Jean has 200 hours each month that she can devote to either leisure (R) or work (L). Her current job pays her $10 an hour. Jean uses her wage income to pay for consumption goods (measured in dollars, or equivalently at a price p_c = 1). At the moment, Jean does not have any source of non-wage income. Jean's preferences for leisure (R) and consumption (C) are given by the utility function U (C, R) = 3C³R.

(a) How many hours a month L will Jean work?

Jean just won the lottery, which pays her a fixed amount m every month.

(b) How many hours a month L will Jean work if m = 2000?

(c) At what level of m will Jean choose to no longer work (L = 0)? Your answer should be the lowest m such that Jean chooses L = 0.

(d) Now assume that Jean's lottery payment m is equal to value you calculated in part (c) Jean's employer would like Jean to come back to work and offers her a wage increase. The wage increase is big enough that Jean chooses to work 50 hours per month. Decompose this increase in hours worked (starting from L = 0) into a substitution effect and an income effect of the wage change.