5. Suppose that consumer's utility function u{c.l 5} depends on consmuption c and leisure E, and has all the standard properties we typically assume. {a} Write down the maximization prohlem assuming that the agent is subject a proportional income tax [as in the question above} and that lump sum txaes T = ll. {h} Write down the 'optimality oondition'. {c} Show the optimal choices in a plot which has .2 in the yaxis and E in the xaxis for two cases: {i} when T = [1 {denote this by point A} and when {ii} 1" 3:- {1 (denote this by B). Assume that preferences are such that the substitution effect is stronger than the income e'ect. [d] Draw the implied lahor supplyr in a plot where w is in the yaxis and N3 is in the xaxis. {e} Redo the plot from the previous question, but assuming that the income effect is stronger than the substitution effect