2. Consider a home country with KH > 0 units of capital and LH > 0 units of labor. There are two consumption goods, indexed by w € {0,1}. Good w can be produced using a technology defined by the production function F(K, L) = K + zwL, where K > 0 is capital and L > 0 is labor. Write po and p₁ for the prices of good 0 and good 1, respectively, and v and w for the factor prices of capital and labor. Everyone has the same homothetic preferences with indifference curves that never hit the axes. a. In a diagram with output of good 0 on the horizontal axis and output of good 1 on the vertical axis, describe the production possibility frontier of this economy. Carefully label everything and show how the diagram changes as parameters change from 1/20 > 11/20 to 21/2011/10 (show both diagrams.) b. What are the possible equilibrium relative prices po/pi in each of these two cases? Explain. c. Show the Lerner diagram for this economy. Describe the cone of diversification. What is the effect of increases in K₁ or Lн on the output of goods 0 and 1, taking the prices po and pi as given? Now suppose there is also a foreign country with consumers who have the same pref- erences as consumers in the home country. The endowments of capital and labor in the foreign country are KF Є (0, KH) and LF = LH, and the technology is the same as in the home country. For the remainder, consider only the case 1/20 >1/10 d. Show the production possibility frontiers of the two countries in one diagram. e. Pick some po/P₁ € (11/10, 1/20) and use the diagram developed in d to show what the equilibrium looks like if this po/p₁ is the equilibrium price ratio. Who exports what? What do you know about factor prices in the two countries? What happens to a/n in

Fig: 1