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 ; {H,F}. Assume that Ku/Ly > K/Lp > 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 Af; for the equilibrium quantity ofc.lpital used in country j. The home country imposes a tariff #,; [0, 1] on imports of consumption goods, and the foreign country imposes a tariff r [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 fyyc, measured in units of home-country consumption, And someone who carries A units of capital through customs into the foreign country has to pay the foreign government 7pupk, measured in units of foreign consumption. d. Givean equation that expresses C'y in terms of (K. Ly, My) and (7, vg). Also express Cy in terms of (Ke, Ly, My) and (fu, vu). 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 a (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 (' on the horizontal axis and Cp on the vertical axis that shows (i) the consumption outcomes when 7y = 0 and #y ranges from 0 to the tariff that shuts down trade, and (ii) the cons!,:.n'lplim 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