H _l . - l d, I I - I; Suppose a consumer has to make intertemporal consumption choices 01,02 for single consumption good over two periods with a utility of consumption u(c) = ln(c) in each period and a personal discount rate of 3 = .95 so that the present utility value of consumption is equal u(cl) + u(02). Assume the consumer has perfect foresight so it is known that the price of the consumption good in each period will be p1 = 18 and p2 = 19 dollars respectively and the endowment of the consumption good in each period will be m1 = 11 and m2 = 9 units respectively. --.. l '- F] E l l l l l\"l= l I H \" l Returning to the extra credit problem on the previous assignment, suppose that there is no ination (i.e. p1 = 332 = 1) and that instead of borrowing and lending at xed interest rates (which is not available) the consumer can choose to invest a in a risky asset that has return 7",, = 3 in the good state with probability 71' = 2 /3 and return n, = 0.1 in the bad state. (a) What is the consumer/investor trying to maximize? What is the constraint? (b) Taking a similar approach to how we solved the two-good consumer's problem (or the two period investment problem), write down the condition on the marginal rate of substitution of consumption for investing that is necessary for the consumers decision to be optimal. (c) Use the condition in (b) to solve for the optimal consumption level 0'; and investment (1*. (Hint: this can be rather involved algebraically so I recommend using Wolfram Alpha, or some other toolbox to check your work) (d) With consumption on the horizontal axis, and investment on the vertical axis, graph three representative indifference curves: the curve tangent to the constraint, and two more indifference curves, one above, and one below. Plot the optimal (Cl: 61*) (e) Infer how much the consumer consumes in the period 2 bad state and in the good state