13. Consider a model in which individuals live for two periods and have utility functions of the form U  ln(C1)  ln(C2). They earn income of $100 in the first period and save S to finance consumption in the second period. The interest rate, r, is 10%.

a. Set up the individual’s lifetime utility maximization problem. Solve for the optimal C1, C2, and S. (Hint: Rewrite C2 in terms of income, C1, and r.) Draw a graph showing the opportunity set.

b. The government imposes a 20% tax on labor income. Solve for the new optimal levels of C1, C2, and S. Explain any differences between the new level of savings and the level in part (a), paying attention to any income and substitution effects.

c. Instead of the labor income tax, the government imposes a 20% tax on interest income.

Solve for the new optimal levels of C1, C2, and S. (Hint: What is the new after -tax interest rate?) Explain any differences between the new level of savings and the level in part (a), paying attention to any income and substitution effects.