QUESTION 3. Intertemporal trade. 25 points. [HARD]. Consider a twoperiod economy. The representative agent has preferences represented by a utility function of the form U ( Cpczl 2']; + [3E . The agent is endowed with 3/, units of the good in period 1 and y2 units of the good in period 2. Let 1" denote the return on a oneperiod 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. 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. [Hintz 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, C1, consumption in the second period, C2 , and the amount of borrowing or lending b, as a function of yLyz, and r. e. 4 points. Suppose that y, =5 , yz :10, and 43 :03. What is the interest rate, I", 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 f2 = 6 and y: =9 , and =03. 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? h. 3 noints. Fill out the followin, table: use the numerical values Home: Current Account Home: Financial Account Period 2