Question

Question: Suppose that the owner of Boyer Construction is feeling the pinch of increased premiums associated with workers’ compensation and has decided to cut the wages of its two employees (Albert and Sid) from \(25 per hour to \)22 per hour. Assume that Albert and Sid view income and leisure as “goods,” that both experience a diminishing rate of marginal substitution between income and leisure, and that the workers have the same before- and after-tax budget constraints at each wage. Draw each worker’s opportunity set for each hourly wage. At the wage of \(25 per hour, both Albert and Sid are observed to consume 12 hours of leisure (and equivalently supply 12 hours of labor). After wages were cut to \)22, Albert consumes 10 hours of leisure and Sid consumes 14 hours of leisure. Determine the number of hours of labor each worker supplies at a wage of $22 per hour. How can you explain the seemingly contradictory result that the workers supply a different number of labor hours?

Short answer

Answer:

The number of hours of labor Albert supplies is 14 hours and Sid supplies is 10 hours.

The contradictory supply is explained by their choices of goods.

Step-by-step solution

Determining the opportunity set and the number of hours of labor for each worker.

The equation of their consecutive income would be:

$Income=25\left(24-L\right)$

As given,

Case:1

At wages of $25 per hour,

$$\begin{gathered} Income=25\left(24-12\right) \\ =25\times 12 \\ =300 \end{gathered}$$

	Albert	Sid
Leisure	12	12
Labor	12	12
Income	$300	$300

So, the opportunity set for both the workers is $600 if both work for 24 hours without leisure and $0 if choose 24 hours for leisure.

Case:2

At wages of $22 per hour,

For Albert,

$$\begin{gathered} Income=25\left(24-10\right) \\ =25\times 14 \\ =308 \end{gathered}$$

$$\begin{gathered} Income=25\left(24-14\right) \\ =25\times 10 \\ =220 \end{gathered}$$

	Albert	Sid
Leisure	10	14
Labor	12	12
Income	$308	$220

So, the opportunity set for both the workers is $528 if both work for 24 hours without leisure and $0 if choose 24 hours for leisure.

Explaining contradictory Choices

The reason behind the contradictory choices of both the workers is because they valuated each commodity to them. Albert chooses more labor hours values to work over leisure. Hence, he chooses more working hours.

Whereas for Sid valuation of leisure is more important than work, hence choosing leisure over work. Thus, Sid only works for 10 hours and Albert works for 14 hours.