2. (State Preference Theory) Suppose there are two securities available: A and B. The price of A today is $100, and the price of B today is $150. There are two states in the future which can affect the payoffs of A and B. If state 1 realizes, then A's payoff is $200, B's payoff is $80. If state 2 occurs, then A's payoff is $20, B's payoff is $240. a. Compute the prices of pure securities. (7.5 points) b. Suppose now there is a new security C with $120 payoffs in state 1 and $100 payoffs in state 2 . What is the price of C today? (7.5 points) c. Suppose now the market only trades pure securities for the two states. The prices of pure securities 1 and 2 are 0.8 and 0.2. The state 1 probability 1=32. Your utility function is u(x)=x. With $100,000 starting wealth, you can consume part of it and invest the rest. Your investment payoffs will be your future consumption. You aim to maximize the sum of your utility of current consumption and the expected utility of future consumption. How much should you consume today, how much do you invest in pure security 1 and pure security 2 respectively? (10 points)