Consider a representative consumer with preferences over consumption c and leisure l given by u(c, l) = 1 4 ln(c) + 3 4 ln(l). Assume that the price of consumption is normalized to p = 1, and the consumer has h = 24 hours of total time available to divide between work and leisure. The consumer's wage per hour of work is w = 8. The consumer also pays lump-sum taxes of T = 32, and she receives no dividend (profit) income so = 0. (a) Write out the consumer's budget equation, and draw a graph of the budget con- straint. (b) Solve for the optimal decisions c and l. How many hours per day is the consumer working?

(c) Suppose the consumer inherits a bunch of stocks from a rich uncle, so the consumer's dividend income increases from = 0 to = 16 (but she still receives the wage of w = 8). Solve for the new optimal choices of c and l. Relative to the solution in part (b), do consumption, leisure, and hours worked increase, decrease, or stay the same? Give an intuitive explanation for why these changes occur. (d) When the dividend income changes in part (c), determine whether the consumer experiences an income effect, a substitution effect, both, or neither. If both income and substitution effects are present, explain which effect is larger and how you determine this. (e) Suppose the consumer's wage now increases to w = 12, and all else remains as in part (c). Solve for the new optimal choices of c and l. Relative to the solution in part (c), do consumption, leisure, and hours worked increase, decrease, or stay the same? Give an intuitive explanation for why these changes occur. (f) When the wage changes in part (e), determine whether the consumer experiences an income effect, a substitution effect, both, or neither. If both income and substitution effects are present, explain which effect is larger and how you determine this.