Hope you solve this problem as soon as possible. Need some details, too. Suppose we have a household with the following (non-differentiable) utility...

Hope you solve this problem as soon as possible. Need some details, too.

Suppose we have a household with the following (non-differentiable) utility function:

U = min{Ct , Ct+1}.

With this utility function, utility equals the minimum of period t and t + 1 consumption.

For example, if Ct = 3 and Ct+1 = 4, then U = 3. If Ct = 3 and Ct+1 = 6, then U = 4. If Ct = 5 and Ct+1 = 4, then U = 4.

1. Since this utility function is non-differentiable, you cannot use calculus to characterize optimal behavior. Instead, think about it a little bit without doing any math. What must be true about Ct and Ct+1 if a household with this utility function is behaving optimally?

2. The period t and t + 1 budget constraints are the same as given in class. Use the condition from (1) and the intertemporal budget constraint to derive the consumption function.

3. Is the MPC between 0 and 1? Is consumption decreasing in the real interest rate?