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) = C₁^a C₂^1-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%.

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.) [1 point]

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

c) The government imposes a 20% tax on labor income. Solve for the new optimal levels of

C1, C2, and S. [0.5 points]

d) 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]

e) 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]

f) 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]

g) 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]