Question: utility function: U(c,l) = c + 1/2 lnl where c is consumption and l leisure. Assume there are no lump-sum taxes and no profit income:

utility function: U(c,l) = c + 1/2 lnl where c is consumption and l leisure. Assume there are no lump-sum taxes and no profit income: ? = T = 0. Also, assume hours available for work or leisure are h = 1 and the wage rate w = 1. George’s budget constraint is then (1+ t)c = 1?l where t is a consumption tax such that for a purchased unit of consumption George pays (1+ t) units

. (a) What is the optimality condition of George and the opportunity cost of leisure?

(b) Calculate his optimal consumption c, leisure l and labor supply Ns as functions of t.

(d) What is government’s tax revenue when t = 0.4?

(e) Explain briefly the difference between results in (c) and (d)

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