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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(C1​,C2​)=C1a​C21−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) 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 $]$

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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 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] Capital Taxation Assignment Discussion Paper