Mr. Cog works in a machine factory. He can work as many hours per day as he wishes at a wage rate of w. Let C be the number of dollars he spends on consumer goods and let R be the number of hours of leisure that he chooses.
(a) Mr. Cog earns $8 an hour and has 18 hours per day to devote to labor or leisure, and he has $16 of nonlabor income per day. Write an equation for his budget between consumption and leisure. ______
Use blue ink to draw his budget line in the graph below. His initial endowment is the point where he does no work and enjoys 18 hours of leisure per day. Mark this point on the graph below with the letter A.
(Remember that although Cog can choose to work and thereby “sell” some of his endowment of leisure, he cannot “buy leisure” by paying somebody else to loaf for him.) If Mr. Cog has the utility function U(R,C) = CR, how many hours of leisure per day will he choose? _____. How many hours per day will he work? _______.
(b) Suppose that Mr. Cog’s wage rate rises to $12 an hour. Use red ink to draw his new budget line. (He still has $16 a day in nonlabor income.) If he continued to work exactly as many hours as he did before the wage increase, how much more money would he have each day to spend on consumption? ____ But with his new budget line, he chooses to work
_____ hours, and so his consumption increases by _____
(c) Suppose that Mr. Cog still receives $8 an hour but that his nonlabor income rises to $48 per day. Use black ink to draw his budget line. How many hours does he choose to work? 6.
(d) Suppose that Mr. Cog has a wage of $w per hour, a nonlabor income of $m, and that he has 18 hours a day to divide between labor and leisure.
Cog’s budget line has the equation ______________. Using the same methods you used in the chapter on demand functions, find the amount of leisure that Cog will demand as a function of wages and of nonlabor income.
Mr. Cog’s demand function for leisure is _____________.
Mr. Cog’s supply function for labor is therefore __________.