Reference no: EM132476884

Samantha lives for two periods, period 1 and period 2. She has no initial wealth. In this first period she works L hours at a wage of w per hour. In the second period of life, she is retired and supplies no labour. There is a perfect bond market on which Samantha saves an amount S in the first period of life, which earns a net interest rate of r. Samantha has a preferences over consumption C1 and C2 and effort L as follows: U(C1, C2, L) = ln C1 + β ln C2 + ln(1 - L) where C1 and C2 are consumption in period 1 and period 2, respectively. β = 1/(1 + ρ) and ρ > 0. The government levies a flat tax at rate τ1 on income earned in the first period of life and a lump-sum tax of T. Samantha owes no tax in the second period of her life.

(a) Write down Samantha's budget constraint in period 1 and period 2 and her intertemporal budget constraint.

(b) Derive Samantha's optimal choices of consumption, work and saving as a function of the tax rate.

(c) How much revenue does the government raise as a function of the tax rate? Find the tax rate at which government revenue is maximized. What is the maximum amount of revenue the government can raise?

(d) Is there a Laffer curve?