f.'l_"" 4. (6 points) The representative household is risk averse and has a utility u(c) = = where v = (1.8 and a subjective discount factor 3 = 0.95. The representative houehold lives for three periods, denoted as periods 0, 1, and 2. Utility from the next period is discounted by 3, and utility two periods from now is discounted by 3% Standing at any point in time and looking one period ahead, one finds that there are two possible states, B (boom) and R (recession). State B occurs with a probability of (0.8 and R with a probability of 0.2, regardless of history. Then the chance of observing state B next period and state R the period after is 0.8 - 0.2 = 0.16. This economy could go through 2 possible paths after period 1, which are denoted by B and R, and 4 possible paths after period 2, which are 85, BR, BB, and RE. The first letter denotes the state realized in period 1 and the second is the state realized in period 2. The path an economy goes through is called its event history. There are 7 different consumption goods indexed by date and event history, denoted by , 1p. Cir. Capp: C2BR; Copp, and capgr. Their prices are go = 1. qis, qir, G285; q2881, (2rEB, and garr, respectively. This is an endowment economy. 3, = 1. Endowment grows at 4% in state B and -2% in state R. The endowment sequence after the first period is the following. g =104 yz=0098 Yapp = 1.04 - 1.04 Yapr = 1.04 - m'i YWopp = n-qg - 1.04 Yapr = ng' : D(}S (a) (3 points) Set up the representative household's problem and define the com- petitive equilibrinm. (b) (2 points) Compute the prices. How do the prices in the second period (g2pg. G26Rr, G2re. and qarr) relate to those in the first period (q1p and q1g)? () (1 point) A financial asset promises 1 unit of consumption good next period no matter what state is realized. What is its price? (The price of an asset is expressed in units of consumption goods at the point when it is offered.) Does the price of this financial asset depend on when it is offered