Suppose that consumer's utility function u(c, () 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 proportional income tax (as in the question above) and that lump sum txaes T = 0. (b) Write down the 'optimality condition'. (c) Show the optimal choices in a plot which has c in the y-axis and l in the x-axis for two cases: (i) when T = 0 (denote this by point A) and when (ii) T > 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 N is in the x-axis. (e) Re-do the plot from the previous question, but assuming that the income effect is stronger than the substitution effect.