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QUESTION 1 There are two countries, indexed by j E {H, F}. Consumers in country j have prefer- ences given by the utility function U

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QUESTION 1 There are two countries, indexed by j E {H, F}. Consumers in country j have prefer- ences given by the utility function U (C;,c) = (1 -a) In(C;) +a / B_ In(c_)aw, where C; is consumption of the non-traded good in country j, and c. is consumption of the traded good w e [0, 1]. The B., are all strictly positive, and they integrate to 1. And a E (0, 1). All consumption goods can be produced using linear labor-only technologies, and every consumer has one unit of labor. The number of consumers originally in country j is L;. The number of migrants who go from the foreign country to the home country is denoted by ME [-LH, LF]. The production technologies in country j E {H, F} are Yj = 1; Nj, and yoj = ajlwj, WE[0, 1]. Here, N; and lej are labor inputs, Y, is output of the non-traded good in country j, and ywj is output of the traded good win country j. The labor productivity parameters r; and zwj are strictly positive. Assume that A(w) = #w,H/24,F is a smooth and strictly decreasing function of w, ranging throughout (0, co)

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