw 2 dp 2 By Cramer s Rule, a22 /D a 12 /D a 21 /D a 11 /D dp1 dw1 dp 2 dw 2 (5) (6) Since X 1 is V 1 intensive, so that a 11 a 12 > a 21 a 22 a 11 a 22 > a 12 a 21 a 11 a 22 a 12 a 21 D > 0 (7) Let p 2 1 and dp 2 0, dw1 dp 1 dp 2 0 > 0 dw2 dp 1 dp 2 0 < 0 (8) Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
21 Heckscher-Ohlin Theorem: a Formal Approach Zero Profit Condition Increase in p 1 Increase in w 1 and decrease in w 2 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
22 Heckscher-Ohlin Theorem: a Formal Approach Zero Profit Condition Increase in p 1 Increase in w 1 and decrease in w 2 Increase in w 1 and decrease in w 2 Increase in a 12, a 22 and decrease in a 11, a 21 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
23 Heckscher-Ohlin Theorem: a Formal Approach Zero Profit Condition Increase in p 1 Increase in w 1 and decrease in w 2 Increase in w 1 and decrease in w 2 Increase in a 12, a 22 and decrease in a 11, a 21 da 11 dp 1 < 0 da 12 dp 1 > 0 da 21 dp 1 < 0 da 22 dp 1 > 0 (9) Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
24 Heckscher-Ohlin Theorem: a Formal Approach Factor Market Clearing Condition a11 a 21 a 12 a 22 X1 X 2 V1 V 2 (10) Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
25 Heckscher-Ohlin Theorem: a Formal Approach Factor Market Clearing Condition a11 a 21 a 12 a 22 X1 X 2 V1 V 2 (10) Apply Eq. (7), a22 /D a 21 /D a 12 /D a 11 /D V1 V 2 X1 X 2 (11) Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
26 Heckscher-Ohlin Theorem: a Formal Approach Factor Market Clearing Condition a11 a 21 a 12 a 22 X1 X 2 V1 V 2 (10) Apply Eq. (7), a22 /D a 21 /D a 12 /D a 11 /D V1 V 2 X1 X 2 (11) Divide the first equation by the second in (11), X 1 V 2 V 1 a 22 a 21 X V 2 a 12 + a 2 (12) 11 V 1 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
27 Heckscher-Ohlin Theorem: a Formal Approach da 11 dp 1 < 0 da 12 dp 1 > 0 da 21 dp 1 < 0 da 22 dp 1 > 0 (9) X 1 V 2 V 1 a 22 a 21 X V 2 a 12 + a 2 (12) 11 V 1 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
28 Heckscher-Ohlin Theorem: a Formal Approach da 11 dp 1 < 0 da 12 dp 1 > 0 da 21 dp 1 < 0 da 22 dp 1 > 0 (9) X 1 V 2 V 1 a 22 a 21 X V 2 a 12 + a 2 (12) 11 V 1 The production ratio X 1 /X 2 rises with p 1 /p 2. The relative supply of good X 1 rises with the relative price of X 1. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
29 Heckscher-Ohlin Theorem: a Formal Approach da 11 dp 1 < 0 da 12 dp 1 > 0 da 21 dp 1 < 0 da 22 dp 1 > 0 (9) X 1 V 2 V 1 a 22 a 21 X V 2 a 12 + a 2 (12) 11 V 1 The production ratio X 1 /X 2 rises with p 1 /p 2. The relative supply of good X 1 rises with the relative price of X 1. The price ratio (p 1 /p 2 ) at which a country just begins to produce X 1 is higher in the V 2 abundant country. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
30 Heckscher-Ohlin Theorem: a Formal Approach da 11 dp 1 < 0 da 12 dp 1 > 0 da 21 dp 1 < 0 da 22 dp 1 > 0 (9) X 1 V 2 V 1 a 22 a 21 X V 2 a 12 + a 2 (12) 11 V 1 The production ratio X 1 /X 2 rises with p 1 /p 2. The relative supply of good X 1 rises with the relative price of X 1. The price ratio (p 1 /p 2 ) at which a country just begins to produce X 1 is higher in the V 2 abundant country. The price ratio (p 1 /p 2 ) at which a country stops producing X 2 is higher in the V 2 abundant country. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
31 Heckscher-Ohlin Model: A Formal Approach Recall that country h is V 1 abundant and country f is V 2 abundant. Figure 8.3 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
32 Heckscher-Ohlin Model: A Formal Approach Recall that country h is V 1 abundant and country f is V 2 abundant. Figure 8.3 Figure 8.4 Each country will export the good using intensively its abundant factor. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
33 Heckscher-Ohlin Model: A Formal Approach Income Distribution Effect of Trade Autarky: the scarcity of one factor make the good using that factor intensively expensive. Trade makes that good cheaper, leads the country to produce less of that good and more of the good which does not use that factor intensively. This is going to lower the demand for the scarce factor, and this will drive down its price in equilibrium. The reverse argument can be made about the abundant factor. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
