Consider a two-period endowment economy. There are two countries, France and Morocco. Consumers in France have log preferences: InCh +1InCy where C and Cy refer to French consumption in period 1 and in period 2. (The same expression holds for Morocco, just write C] and C3 instead.) Endowments in France are Y7 and Ya, whereas endowments in Morocco are 7" and Y5 1. 2: Find expressions of C1, Co and By in France. All these expressions should be functions of Y1, Yo and r. Hint: this is IDENTICAL to the problem we solved in class. Find expressions of CY, C5 and B3 in Morocco. All these expressions should be functions of Y|*, Y3 and r*. Hint: this is idenlical to 1, except that all variables have an asterisk. The expressions in 1. and 2. above will be very useful for the subsequent questions. Now assume that Y1 =10, Yo =11, Y{* = 8 and Y, = 10. 3. Compute the autarky (closed economy) interest in France, r*, and the autarky (closed economy) interest rate in Morocco, % Give numbers. Hint: recall that under autarky, no one borrows and no one lends, so that Cy = Y1 and C} = Y|*. This is the same as assuming that Bo =0 and B3 = 0. . Compute the utility level in both countries under autarky. Give numbers. Hint: substitute Cy and Cy into the log utility function. Do the same with CT and C5. . Compute the free trade interest rate. Give a number. Hint: since in free trade the borrowing of one country should be equal to the lending of the other, you can determine the free trade interest rate v by imposing the condition By = B3 and solving out for the interest rate. . Determine the trade balances in period 1 and period 2 in both France and Morocco. Give numbers. Hint: the trade balance in France is Y1 C1 in period 1 and Yo Cs in period 2. . Compute the utility level in both countries under free trade, and compare them to the autarky utility levels. Hint: follow the same procedure as in question 4