Under the Diamond-Dybvig framework, assume that individuals have the option to invest a fraction of their currency at a bank and put the remainder under a mattress. Suppose the variable I = fraction invested at the bank. Suppose that ex-ante utility is represented by:

U = (1/2) u(C1) + (1/2) u(C2)

where C1 is consumption in period 1 and C2 is consumption in period 2, and

C1 = 1 - (3/4) I

C2 = 1 + 3I

With u(C) = - 1 / C

a) What is the optimal level of investment, I*?

b) What is the optimal level of period 1 consumption, C1*?

c) What is the optimal level of period 2 consumption, C2*?

d) What is the optimal level of expected utility, U*?