Work, leisure, and healthy time

The time constraint

Health time and sick days come off the top of the year; Ed splits what is left, S, between work and leisure.

Work, T_W

Days at the job. Each one pays the wage, so work is the only way income appears.

Leisure, T_B

Days off: a Saturday hike, dinner with friends, a week at home over the holidays. No pay, but Ed wants them.

Health time, T_H

Days spent making himself healthier: workouts, cooking instead of ordering in, the dentist, a yearly physical, physical therapy after an injury.

Sick days, T_L

Days illness takes from him: the flu, a migraine, recovering from surgery. No pay and no fun, which is why cutting them frees real time.

Try this: raise the wage. Which end of the line moves, and which stays put? Why?

Ed’s preferences

Ed wants more income and more leisure. Each indifference curve links combinations he likes equally, and higher curves are better. The slope of a curve, the marginal rate of substitution (MRS), is how much income he would give up for one more day off.

Try this: slide to 30 days, then to 250. Why would Ed give up so much more income for a day off when he has little leisure?

Ed’s best choice

Ed can only pick points on his line. Drag his dot and compare what one more day off is worth to him (his MRS) with what that day would pay (the wage). The green area holds affordable points he likes better.

Try this: find the point where the curve just touches the line. Why can’t Ed reach a higher curve than that one?

More healthy time

Ed spends more days on health-producing activities. That uses time, but it also cuts his sick days. If he saves more sick days than he spends, his available time S grows and the whole line shifts out, parallel, because his wage hasn’t changed.

Result: investing in health leads to higher income and more leisure.

Try this: keep adding health days past 40. Does available time keep growing? This is the slide’s “assuming there’s a positive net effect.”

Check yourself