Oct 02, 2017 term paper 2

# CONSIDER AN INDIVIDUAL WHO LIVES FOR TWO PERIODS AND HAS UTILITY OF LIFETIME CONSUMPTION U = LOG(C…

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Consider an individual who lives for two periods and has utility of lifetime consumption U = log(C1) + 1/1+δ log(C2), where C1 and C2 are the consumption levels in the first and second period respectively, and δ, 0 1 > 0 in the first period and no income in the second period, so Y2 = 0. He can transfer some income to the second period at a before-tax rate of return of r, so saving \$S in the first period gives \$[1 + r]S in the second period. The government levies a capital tax at rate τ on capital income received in the second period. The tax proceeds are paid as a lump-sum transfer to the following generation. The present generation does not care about the next one.

a. What is the lifetime consumption profile of this individual? What is his lifetime indirect utility function expressed as a function of Y1 and

b. Evaluate the change in initial income Y1 that is required to compensate the individual for the welfare loss due to the capital income tax τ.

c. What is the impact of a tax rate change on consumption level in the first period? And in the second period? What conclusion about the welfare cost of capital income taxation can you draw from your analysis?

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