In a two-period model, suppose that a consumers utility function is: U(c₁, c₂) = log(c₁) + log(c₂)

where c₁,c₂ are the consumption of a good (orange) in the two periods. The price of an orange is 1 in period 1, and 2 in period 2.

The nominal interest rate is 25%.

The endowments in the two periods are 1 and 2 oranges respectively.

Part a) State the period budget constraints for the two periods.

Part b) State the lifetime budget constraint

part c) Solve for the optimal consumption path (c₁, c₂)

Part d) Using the Fisher equation, find the real interest rate.