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 the mattress. Suppose the variable I=fraction investead at the bank. Suppose the 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

Question: What is the optimal level of Investment, I*, the optimal level of period 1 consumption, C₁*, the optimal level of period 2 consumption, C₂*, and the optimal level of expected utility, U* ?