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Appendix 4.1. Alternate Proofs of Selected HO Theorems. Production Isoquant. An isoquant shows the various combinations of labor and capital required to produce a fixed quantity of a product.
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Appendix 4.1 Alternate Proofs of Selected HO Theorems
Production Isoquant An isoquant shows the various combinations of labor and capital required to produce a fixed quantity of a product. The curvature of an isoquant indicates the ease of subsitutability between the two inputs, holding output constant. A straight line isoquant indicates that the inputs are perfect substitutes; right angles indicate that inputs are not substitutable.
Heckscher-Ohlin Theorem (Price Definition) If country A (B) is relatively abundant in K (L) and if good S (T) is relatively K (L)– intensive in its production, then country A (B) should have a comparative advantage in the production of good S (T).
Proof of HO Theorem See Figure A4.2 There are two isoquants, each representing the production of one unit of good S (T). The S isoquant is closer to the K-axis indicating that S is more K-intensive. The least costly input combination for producing a desired output level occurs at the tangency of an isocost line (such as GH) and an isoquant (such as point R for good S).
HO Theorem Proof (cont.) • If isocost line GH is tangent to both S and T isoquants (at points R and Q), then the cost of producing each product must be identical. • The slope of isocost line GH is equal to country A’s autarky wage/rent ratio; GH cannot apply to country B. • Since B is more labor abundant than A, its wage/rent ratio is lower than A’s. • The isocost line to produce good S in country B is higher than the isocost line to produce T; thus, B has a comparative advantage in good T.
Proof of the Rybczynski Theorem • Refer to Figure A4.3 • Given isoquants representing $1 each of goods S and T and an isocost line tangent to both, the tangency points F and D represent optimal input combinations. • The slopes of the rays from the origin passing through F and D indicate the optimal capital/labor use ratios.
Rybczynski Theorem (cont.) • Given factor endowments represented by point E, draw a parallelogram connecting E to the two rays from the origin. Adding the factor combination OG (OH) to point H (G) will result in total endowment level E. • When the country’s labor rises (capital and prices constant), the endowment level moves from E to E’. As a result, the output of S falls to G’ while T rises to H’.
Proof of Stolper-Samuelson Theorem • Refer to Figure A4.4 • The initial optimal input combinations are indicated by the tangency points F and D. • If the price of T rises, then a $1 worth of this good is now on a lower isoquant T’. A new isocost line is tangent to the isoquants S and T’. • A comparison of the isocost lines shows that wages have risen while rents have fallen. As a result, labor (capitalists) can purchase more (less) of both goods.
Appendix 4.2 The Specific Factors Model
Specific Factors (Ricardo-Viner) Model • Same assumptions as HO Model except capital is immobile between industries • Refer to Figure A4.5 • The horizontal axis measures labor input in A, with labor units in S (T) industry measured from point 0S (0T). The vertical axes measure wage rate in A. • The VMPS curve shows the S industry’s demand for labor; the industry will hire labor until W =PS x MPLS. Likewise for VMPT curve.
Equilibrium in Specific Factors Model • Labor market equilibrium occurs at the intersection of the VMPS and VMPT curves. • 0SD workers are employed in the S industry and D0T workers in the T industry. • Wage rate paid to workers in both sectors is W0.
Effects of a Rise in Price of Good S • Country A has a comparative advantage in S. When trade opens up, the price of S rises. • Demand for labor will increase in industry S; employment in S rises while employment in the T sector falls. Wages also increase. • Capital owners in industry S are better off as their rental payments rise.
