Suppose a worker gets a weekly check equal to $1,000 from a risk-free investment, has 60 hours of weekly leisure that can be devoted to work and can earn a wage of $40 per hour.
a. Illustrate this worker's budget constraint, with weekly leisure hours on the horizontal and weekly consumption (in dollars) on the vertical.
b Illustrate what happens to this worker's budget constraint when the weekly investment check increases to $1,500.
c. Illustrate what happens to this worker's budget constraint when instead the wage increases to $50 per hour.
d. Suppose the worker can hire help at $20 per hour, and each hour of help adds a half an hour to his available leisure. Will the budget constraint described in (a) change?

What will be an ideal response?

a. This budget constraint has a vertical intercept of $3,400 and a slope of -40 up to 60 hours of leisure (at which point the consumption level is $1,000). It then becomes a vertical line down to the horizontal axis (because the worker cannot buy leisure with the investment income.)


b. When the investment check increases by $500, the vertical intercept increases by $500, the slope does not change and the budget constraint still becomes vertical at 60 hours of leisure.


c. The vertical intercept now goes to $4,000, and the slope up to 60 hours of leisure increases (in absolute value) to -50. At 60 hours of leisure, consumption has fallen to $1,000, with the budget constraint become perfectly vertical at that point.


d. Yes --- the budget constraint would now have a slope of -40 throughout, all the way down to the horizontal axis. This is because the worker can now not only sell leisure for $40 her hour but also buy it for $40 per hour, which implies that he can get as much as 25 additional hours of leisure by spending the $1,000 of investment income.