?-_ Cnnsiaer a ()me country with Ky > 0 units of--capi_ta] and_iu > (_]uni.ts o_f_ laimr. :l'_l'tere 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) =z K + z,L, where K > 0 is capital and L > 0 is labor. Write p, and p, 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 z, /2y > x1 /1 to z;/z; (show both diagrams.) b. What are the possible equilibrium relative prices py/p; in each of these two cases? Explain. . Show the Lerner diagram for this economy. Describe the cone of diversification. What is the effect of increases in Ky or Ly on the output of goods 0 and 1, taking the prices py and p, 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 Ky (0. Ky) and Ly = Ly, and the technology is the same as in the home country. For the remainder, consider only the case z;/z; > /. d. Show the production possibility frontiers of the two countries in one diagram. e. Pick some py/p1 (x1/20, 21/20) and use the diagram developed in d to show what the equilibrium looks like if this po/p is the equilibrium price ratio. Who exports what? What do you know about factor prices in the two countries? What happens to pg/p; in each of the two countries when trade is shut down? Hint: first draw budget constraints, not indifference curves; then reverse engineer what indifference curves must be like