Optimal Taxation
Consider a two-period economy, where households have preferences
u(c1, c2) = lnc1 + βlnc2.
Households receive an income endowment y in the first period only, and decide optimally how to allocate it between consumption in the two periods. They can save at rate (1 + r) to finance consumption in the second period. The government has expenditures g in the first period that finances with consumption taxes {τ1, τ2} in the two periods.
Assume, to simplify the algebra, that β = 1 and r = 0.
(a) Write the household problem and determine optimal consumption {c*1, c*2} as a function of {y, τ1, τ2}.
(b) Suppose the benevolent government chooses the tax rates {7'1} 7'3} in order to maximize household welfare. Write the government problem and prove that the government choice satisfies "tax smoothing", i.e. τ*1 = τ*2.
(c) Explain the intuition for your result.