34 Heckscher-Ohlin Model: A Formal Approach Income Distribution Effect of Trade Autarky: the scarcity of one factor make the good using that factor intensively expensive. Trade makes that good cheaper, leads the country to produce less of that good and more of the good which does not use that factor intensively. This is going to lower the demand for the scarce factor, and this will drive down its price in equilibrium. The reverse argument can be made about the abundant factor. Trade increases the return to the abundant factor, lowers the return to the scarce factor. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
35 Factor-Price-Equalization Theorem (FPE) Assumptions: Both countries have identical CRS technologies. Trade is completely costless so that goods price are equalized. Both countries produce both goods in free-trade equilibrium. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
36 Factor-Price-Equalization Theorem (FPE) Assumptions: Both countries have identical CRS technologies. Trade is completely costless so that goods price are equalized. Both countries produce both goods in free-trade equilibrium. The Factor-Price-Equalization Theorem (A) if trade is costless such that trade equalizes commodity prices between countries and (B) if countries are not too different" such that both continue to produce both goods after trade, then the price of each factor is equalized across countries. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
37 Factor-Price-Equalization Theorem (FPE) Unit Value Isoquant and Unit Value Isocost For both countries, a 22 a 21 > V 2 V 1 > a 12 a 11 Figure 8.5 Identical technologies, equalized commodity prices Same unit-value isoquants Same unit value isoquants Same isocost line FPE Endowment point at E 1 or E 2 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
38 Factor-Price-Equalization Theorem (FPE) World Edgewood Box Figure 8.6 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
39 Rybczynski Theorem Assumptions and Intuition Start from FPE, subject to producing both goods: Hold commodity prices constant Hold factor prices constant Hold optimal a ij s constant Changes in endowments can be absorbed through changes in the composition of output rather than changes in factor prices. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
40 Rybczynski Theorem Assumptions and Intuition Start from FPE, subject to producing both goods: Hold commodity prices constant Hold factor prices constant Hold optimal a ij s constant Changes in endowments can be absorbed through changes in the composition of output rather than changes in factor prices. The Rybczynski Theorem Holding commodity prices constant, an increase in the endowment of factor j leads to a more than proportion increase in the output of the good using that factor intensively, and to a fall in the output of the other good. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
41 Rybczynski Theorem: Graphical Presentation Figure 8.7 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
42 Rybczynski Theorem: Graphical Presentation Figure 8.7 Figure 8.8 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
43 Rybczynski Theorem: Formal Proof a11 a 21 X1 a 12 a 22 X 2 V1 V 2 (10) Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
44 Rybczynski Theorem: Formal Proof a11 a 21 Total derivative of (10): a 12 a 22 X1 X 2 a 11 dx 1 + a 21 dx 2 dv 1 a 12 dx 1 + a 22 dx 2 dv 2 V11 X 1 V12 X 1 V1 V 2 dx 1 + dx 1 + V21 X 2 V22 X 2 (10) dx 2 dx 2 (13) Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
45 Rybczynski Theorem: Formal Proof a11 a 21 Total derivative of (10): a 12 a 22 X1 X 2 a 11 dx 1 + a 21 dx 2 dv 1 a 12 dx 1 + a 22 dx 2 dv 2 V 2 V11 X 1 V12 X 1 V1 V 2 dx 1 + dx 1 + V21 X 2 V22 X 2 (10) dx 2 dx 2 (13) Dividing the total factor endowments V 1 and V 2, V11 dx1 V21 dx2 + dv 1 (14) V 1 X 1 V 1 X 2 V 1 V12 dx1 V22 dx2 + dv 2 (15) X 1 X 2 V 2 V 2 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
46 Rybczynski Theorem: Formal Proof The share of factor j used in good i λ ij Proportional change in a variable ˆ λ11 λ 21 ˆX 1 ˆV 1 λ 12 λ 22 ˆX 2 ˆV 2 (16) Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
