Assume two goods, X and Y, and two factors of production capital and labor, 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, but both countries have the same consumer preferences. (i) Based on this information, use a diagram in input space (isoquants) and one in goods space to explain the location of the production possibility frontiers for each country. (ii) Use the production possibility frontiers for each country and their consumer preferences to illustrate each countries autarky relative prices. (iii) Using the relevant diagram, carefully describe the trade pattern that will occur when the two countries move from autarky to open trade. Pay particular attention to describing how each country's relative autarky prices adjust to trade. (iv) Why do the trade triangles for each country have to have the same dimensions? (v) From your discussion in (iii), state and explain the Heckscher-Ohlin theorem.