Suppose you have 24 hours per day that you can allocate between leisure and work

Question

Suppose you have 24 hours per day that you can allocate between leisure and working at a wage of $2 per hour.

a.Draw your budget constraint between “leisure hours” on the horizontal axis and “income” on the vertical.

b.Draw in your optimum point. Keeping in mind that the number of hours you spend working is equal to 24 minus the number of hours that you spend at leisure, plot a corresponding point on your labor supply curve.

c.Now suppose that the wage rate rises to $3 per hour. Draw your new budget constraint, your new optimum, and a new point on your labor supply curve.

d.On your indifference curve diagram, decompose the effect of the wage increase into a substitution effect and an income effect. What is the direction of the substitution effect? What is the direction of the income effect if leisure is a normal good? What is the direction of the income effect if leisure is an inferior good?

e.True or False: If leisure is an inferior good, the labor supply curve must slope upward, but if leisure is a normal good, the labor supply curve could slope either direction.

f.Whose labor supply curve is likely to slope upward more steeply: somebody whose income is derived entirely from wages, or somebody who has a large nonwage income? Why?

Explanation / Answer

a) The worker’s income Y is given by

            Y = wh

Where Y is the worker’s income

            h is the number of hours worked

            w is the hourly wage rate

Since wage rate is $2 and the number of hours worked is total endowment of time minus leisure hours, the worker’s income Y is given by

            Y = 2 (24 – L)

            Y + 2L = 48                …. (1)

which is the budget constraint. The maximum income is 48 (=24×2). The maximum leisure is 24 hours. So the budget line is shown below.

b) The preferences of the consumer are not known. We arbitrarily pick income of $36 and leisure of 6 hours as the worker’s optimum.

(c) The wage is $3. The worker’s income Y is given by

            Y = 3 (24 – L)

            Y + 3L = 72                …. (1)

which is the budget constraint. The maximum income is 72 (=24×3). The maximum leisure is 24 hours. So the new budget line is shown below as CB. The new optimum is point F.

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