A Refresher Course On Labor Markets

Professor Casey B Mulligan is by all accounts a better mathematician than Wonks Anonymous and holds a professorship at Chicago while Wonks Anonymous is a mere data harvester at a cube farm. Wonks Anonymous will, however, presume to challenge Professor Mulligan's recent post in Economix - click his name to read it.

Professor Mulligan believes that we will have continued slow growth for two reasons:
A variety of models can help explain the recession so far, and topredict where it may be going, but here I’d like to focus on the twovariables emphasized in my own research: productivity, and what are known as labor market distortions.
To be more specific. Productivity is rising so that output can grow faster than employment but at the same time various "well intentioned" government programs are preventing workers from taking advantage of this increased productivity. Instead they are withholding labor in order to collect food stamps and generous unemployment benefits.

In order to discover Professor Mulligan's fallacy and to see what is really going on in labor markets we will need to consider some simple geometry and economic theory. Here is a picture of a normal labor market:

Labor supply is determined by the human conflict between greed and sloth. The higher the wage the more labor is supplied. Labor demand is determined by the value or the marginal product of labor. That would usually be the price of the output produced by the last hour worked. This is sloped down because, in the short run, each additional hour worked produces less additional output. It may also reflect the fact that price needs to go down to sell more output.

The market is stable where the amount of labor offered is equal to the amount of labor demanded by firms. In this model firms take the wage as given and they always hire labor until the value of the output produced by the last hour worked/worker hired is equal to the marginal product of labor.

Now Professor Mulligan rightly observes that productivity - the economist would say average product of labor - is rising. Wonks Anonymous will go further to observe the marginal product of labor is also rising. Think about batting averages or grade point averages. If a batter is doing better than average or your test scores are improving then the most recent - that would be marginal - scores are drawing up the average.

We could move the labor demand curve but this will really introduce some unneeded complications to the analysis of Professor Mulligan's case. Professor Mulligan, you see, asserts that employment is down because of labor market distortions:

Labor market distortions are a collection of factors that hold back employment, even when employees are creating a lot of value.

These distortions include difficulties in job search, income taxes, minimum-wage laws and incentives that are eroded by means-tested government benefits(determining whether someone should receive benefits based on thingslike the person’s income). These factors can be difficult to quantifyindividually, but we know from the poor employment results that atleast some of them are important.

Reading this as an economist, Wonks Anonymous would guess that the good professor means that government programs have given greater weight to sloth in the eternal conflict between sloth and greed. For every wage less labor is supplied. Geometrically the labor supply curve has shifted back:

 

Employment declines from 146 million in December 2007 to about 144 million in December 2008. See table B-36 of the 2009 Economic Report of the President for details.

But something else happens in this simple model that stands in clear contradiction to reality. In this model the labor supply curve shift - less labor at any wage - should result in an increase in the wage but the real wage has been stagnant or declining since December 2007. For details see table B-47 of the Economic Report of the President.

Employers are faced with a sudden attack of labor laziness. They must pay a higher wage and they demand less labor. Employment falls, the marginal product of labor rises and the wage increases.

We might want to shift the labor demand curve out to indicate that productivity has risen for all levels of employment. This only makes Professor Mulligan's case worse. In this event the wage should rise even more.

Wonks Anonymous would like to see a labor market model of the usual sort, with continuous smooth demand and supply curves, that is consistent with the observed facts: lower employment, rising productivity and stagnant wage. Until one of the readers supply this model he will propose an ad-hoc and rather kinky model:

 

We have returned to the previous labor supply. The old labor demand curve is also retained for reference. A new, limited labor demand curve, follows the old labor demand curve until it reaches the current employment level - that would be 144 million. After that labor demand abruptly goes south. Firms might think about hiring more labor but they believe that they will be unable to sell the output. The value of the marginal product of labor more or less goes to zero.

In this market we see that productivity is up because we have moved back along the labor demand curve. At the same time the wage can be anywhere between $15 and $25. At wages less than $15 employers will have trouble finding the full complement of workers. At wages above $25 employers will cut back on employment.

At the current wage, call it $18, more labor is supplied than is demanded. Why don't employers cut wages?

  1. Incentives to cut wages are not so great. The wage is already significantly less than the marginal product of labor. Profits on the limited output sold are already high.
  2. Any wage cut will tend to drive away those workers who might have other opportunities. The marginal worker will grin and bear it. The most productive workers might pursue other opportunities.
In this model wages are sticky but flexible wages do not solve the employment problem. This problem is coming from limited demand for goods which has its origins in an entirely different market failure. More on this next post.

 

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