Morty lives for two periods and has the following utility function: U(C1, C2) = (1 + r) ln C1 + ln C2 where C1 and C2 are his consumption in period 1 and period 2, respectively, and r is a parameter that you should take as given. All we know is that r > 0. Morty has a labor income of $100 in period 1 and no labor income in period 2. If he consumes less than $100 in period 1, he can save the remainder in the bank and earn some interest. The interest rate is also r.

(c) (10 points) Now the government imposes a 10% tax on peoples interest income. That is, only the interest Morty earns on his savings is taxed, the principal is NOT taxed. Solve for the new optimal levels of consumption, C 1 and C 2 . What are the substitution effect (SE) and the income effect (IE) of the tax on C1, respectively? Which effect dominates?