(3} Assume two goods, X and Y, two factors, capital and labor, constant returns to scale, and a technology where good Y is relatively intensive in its use of capital, and good X is relatively intensive in its use of labor. In addition, assume two countries, where the home country is relatively well endowed with capital, and the foreign country with labor. (a) From this information, use the appropriate diagrams in input-space [isoquants} and goods-space to pin down the location of the production possibility frontiers for each country. (b) Show each country's autarky equilibrium, assuming they have similar consumer preferences. What do each country's relative prices tell you about their comparative advantage? (c) Using the production possibilities diagram, carefully describe the trade pattern that will occur when the two countries move from autarky to open trade. ((1) From your discussion in (c), state and carefully explain the HeckscherOhlin theorem. (e) Suppose the home country's supply of capital increases, and relative goods' prices remain constant. Using the Edgeworth Box of production, explain what happens to output of Yand X, and how does it affect the shape of its production possibility frontier