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2. Two-period Open Economy. Consider a model of two countries (call them Home and Foreign), in which equilibrium holds when S, + S; = I + /; (world wide saving = world wide investment). Home's gen- eral utility function is U(C1) + AU(C2). Foreign has an analogous util- ity function with consumption levels and time preference parameters distinguished by asterisks. Date 2 Home output is a strictly concave function of the capital stock in place Ya = F(K;). with an analogous production function in Foreign. Date 1 outputs in both countries are exogenous since they depend on inherited capital stocks (i.e., Ki, Kj are given); hence, Y, = F(K,) is given. Home's budget constraint is: 1 +r 1+r and investment is / = Ka - K, and /2 - -K's. (a) Set up Home's maximization problem and compute the two Euler conditions. Interpret the Euler conditions. (b) Now suppose that the production and utility functions are: Y - KoandU(C) = ci Using these functional forms, re-write the Euler equations. Then derive solutions for K's, Ci,and the current account CA,, in that order. (Proper solutions will only be functions of the interest rate, parameters, and known variables)