Consider a rational risk-averse investor with vNM utility u(c) = lnc and = 0:8 who lives for two periods t = 0;1: In period t = 0; they invest in a non-dividend paying stock priced at S0. Consumption in period zero is c0 = 1;000: There are four possible states of nature at t = 1; occurring with probability pk for k = 1;2;3;4: State-contingent consumption and the stock prices are the following: State 1 2 3 4 p 0:1 0:2 0:5 0:2 c S 1; 000 1;100 1;200 800 100 105 90 110

2. Consider a rational risk-averse investor with vNM utility u(c) = Inc and 8 = 0.8 who lives for two periods t = 0, 1. In period t = 0, they invest in a non-dividend paying stock priced at So. Consumption in period zero is co = 1, 000. There are four possible states of nature at t = 1, occurring with probability p* for k = 1, 2, 3, 4. State-contingent consumption and the stock prices are the following: State 1 2 3 4 p 0.1 0.2 0.5 0.2 C 1, 000 1, 100 1, 200 800 S 100 105 90 110 (a) Solve for the equilibrium stock price So. (b) Find the Arrow price and the risk-neutral probability for state one