Someone who earns $20/hour in the labor market and receives $50 per week in non-labor income.  Total number of hours available for work (h) and leisure (L) is 168 hours per week (i.e., T = 168=h+L).

a. Draw the budget constraint for this individual. Label the endowment point.
b. What is the maximum value of consumption that this individual could achieve in a week?
c. In the United States, the Fair Labor Standards Act requires workers to be paid 1.5 times their usual hourly wage for "overtime" work, defined as work in excess of 40 hours in a week. If this law applies to the worker described above, how does it change the budget constraint?
d. Now suppose Congress passes an income tax. The income tax applies to labor and non-labor income. The Fair Labor Standard Act is still in effect. The first $1,000 in weekly income is exempt from the tax. However, every dollar above $1,000 is taxed at a rate of 10%. (To be clear: the tax on $1,000 in income is 0, the tax on $1,001 is $0.10, the tax on $1,002 is $0.20, and so on.) Show how this new tax alters the budget constraint.

2. Jimmy has a utility function of U=CL, so his marginal utility of consumption is L and his marginal utility of leisure is C. Chuck has a utility function of U = C^2*L, so his marginal utility of consumption is 2CL and his marginal utility of leisure is C^2.

a. Suppose Chuck and Jimmy face the same budget constraint. Assuming both of them work at least a little bit, who spends more time at work?
b. Chuck and Jimmy have non-labor income of $500 per week. There are T = 168 hours available for work and leisure each week. What are Chuck and Jimmy's reservation wages?
c. In addition to their non-labor income, Chuck and Jimmy earn an hourly wage of $50 per hour. How many hours does Chuck work? How many hours does Jimmy work?
d. Jimmy buys a winning lottery ticket. His winnings will be paid out in tax-free installments of $2,000 per week for the rest of his life, bringing his non-labor income to $2,500 per week. How many hours per week does he work after winning? In your own words, describe how we can interpret this shift.
e. Chuck's hard work earns him a pay raise: His hourly wage is now $75 per week. How many hours per week does he work? Which is larger for Chuck: The income effect, or the substitution effect?