Fred has just arrived at college and is trying to figure out how to supplement the meager checks that he gets from home. “How can anyone live on $50 a week for spending money?” he asks. But he asks to no avail. “If you want more money, get a job,” say his parents. So Fred glumly investigates the possibilities. The amount of leisure time that he has left after allowing for necessary activities like sleeping, brushing teeth, and studying for economics classes is 50 hours a week. He can work as many hours per week at a nearby Taco Bell for $5 an hour. Fred’s utility function for leisure and money to spend on consumption is U(C,L) = CL.
(a) Fred has an endowment that consists of $50 of money to spend on consumption and ______hours of leisure, some of which he might “sell” for money. The money value of Fred’s endowment bundle, including both his money allowance and the market value of his leisure time is therefore $______. Fred’s “budget line” for leisure and consumption is like a budget line for someone who can buy these two goods at a price of $1 per unit of consumption and a price of $5 per unit of leisure. The only difference is that this budget line doesn’t run all the way to the horizontal axis.
(b) On the graph below, use black ink to show Fred’s budget line.
On the same graph, use blue ink to sketch the indifference curves that give Fred utility levels of 3,000, 4,500, and 7,500.
(c) If you maximized Fred’s utility subject to the above budget, how much consumption would he choose? $______.
(d) The amount of leisure that Fred will choose to consume is ______hours. This means that his optimal labor supply will be ______