Advanced International Trade—Problem Set 3 1. Consider a world with two countries and three goods. Both countries can use linear labor-only technologies to produce these goods. The labor productivities in

the home country are denoted by Zn,H, and in the foreign country by Zn,F, where n = {1, 2, 3}. These productivities are positive and satisfy 21,H 22,H Z3,H Z1,F 22,F Z3,F = 1. The home- and foreign-country labor supplies LH and LF are supplied inelastically, and consumers have identical preferences over the three consumption goods, described by the utility function u(C1, C2, C3) B₁ln(c₁) + B2 ln(c2) + ß3 ln(c3), where ß₁ + ß2 + ẞ3 Write Cn,j for consumption of good n in country j, pn for the world price of good n, w; for the wage in country j, where n = {1, 2, 3} and j = {H, F}. = and Assume that the equilibrium pattern of specialization is such that both countries produce strictly positive amounts of good 2. a. Determine the wage ratio wĤ/WF and the relative prices pn/w; for n = {1,2,3} and jЄ {H, F}. b. Given these wages and prices, determine Cn.j for n = {1, 2, 3} and j = {H, F}. c. Combine the results from a and b with market clearing conditions to determine the amounts of labor ln,j used to produce good n in country j, for n € {1, 2, 3} and j = {H, F}. d. Considering only small changes that do not affect the pattern of specialization, describe what happens to utility in the home country and to utility in the foreign country in the following four distinct scenarios: (1) 21,F increases; (2) 22,F increases; (3) 23,F increases; and (4) vector (21,F, 22,F, Z3,F) is scaled up by factor > 1. Υ 1