Evan Soltas
Jul 5, 2012

Facing Hour Problems

Dean Baker has an opinion piece in The Guardian in which he argues that hours-reduction legislation could solve the problem of unemployment in the United States. Baker is wrong, but instead of shouting "lump of labor fallacy" and leaving it at that, I want to go into a little bit of depth about why he is wrong and how he confuses the issues.

Baker writes:

[Government] can also employ people by encouraging employers to divide work among more workers. There is nothing natural about the length of the average work week or work year and there are, in fact, large variations across countries. The average worker in Germany and the Netherlands puts in 20% fewer hours in a year than the average worker in the United States. This means that if the US adopted Germany's work patterns tomorrow, it would immediately eliminate unemployment.
This is not how it works. Assuming a labor supply SL and demand curve DL, there is no relationship in the form of DL = h · n, where h is average weekly hours worked and n is number of workers, which can be exploited in the long run. In other words, the idea that we can reduce h by 20 percent and thereby induce an increase of n of 20 percent is incorrect.

Hours reduction fails because it doesn't resolve the most reasonable dynamic response of employees: to seek additional employment. If the welfare-maximizing use of their time is 40-hour workweeks which furnish them an income of 40 · w, where w is the hourly wage, these workers aren't suddenly going to change their minds (or more rigorously, their preferences or indifference curves) and accept a pay cut of 20 percent. What may very well result, however, is a more intense competition for the few created part-time jobs, such that the unemployed and and marginally employable must compete with the entire labor force, thus further disadvantaging them. (There is an argument that government intervention corrects the monopsony power of employers.)

Nor will Baker's proposal of a wage subsidy of the lost wages 0.2 · h · w be sufficient -- assuming that employees choose their allocation of labor and leisure according to the intersection of an indifference curve with an isocost line, then it follows that Baker's wage subsidy pushes out the isocost function such that they can earn more income at all amounts of leisure time, and thus it will only marginally reduce hours worked. The subsidy would need to fully undo the substitution effect. Depending on the shape of Americans' labor-leisure indifference curves, Baker's subsidy would have to be far more generous. (This entire discussion, however, overlooks the nature of Baker's argument for a subsidy, which conflates the cyclical shortfall of aggregate demand with a structural policy which cannot be easily or costlessly altered.)

On the labor-demand side, there are three reasons why there is no tradeoff between h and n. First, there are costs to transitioning between points (h, n); second, labor costs are not constant among all points (h, n); and third, the value to employers is not constant among all points (h, n). In the face of these problems, it is likely that firms will decrease their demand for labor in response to any maximum-hours legislation.

Baker cites Germany, of course, as his example of the success of hours reduction. Two, of course, can play that game. France has reduced average annual hours worked just as Germany has. That did not solve its unemployment problems.

Rather, Germany's employment recovery has nothing to do with its permanent reduction in hours. Its Kurzarbeit program has been helpful -- note the downturn in average hours worked in Germany in the previous graph -- but Baker falsely likens Kurzarbeit to permanent hours reduction. Also, Baker implies that the health benefits may justify hours reduction; that is, of course, an entirely separate argument about which I cannot comment.