Capital Taxation Assignment Discussion Paper

3 Capital Taxation [5 points] Consider a model in which individuals live for two periods and have Cobb-Douglas utility functions of the form $U(C_{1},C_{2})=C_{1}C_{2}$ 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 $C_{1}$, $C_{2}$, and $S$. (Hint: Rewrite $C_{2}$ in terms of income, $C_{1}$, and $r$.) (1 point) 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 $C_{1},C_{2}$, and $S.[0.5$ points $]$

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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 $C_{1},C_{2}$, 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]

Capital Taxation Assignment Discussion Paper