Consider a two-period endowment economy. There are two countries, France and Morocco. Consumers in France have log preferences: In C + In C2 where C1 and C2 refer to French consumption in period 1 and in period 2. (The same expression holds for Morocco, just write C and C instead.) Endowments in France are Y and Y2, whereas endowments in Morocco are Y* and Y**. 1. Find expressions of C1, C2 and B2 in France. All these expressions should be functions of Y, Y2 and r. Hint: this is IDENTICAL to the problem we solved in class. 2. Find expressions of C, C and B in Morocco. All these expressions should be functions of Y, Yand r*. Hint: this is identical 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 Y = 10, Y = 11, Y* = 8 and Y** = 10. 3. Compute the autarky (closed economy) interest in France, A, and the autarky (closed economy) interest rate in Morocco, A*. Give numbers. Hint: recall that under autarky, no one borrows and no one lends, so that C = Y and C = Y. This is the same as assuming that B = 0 and B = 0. 4. Compute the utility level in both countries under autarky. Give numbers. Hint: substitute C and C into the log utility function. Do the same with C and C+ 5. 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 rFT by imposing the condition B = -B and solving out for the interest rate. 6. Determine the trade balances in period 1 and period 2 in both France and Morocco. Give numbers. Hint: the trade balance in France is Y-C in period 1 and Y2 - C in period 2. 7. 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.