Two sectors : Factor Price Equalization Two sectors ... - Gregory Corcos
If endowments are in the diversification cone in both countries, the diagrams will be identical and relative factor prices will be equal in both countries (even ...
Figure 1: Lerner diagram in a two sector model. If endowments are in the diversification cone in both countries, the diagrams will be identical and relative factor prices will be equal in both countries (even though international mobility of factors is ruled out by assumption).
Two sectors: Rybczynski theorem
Figure 2: Factor use in both sectors The parallelogram describes factor use by both sectors that is consistent with both profit maximization and the full employment of both factors: each sector’s capital-labor ratio is given by the 1
slope of rays Ok˜X and Ok˜Y (profit maximization) and the sum of both sectors’ factor demand equals factor supply (full employment).
Figure 3: The Rybczynski theorem when the capital endowment increases (note: you were not asked to discuss point E” in the problem).
Two sectors: Stolper-Samuelson Consider an increase in pY while pX is constant. Denote by p0Y the new price. Sector Y’s isovalue curve shifts inward.
w˜00 represents the wage that would apply if the wage-rental ratio remained constant after that 2
price change. It can be shown that this wage changes relative to the initial wage w ˜ in proportion to the pY change. Given the price change, the Stolper Samuelson theorem predicts that the real wage will increase (since Y is labor-intensive) while the real rental price of capital will decrease. It can be seen from the shift in the isocost curve that the nominal wage rises while the nominal rental falls. Since pX is unchanged, real factor rewards expressed with pX as the numeraire move in exactly the same way. Now consider real factor prices expressed with pY as the numeraire. Since r falls and pY increases, ˜00 the real rental falls too. Finally, since w = pw˜Y , and the graph shows that w˜00 < w˜0 , it follows that p0 w˜0 p0Y
Y
> pw˜Y . Therefore the real wage also increases when expressed with pY as the numeraire. The graph thus shows that the Stolper-Samuelson theorem holds no matter which good is chosen as the numeraire.
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