47 Rybczynski Theorem: Formal Proof The share of factor j used in good i λ ij Proportional change in a variable ˆ λ11 λ 21 ˆX 1 ˆV 1 λ 12 λ 22 ˆX 2 ˆV 2 Invert the equation system, λ22 /D λ λ 21 /D λ λ 12 /D λ λ 11 /D λ ˆV 1 ˆX 1 ˆV 2 ˆX 2 (16) (17) D λ λ 11 λ 22 λ 12 λ 21 > 0 where λ 22 λ 11 λ 22 λ 12 λ 21 > 1 given 0 < λ ij < 1 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
48 Rybczynski Theorem: Formal Proof The magnitudes and signs of the mapping in (17) are as follows. > 1 < 0 < 0 > 1 ˆV 1 ˆX 1 ˆV 2 ˆX 2 (18) Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
49 Rybczynski Theorem: Formal Proof The magnitudes and signs of the mapping in (17) are as follows. > 1 < 0 < 0 > 1 ˆV 1 ˆX 1 ˆV 2 ˆX 2 (18) Given ˆV 1 > 0 and ˆV 2 0 or ˆV 1 0 and ˆV 2 > 0, The Rybczynski theorem ( Magnification" effect): ˆX 1 > ˆV 1 > ˆV 2 0 > ˆX 2 ˆX 2 > ˆV 2 > ˆV 1 0 > ˆX 1 (19) Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
50 Rybczynski Theorem: Formal Proof The magnitudes and signs of the mapping in (17) are as follows. > 1 < 0 < 0 > 1 ˆV 1 ˆX 1 ˆV 2 ˆX 2 (18) Given ˆV 1 > 0 and ˆV 2 0 or ˆV 1 0 and ˆV 2 > 0, The Rybczynski theorem ( Magnification" effect): ˆX 1 > ˆV 1 > ˆV 2 0 > ˆX 2 ˆX 2 > ˆV 2 > ˆV 1 0 > ˆX 1 (19) Small open economy East and South-East Asia Development High saving and investment rates (falling birth rates) Increase in the relative capital abundance Sectoral shifts toward manufacturing Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
51 Stolper-Samuelson Theorem: Intuition Note that the opening of trade shift production in each country toward the sector which uses intensively the country s abundant factor. The problem is that, at constant factor prices, the expanding sector is going to demand factors in different proportions to those being released by the contracting sector. Relative to the contracting sector, the expanding sector will demand too much" of the abundant factor and too little" of the scarce factor. Constant factor prices will NOT lead to an open to trade equilibrium. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
52 Stolper-Samuelson Theorem: Intuition At constant factor prices, X 2 releases factors in the proportion a 22 /a 21. X 1 demands factors in the proportion a 12 /a 11. a 22 /a 21 > a 12 /a 11 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
53 Stolper-Samuelson Theorem: Intuition At constant factor prices, X 2 releases factors in the proportion a 22 /a 21. X 1 demands factors in the proportion a 12 /a 11. a 22 /a 21 > a 12 /a 11 Price changes due to the opening of trade Changes in outputs Excess demand for the abundant factor Excess supply of the scarce factor Increased price of the abundant factor Decreased price for the scarce factor Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
54 Stolper-Samuelson Theorem: Graphical Presentation Figure 8.9 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
55 Stolper-Samuelson Theorem: Graphical Presentation Figure 8.9 Figure 8.10 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
56 Stolper-Samuelson Theorem: The Theorem Stolper-Samuelson Theorem: Holding factor endowments constant, an increase in the price of one good leads to a more than proportional increase in the price of the factor used intensively in producing that good, and to a fall in the price of the other factor. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
57 Stolper-Samuelson Theorem: A Short Proof Value of marginal product conditions for competitive equilibrium w 1 p 1 MP 11 p 2 MP 21 w 1 /p 1 MP 11 w 1 /p 2 MP 21 w 2 p 1 MP 12 p 2 MP 22 w 2 /p 1 MP 12 w 2 /p 2 MP 22 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
58 Stolper-Samuelson Theorem: A Short Proof Value of marginal product conditions for competitive equilibrium w 1 p 1 MP 11 p 2 MP 21 w 1 /p 1 MP 11 w 1 /p 2 MP 21 w 2 p 1 MP 12 p 2 MP 22 w 2 /p 1 MP 12 w 2 /p 2 MP 22 An increase in p p 1 /p 2 raises w 1 /w 2, and therefore raises the ratio of V 2 /V 1 in both industries. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
