d. Give an equation that expresses C'y in terms of ( Ky, Ly, My) and (75, vp). Also express C].' in terms of {I{[.'. Ly, .1.{1'} and {61[ 'l'H}. e. Suppose country i {H.F} sets a positive tariff that is not large enough to shut down trade by itself. Explain why country j # i has an incentive to respond with a positive tariff of its own. Now suppose that F(K, L) = K'"*L*, where o (0, 1). f. Calculate the equilibrium capital-labor ratios analytically and give expressions for the equilibrium consumption levels, assuming the tariffs are not large enough to shut down trade. g. Produce a graph with C'y on the horizontal axis and Cr on the vertical axis that shows (i) the consumption outcomes when 7 = 0 and #y; ranges from 0 to the tariff that shuts down trade, and (ii) the consumption outcomes when #y; = 0 and 7y ranges from 0 to the tariff that shuts down trade. h. Add the Pareto frontier of this economy to your diagram in g. Explain. Consider a world with two countries, the home country, indexed by H, and the foreign country, indexed by F. The two countries are endowed with K; units of capital, and L; units of labor, where j {H,F}. Assume that Ky /Ly > Ky/Ly > 0. There is a produc- tion function F'(K, L) that is strictly increasing in both arguments, concave, and exhibits constant returns to scale. Everything can be traded domestically, and consumption and capital goods can be traded internationally. Markets are competitive. In country j, the factor prices of capital and labor are v; and w;, measured in units of domestic consumption. Write M; for the equilibrium quantity of capital used in country j. The home country imposes a tariff #y; [0.1] on imports of consumption goods, and the foreign country imposes a tariff 7 [0, 1] on imports of capital goods. More precisely, someone who carries units of consumption through customs into the home country has to pay the government , measured in units of home-country consumption. And someone who carries /X units of capital through customs into the foreign country has to pay the foreign government 7rvrk, measured in units of foreign consumption. a. Suppose all tariffs are zero. Give the equilibrium conditions that can be used to de- termine the capital-labor ratios, taking for granted that capital will be used to produce in both countries. Set up a diagram with My /Ly on the horizontal axis and Ay /Ly on the vertical axis that shows these equilibrium conditions. Who exports what? b. Now suppose that #; and 7 are positive, and there is still some trade between these countries. What do you know about the relation between vy and vz? Produce a new version of the diagram mentioned in part a. What happens to the equilibrium capital- labor ratios of the two countries when there is an increase in iy or 7#? What happens to Ky My and Ky Mg? c. Verify that the equilibrium capital-labor ratios only depend on the tariff parameters via the composite parameter (1 74 )(1 #y) [0,1]. Give an expression for the largest value of this composite parameter for which there is no trade