QUESTION 3. Intertemporal trade. 25 points. [HARD]. Consider a two-period economy. The representative agent has preferences represented by a utility function of the form U(C,, C2) = Vc, + BVc2 . The agent is endowed with y, units of the good in period 1 and y2 units of the good in period 2. Let / denote the return on a one-period bond, and b denote the quantity of bonds. a. 2 points. Write out the budget constraint for period 1 and a separate budget constraint for period 2. ~ L b. 2 points. Combine the two per-period budget constraints to form the intertemporal budget constraint. c. 4 points. Write out the consumer's maximization problem (maximize utility subject to the intertemporal budget constraint. Take the first order conditions and derive the Euler Equation. [Hint: the Euler equation relates marginal utility in the two periods to 1+ the interest rate.]~ d. 4 points. Derive the consumer's choice of consumption in the first period, c,, consumption in the second period, c2, and the amount of borrowing or lending b, as a function of y1, y2, and r. e. 4 points. Suppose that y, =5, y2 =10, and B =0.9. What is the interest rate, r, in the closed economy? What is the value of b?~ f. 3 points. Suppose there is another country, (the foreign country) whose preferences are identical to those in the first part of this question. This country has endowments of y*2=6 and y2 =9, and B =0.9. What is the interest rate in the closed foreign economy, r"? What is the value of b?~ g. 3 points. When the home and foreign country open to trade, what will the world interest rate be? ~