There’s been a fair amount of discussion on the web lately (here and here, for instance) about the minimum wage and monopsony. As is well known in economics, a skillfully set minimum wage, in the presence of monopsony in the labor market, can actually increase employment. I don’t have a graphical proof handy but I expect that many labor economics texts have such a graphical proof.

Here’s the proof in words. To say that a firm has monopsony power is to say that the supply curve of labor to the firm is upward-sloping. That is, the firm is not a price-taker in the labor market. So when the firm that employs n workers and pays Wn per worker wants to hire one additional worker, it needs to pay more to each worker than it paid when it hired n workers. Call this new wage Wn + x. But that means that the cost of hiring that n + 1st worker is not the wage, Wn + x, that the firm pays the worker: it’s that wage, Wn + x, plus x times n. The reason: it pays all the other n workers that increment, x, also. Because the firm recognizes this, it hires up to the point where the value of marginal product = Wn + x + x*n. Now, if the government skillfully sets a minimum wage a little above Wn + x, the firm knows that it can’t reduce the wage by hiring fewer people and also knows that it won’t raise the wage by hiring a few more people and so it hires more people.

The main reason people started talking about monopsony in the context of the minimum wage in the 1990s was the study, and later the book, by David Card and Alan Krueger. They were trying to explain why they found their result, which was that an increase in the minimum wage in New Jersey, while the minimum wage in Pennsylvania held constant, did not decrease employment in fast food restaurants in New Jersey relative to in Pennsylvania. Various people, most notably David Neumark and William Wascher, criticized the Card/Krueger data and, using better data, found the more-standard result. I don’t want to get into that here.

Instead, I want to note something about the monopsony explanation. Here’s what I wrote in my review of their book:

What would have to be true for the minimum wage not to destroy jobs? As George Stigler (1946) pointed out in his seminal article on minimum wages, if the employer has monopsony power in the labor market, a skillfully set minimum wage can actually increase employment. Card and Krueger are aware of this exception, and they speculate in Chapter 11 that the market for unskilled labor is indeed monopsonistic. How could the market for unskilled labor be monopsonistic when so many employers are competing for unskilled labor? Card and Krueger have a few answers and, at the same time, no answers. They discuss (pp. 373-83) various models in which firms set different wage rates for the same quality of labor, but they don’t ever say which model they think explains their results. In two models they analyze, some firms set high wages and workers respond with lower turnover, while other firms set lower wages and accept higher turnover. A minimum wage, then, could reduce turnover at the low-wage firms. Card and Krueger claim that lower turnover implies higher average employment. I don’t think so. There’s reason to believe that employment would, on average, be lower. Presumably, low-wage, high-turnover employers believed themselves to be maximizing profits. That is, the loss from the increment of turnover was less than the loss from paying higher wages to avoid that increment of turnover. Given that assumption, when the government steps in and imposes a minimum wage, the net cost of an employee is higher. By the law of demand, the employer will hire fewer employees.

Interestingly, Card’s and Krueger’s own data on price contradict one of the implications of monopsony. If monopsony is present, a minimum wage can increase employment. These added employees produce more output. For a given demand, therefore, a minimum wage should reduce the price of the output. But Card and Krueger find the opposite. They write: ‘[P]retax prices rose 4 percent faster as a result of the minimum-wage increase in New Jersey…’ (p. 54). If their data on price are to be believed, they have presented evidence against the existence of monopsony. David R. Henderson, “Rush to Judgment,” MANAGERIAL AND DECISION ECONOMICS, VOL. 17, 339-344 (1996)