2. Draw a graph showing the opportunity set. [0.5 points]

3. The government imposes a 20% tax on labor income. Solve for the new optimal levels of C1, C2, and S. [0.5 points]

4. Draw the new graph under the 20% tax on labor income. Explain any differences between the new level of savings and the level. What can you say about the income and substitution effects? [1 point]

5. 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?) [0.5 points]

6. Draw the new graph under the 20% tax on interest income. Explain any differences between the new level of savings and the level compared to the no-tax scenario, paying attention to any income and substitution effects. [1 point]

7. Returning to the labor income tax in part (a): What consumption tax rate would result in the same effects as the 20% labor income tax rate? [0.5 point]

3 Capital Taxation (5 points] - Consider a model in which individuals live for two periods and have Cobb-Douglas utility functions of the form U(C1,C2) = CC)-a where a = 0.5. They earn income of $1,000 in the first period and save S to finance consumption in the second period. The interest rate, r, is 5%. = 1. 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.) [1 point] 3 Capital Taxation (5 points] - Consider a model in which individuals live for two periods and have Cobb-Douglas utility functions of the form U(C1,C2) = CC)-a where a = 0.5. They earn income of $1,000 in the first period and save S to finance consumption in the second period. The interest rate, r, is 5%. = 1. 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.) [1 point]