Economies of Scale in Individual Labor Supply

Here are two stylized facts about labor economics:

  1. Utility is roughly logarithmic in income
  2. People who earn more per hour also work longer hours.

Together they present a puzzle – those higher income people are higher income primarily because they earn more dollars/hour, not because they work more hours. Yet if utility is logarithmic, there are diminishing returns to income, so we should expect people with higher hourly rates to work fewer hours.

Essentially, the first stylized fact suggests the income effect dominates, while the second suggests the substitution effect dominates.

One solution to this conundrum would be if the hourly rate changed with the number of hours worked. Maybe there are some jobs that simply cannot be done unless you put a huge amount of effort into them: you can’t be a part-time investment banker or corporate lawyer. If so, your productivity would increase dramatically with hours worked, so the demand curve for your labor would be upwards sloping. It’s a bit like a Giffen Good, except the causation goes

  • Higher Quantity -> More Valuable -> Higher Demand -> Higher Price

rather than

  • Higher Price -> More Valuable -> Higher Demand -> Higher Quantity

At the same time, every extra dollar is worth less and less to you, and each hour of leisure lost hurts more than the previous one, so you demand a higher hourly wage the more hours you work. So your supply curve is upwards sloping, roughly exponentially (to offset the logarithmic dollars->utility conversion)

When both supply and demand curves and upwards sloping, it is not clear there is a unique equilibrium – there could be multiple equilibria.

This could explain why we see such a difference between the incomes of

  1. The increasing number of people who do not work at all
  2. People who do ordinary jobs for around 40 hours a week
  3. Extremely high earning extremely hard working people

each group occupies a different one of these equilibria.

 

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s