3. Consider a nancial economy consisting of a single representative agent that solves the following two-period utility maximization problem with uncertainty in the second period: 1 1 . mic1(21)ax(H)?aln(c0) + 1n(c1(L)) + 1n(c1(H)) subject to co+Pa = 2+Pa0 c1(L) : 1 +D(L)a c1(H) = 3+D(H)a I'll now describe the various variables. The agent's period utility function is ln(-), and the agent derives utility from initial consumption c0 and the expected utility from future consumption. In the second period (t = 1) there are two possible states, the \"low\" state L (which arrives with probability 1/2) and the \"high\" state H (which arrives with probability 1/2). c1(L) is consumption in the low state, and c1(H) is consumption in the high state. The agent has two sources income. The first is an exogenous endowment of goods, which is 2 in the initial period, 1 in the low state, and 3 in the high state. Additionally, there is a \"stock\" with a xed supply of one. The stock trades at price P in the rst period, and the agent initially owns the stock (a0 = 1). The stock pays D(L) per share in the low state and D(H) per share in the high state. The agent decides how many shares a to buy or sell. A nancial equilibrium consists of agent choices (00,01 (L),c1(H),a) and a stock price P such that (i) the choices are optimal given P and (ii) markets clear, that is, a = 1, c0 = 2, c1(L) = 1 +D(L), and 01(11): 3+D(H). (a) Suppose D(L) = O and D(H) = 1. What is the equilibrium stock price P? (Hint: from class, we know that agent optimality is described by Per/(co) = %u'(cl(L))D(L) + %u'(cl(H))D(H). Calculate the price by using market clear- ing and u = 1n.) (b) Now suppose D(L) = 1 and D(H) = 0. What is the equilibrium stock price P now? (c) Give a brief intuitive explanation for why the price changes across parts (a) and (b)