59 Stolper-Samuelson Theorem: A Short Proof Value of marginal product conditions for competitive equilibrium w 1 p 1 MP 11 p 2 MP 21 w 1 /p 1 MP 11 w 1 /p 2 MP 21 w 2 p 1 MP 12 p 2 MP 22 w 2 /p 1 MP 12 w 2 /p 2 MP 22 An increase in p p 1 /p 2 raises w 1 /w 2, and therefore raises the ratio of V 2 /V 1 in both industries. MP i1 raises and MP i2 falls. w 1 /p 1 w 2 /p 1 w 1 /p 2 w 2 /p 2 Wage of V 1 rises relative to both commodity prices. Wage of V 2 falls relative to both commodity prices. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
60 Stolper-Samuelson Theorem: A Short Proof Value of marginal product conditions for competitive equilibrium w 1 p 1 MP 11 p 2 MP 21 w 1 /p 1 MP 11 w 1 /p 2 MP 21 w 2 p 1 MP 12 p 2 MP 22 w 2 /p 1 MP 12 w 2 /p 2 MP 22 An increase in p p 1 /p 2 raises w 1 /w 2, and therefore raises the ratio of V 2 /V 1 in both industries. MP i1 raises and MP i2 falls. w 1 /p 1 w 2 /p 1 w 1 /p 2 w 2 /p 2 Wage of V 1 rises relative to both commodity prices. Wage of V 2 falls relative to both commodity prices. ŵ 1 > ˆp 1 > ˆp 2 0 > ŵ 2 Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
61 Stolper-Samuelson Theorem: A Formal Proof Start from equation (5) from zero profit condition, a11 a 12 dw1 dp1 a 21 a 22 dw 2 dp 2 (5) Rewrite the system of equation into V11 V12 X 1 dw 1 + X 1 dw 2 dp 1 V21 X 2 dw 1 + V22 X 2 dw 2 dp 2 w1 V 11 dw1 p 1 X 1 w1 V 21 p 2 X 2 dw1 w 1 + w 1 + w2 V 12 dw2 p 1 X 1 w 2 dp 1 p 1 w2 V 22 p 2 X 2 dw2 w 2 dp 2 p 2 (20) The terms in brackets are the shares of each factor s earnings (j) in the total revenue of the industry (i), denoted by θ ij, and 0 < θ ij < 1. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
62 Stolper-Samuelson Theorem: A Formal Proof Start from equation (5) from zero profit condition, a11 a 12 dw1 dp1 a 21 a 22 dw 2 dp 2 (5) Rewrite the system of equation into V11 V12 X 1 dw 1 + X 1 dw 2 dp 1 V21 X 2 dw 1 + V22 X 2 dw 2 dp 2 w1 V 11 dw1 p 1 X 1 w1 V 21 p 2 X 2 dw1 w 1 + w 1 + w2 V 12 dw2 p 1 X 1 w 2 dp 1 p 1 w2 V 22 p 2 X 2 dw2 w 2 dp 2 p 2 (20) The terms in brackets are the shares of each factor s earnings (j) in the total revenue of the industry (i), denoted by θ ij, and 0 < θ ij < 1. θ11 θ 12 θ 21 θ 22 ŵ1 ˆp1 ŵ 2 ˆp 2 (21) Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
63 Stolper-Samuelson Theorem: A Formal Proof Invert the equation system, θ22 /D θ θ 12 /D θ θ 21 /D θ θ 11 /D θ ˆp1 ˆp 2 ŵ1 ŵ 2 (22) where D θ θ 11 θ 22 θ 12 θ 21 > 0 and 0 < θ ij < 1. Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
64 Stolper-Samuelson Theorem: A Formal Proof Invert the equation system, θ22 /D θ θ 12 /D θ θ 21 /D θ θ 11 /D θ ˆp1 ˆp 2 ŵ1 ŵ 2 (22) where D θ θ 11 θ 22 θ 12 θ 21 > 0 and 0 < θ ij < 1. The magnitudes and signs of the mapping in (22) are as follows. > 1 < 0 ˆp1 ŵ1 < 0 > 1 ˆp 2 ŵ 2 (23) The S-S Theorem is given formally by the magnification relationships: ŵ 1 > ˆp 1 > ˆp 2 0 > ŵ 2 ŵ 2 > ˆp 2 > ˆp 1 0 > ŵ 1 (24) Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
65 Stolper-Samuelson Theorem: Policy Implication There will be political fights over changes in trade policy. While free trade results in aggregate gains in income, those gains are very unevenly distributed. Some factor owners generally lose. This is in turn the source of considerable political controversy over protection and liberalization A country s scarce factors may lose following trade liberalization. There is a sense in which American unskilled workers compete against workers in the developing world. However, the policy options are not just free trade versus restricted trade, but possibly include free trade versus various measures to help adversely affected workers (education, training, relocation assistance). Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
66 Summary A country s comparative advantage, production and trade are determined by underlying factor endowments intersected with technologies. Relative factor endowments across countries + Relative factor intensities across industries Comparative advantage Changing the underlying factor endowment can have very biased effects on production and trade (Rybczynski). Higher savings rates and capital formation in Asia naturally lead to a shift in capital intensive manufacturing toward Asia. While free trade results in aggregate gains in income, those gains are very unevenly distributed. Some factor owners generally lose (Stolper-Samuelson). Yiqing Xie (Fudan University) Int l Trade - H-O July, / 33
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