,kindly solve the following
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),wherezandlt denote, raspeclively,a.rmtrtinperiod2am investment inperiod 1. Assmuttereerdstseeintammalcapitdnmmmatmewldmm rate, r', is 10%perperiod tie, r' :01}. Finally, assurnethatthe ecmomvsirilid net fu'eimassetpositioniszerorj '20]. 91. it] p l'Considera two-period model ofa small open economy with a single good each period. Let preferences of the representative household be described by the utility function WEI} + r'nr'CEJ, where C1 and C2 denote consumption in periods 1 and 2, respectively, and lo denotes the natural logarithm. ln period 1, the household receives an endowment of G1 = 5. In period 1 the household receives profits, denoted by ?2, 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 D1f in period 1 to make investment l1 that enable the firm to produce goods in period 1 The production technology in period 2 is given by D2 = ?[l1]|, where (13'. and I1 denote, respectively, output in period land investment in period 1. Assume that there exists free international capital mobility and that the world interest rate, r*, is 1D% per period {i.e., r* = #11}. Finally, assume that the economy's initial net foreign asset position is zero {50* = CI]. e} Assume 02 = Milt} due to investment surge, but the rm feces a newly imposed collateral constraint of the form [)1f 5 K1 where l-tr denotes the value of the rm's collateral- Suppose that \":1 equals {15. Is the collateral constraint binding in period 1? What are the amount of investment in period1 , 02, and prot for period2'? \fConsider 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
