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e) Assume Q2 = 2?(11) due to investment surge, but the firm faces a newly imposed collateral constraint of the form Dif ? ?1 where ?1 denotes the value of the firm's collateral. Suppose that ?1 equals 0.5. Is the collateral constraint binding in period 1? What are the amount of investment in period-1, Q2, and profit for period-2? Q1. 10 p Consider a two-period model of a small open economy with a single good each period. Let preferences of the representative household be described by the utility function In(C1) + In(C2). where C1 and C2 denote consumption in periods 1 and 2, respectively, and In denotes the natural logarithm. In period 1, the household receives an endowment of Q1 = 5. In period 2, the household receives profits, denoted by T12, from the firms it owns. Households and firms have access to financial markets where they can borrow or lend at the interest rate r1. (r1 is the interest rate on assets held between periods 1 and 2.)! Representative firm borrows D,* in period 1 to make investment I1 that enable the firm to produce goods in period 2. The production technology in period 2 is given by Q2 = V(11),Consider a pine exchange economyr that consists of two consumers, A and B and two goods X and Y. Consumer A's utilityF mction is U A = xfyj'\" and consumer B's utility fimction is ll}r = xgyg-B. Suppose the total amount of good X available to both is 10!] and the total amount of good '1' is 50. Suppose consumer A has 26 units of good X and consumerB has 10 units ofgoodY. Let cr = 13'2 and!)I = 4.5. Assume there is no production of X and Y, but the two consumers can exchange one good for another. Starting from the initial altocation of goods X and '1' for each consumer, is it possible for consumer A and consumer B to trade with each other so that both consumers are better off? If so, explain how they should trade. if not, explain why:r not? Draw a graph illustrating your answers Consider a simple economy with two consumers, a single consumption good at and two time periods. Consumption of the good in period i is denoted b xt fort = 1, 2. Irrtertem poral utility functions forthe two consumers are: u' (31,12) =1l-Tl} +lnlil=t = 1 l...- Endowments are el = {10, ] and el = [2D, 5]. The good is perfectly storable, so what is not consumed in the first period can be saved and consumed in the second period. [a] Suppose the two consumers cannot trade with one another. How much does each consumer in each period? HDW well off is each consumer? [bl Now suppose that there are competitive 'spot' and'futures' market for this good. Let p1 be the {spot} price per unit in period 1, and let p2 be the [futures] price prevailing in period 1 for delivery of 1 unit of the good in period 2. 1|.I'l.lhat will be the equilibrium relative price, plfpl? For any of the exchange economy problems above for which you have calculated the Walrasian equilibrium: [a] Characterize the core of the economy when there is one agent of each type. [bl Showr that if you replicate the economy once, that there is at least one allocation which no longer belongs to the core. [c] Pick a Pareto efcierrt allocation which does not belong to the set of 1|.I'l.la|rasian equilibrium allocation, and construct a system of lumpsum taxes and transfers so that it is supported as a Walrasian equilibrium.
