What shape does the backward-bending labor supply curve have in practice?

What shape does the backward-bending labor supply curve have in practice?

by Anna and Yue

In microeconomic theory, the Slutsky equation tells us that when someone’s wage rate increases, due to the substitution effect she starts to work more in order to substitute consumption for leisure. But when the wage rate increases the value of the endowment goes up as well so the person may take extra leisure to consume this extra income. Which is the larger effect is an empirical matter and depends on the individual’s initial conditions and preferences. However, the theory states that in general the labor supply curve bends backward meaning that at some point the income effect will outgrow the substitution effect: We conducted a survey to find out whether this theoretical assumption holds. 

The survey included the following questions:

1. Imagine you work at MHC 10 hours per week and you are paid $8 an hour. Your wage increases to $12 an hour. Will you work more or less, and how many hours in total will you work assuming you are taking the standard load of 16 credits?
2. Now imagine your hourly wage increases to $20. How many hours will you work per week?
3. Your wage increases to $30. How many hours will you work per week?
4. Your wage increases to $50. How many hours will you work per week?
5. By how much must your hourly wage increase to make you work less and spend more time on studying and leisure?

22 students from Microeconomic theory class answered the survey questions. Below are the average results.

1. If wage rate rises from $8 to $12 an hour, students will work 11.5 hours per week on the average.
2. If the wage rate goes up to $20 an hour, students will work 12.48 hours per week on the average.
3. If the wage rate increases to $30 an hour, students will work 12.18 hours per week on the average.
4. If the wage rate rises to $50 an hour, students will work 12.68 hours per week on the average.
5. The answers vary from $8 to $1,000.

The survey results indicate that the labor supply curve for the 22 respondents will look like this:

In order to understand what happens to our labor supply curve and what gives it this shape, we divided the respondents into 5 categories based on their responses.

• For two people, an increase in the current $8/h wage rate will motivate them to work less.
• For six people any increase in the wage rate will not change the amount of time they already work (assumingly 10 hours per week).
• Six people will always work more as their wage rate increases from $8 to $50.
• Three people will work more at first, and as the wage rate rises even more, they will work less. These are the people who demonstrate the backward-bending labor supply curve.
• Five people will work less at first, but as their wage rate increases, they will work more.

What do these results tell us? The most important conclusion is that the wage rate at which the income effect will outgrow the substitution effect is different for each person, and only for 3 people in our sample this “break-even wage rate” is captured by the $8-$50 hourly wage range.