Question

Two individuals, Sam and Barb, derive utility from the hours of leisure (L) they consume and from the amount of goods (G) they consume. In order to maximize utility, they need to allocate the 24 hours in the day between leisure hours and work hours. Assume that

all hours not spent working are leisure hours. The price of a good is equal to $1 and the price of leisure is equal to the hourly wage. We observe the following information about the choices that the two individuals make:

Graphically illustrate Sam’s leisure demand curve andBarb’s leisure demand curve. Place price on the vertical axis and leisure on the horizontal axis. Given that they both maximize utility, how can you explain the difference in their leisure demand curves?

Short answer

The leisure demand curve of Barb and Sam are given below:

The demand curve of Sam is downward sloping, and the demand curve of Barb is upward sloping.

Step-by-step solution

Sam’s leisure demand curve 

The price is taken on the x-axis and leisure on the Y-axis.

It must be noted that the more a person will work, the less leisure they choose and vice-versa. In the graph above, the price of L increases from 8,9,10, and 11. The number of leisure hours for Sam is decreasing from 16,15,14 and 14. This indicates that Sam prefers less leisure over work.

Barb’s leisure demand curve

The price is taken along the x-axis, and Barb’s leisure on the x-axis.

The price is increasing from 8,9,10, and 11, and so are Barb’s leisure hours from14,14,15, and 16; this indicates that Barb prefers more leisure over work.

Difference between Sam’s and Barb’s Leisure demand curve.

Sam’s leisure demand curve is downward sloping, indicating that he prefers more work than leisure; on the other hand, Barb’s leisure demand function is upward sloping, depicting he prefers leisure than work.

This difference arises due to the income and substitution effect. To increase his income, Sam is substituting more work with leisure. Thus substitution effect is more than the income effect. Barb may have reached his substantial level of income. Therefore, despite a wage increase, he prefers more leisure than work, implying the income effect is greater than the substitution effect.