Suppose that consumer's utility function u(c, l) depends on consumption c and leisure l, and has all the standard properties we typically assume.
(a) Write down the maximization problem assuming that the agent is subject a pro- portional income tax (as in the question above) and that lump sum taxes T = 0.
(b) Write down the 'optimality condition'.
(c) Show the optimal choices in a plot which has c in the y-axis and in the x-axis for two cases: (i) when 7 = 0 (denote this by point A) and when (ii) 7 > 0 (denote this by B). Assume that preferences are such that the substitution effect is stronger than the income effect.
(d) Draw the implied labor supply in a plot where w is in the y-axis and Ns is in the x-axis. 3 (e) Re-do the plot from the previous question, but assuming that the income effect is stronger than the substitution effect.
