# Minimum wage and monopsony

A friend pointed me towards a description of a labor market where a minimum wage would increase employment and output from two economists at the Cleveland Fed.  I’m not sure whether the model they propose is novel, or from the literature.  I wanted to explore this claim in more detail, since I am told that the presence of monopsony employers is an important feature of arguments in favor of the minimum wage.

Consider a local labor market in which a large coal mine is the community’s dominant employer (a monopsony). Because the mine has negligible competition from other firms, it can set a wage that maximizes its profits. Unlike a competitive firm, however, a monopsony cannot hire as many workers as it wants at a constant wage. If the mine wants to add workers, it must offer a higher wage to attract new labor-force entrants. Suppose, for instance, that 10 potential hires have reservation wages below \$5 and another candidate has a \$6 reservation wage. If the mine wants to hire 11 workers, it must raise its wage from \$5 to \$6 across the board. Thus the mine’s cost of adding one worker, the marginal cost of labor, has two elements: the \$6 hourly wage it pays one person plus a \$1 hourly increase for each of the other 10. In this case, the marginal cost of labor is \$16 (\$6 + \$10).

The firm maximizes its profits when the cost of having an additional worker equals the value of that person’s output. Thus, in the right-hand panel of figure 2, the point where the marginal product of labor intersects with the marginal cost of labor is the employment level for a monopsonistic firm. Notice that the employment level is lower than it would be in a competitive labor market. The wage, which can be read on the labor supply curve for the monopsonistic employment level (denoted wM in figure 2), is lower than the competitive wage. So a monopsonistic firm employs fewer workers and pays them less than their marginal product.

Suppose that Congress sets a federal minimum wage that is higher than the monopsony’s wage but still below the competitive one. In that case, the curve representing the marginal cost of labor (right-hand panel of figure 2) flattens until it intersects with the labor supply curve. This happens because the cost of an additional worker is now simply the minimum wage (as long as the firm does not want to hire more workers than the number willing to work at or below this minimum wage). In this case, a minimum wage increases employment by mitigating the negative effects of a monopsony’s power. All workers gain: More of them have jobs, and those who do receive a higher wage. The employer loses because the minimum wage policy reduces its profits. In fact, the optimal level for the minimum wage is the competitive wage that maximizes employment (right-hand panel of figure 2).

I think this model fails to accurately portray the economics of a monopsony employer.

1. Suppose the firm knows the reservation wage of each worker.  If it were truly a monopsony it would just pay that amount, since it has all the bargaining power it would not be constrained by a constant wage rate.
2. Suppose the firm does not know the reservation wage of each worker.  It would just announce how much it would be willing to pay the nth worker for n = 1 to n = population and accept bids for employment.  Without unionization or collusion this handles heterogeneity in reservation wage.  This obviously would not happen in reality, but nor would total monopsonies, if that’s our metric.  The firm probably also has reasonably good heuristics about reservation wages based on easily observable factors.  (Additionally, in the above case it is almost certainly true that the government in charge of a minimum wage has substantially less information about reservation wages, preventing a reasoned ability to set policy.)
3. Suppose a monopsony initially hires 5 workers at \$1 and another 3 workers at \$2.  The imposition of a minimum wage at \$2, assuming the premise about equal productivity and everything else is correct, would increase wages for low-reservation workers and reduce profits by \$5.  This effect remain true even if all workers had a reservation wage of \$1.  This suggests the premise is unnecessarily complex and noisy; or relies on odd assumptions about ability to pay heterogenous wages for a supposed monopsony.
4. Furthermore the reduction in profits from the minimum wage is realized as an increase in the cost of capital.  This increases the required rate of return from workers on new projects, which unfairly hurts those whose necessary value to firms falls below the minimum wage as required rate of return increases.  The minimum wage is not statically imposed but affects future periods, cost of capital, etc.
5. The example in (3) provides a distributional effect.  However this could just be accomplished through tax and transfer.  There is the concern that this would let the monopsony underpay the higher reservation wage worker since the government pays some or all of the difference.  To the extent that is the case, the government can just increase the tax rate.  This doesn’t matter as it normally would since the only taxable entity is a monopsony.
6. It seems unrealistic that there is no correlation between reservation wage and quality of labor.  For example, the higher reservation may reflect greater talent in normal economies.  In a monopsony it just reflects a higher labor preference.  However, that means the increase in employment is not welfare increasing per se.  Even in the contrived example of constant wages, imposing a minimum wage at the higher reservation only results in surplus for the lower wage employees, as the new entrants sacrifice equally-valuable leisure.
7.  In reality there are probably not monopsonies like the ones described above.  Congress should not set a federal minimum wage on that basis.

Let me briefly address the idea that minimum wage addresses the problem of market wages being far lower than return to each worker.  Surplus has to be distributed between two parties in some way.  If workers receive less because they have lower bargaining power, it might be a good idea to encourage union formation.

It’s unclear why the minimum wage would increase bargaining power – especially since it prohibits threat of competition for those who have a preference for easier jobs.  Some unskilled workers that like peace and quiet might have worked for \$5/hr folding clothes for college students in a remote suburb.  The imposition of a \$15/hr minimum wage might force such workers into low-end construction or other harder jobs.  Employment does not fall and wages increase but happiness and freedom does.

In any case, the normative claim should not be “workers should deserve x percent of surplus” but rather “workers should be rich enough to buy y“.  A tax and transfer looks like a better solution here, even in the face of contrived examples.

I also don’t understand the following claim from the article.

If the market wage is too low and workers lack bargaining power, the introduction of a binding minimum wage strengthens labor force participation, even though the duration of unemployment increases. In contrast, if the market wage is high, a minimum wage reduces the supply of vacancies and increases unemployment duration, which discourages workers from entering in the labor force.

1. Market wages may be low relative to productivity if reservation wages are also low for some reason.  Meaningful lack of labor force participation occurs when market < reservation < value.  For one, this is unlikely to occur with heterogenous wages which would be attempted in any number of creative ways were such a situation to ever exist.
2. The existence of low participation could just as easily reflect value < reservation as it does market < reservation.  In normal economies, increasing the minimum wage will result in mandatory productivity that may be greater than some people can reasonably muster, reducing participation.

Finally let’s just observe that we aren’t capable of measuring productivity, marginal revenue product, reservation wage, competitive equilibrium wage, bargaining power in at the conceptual and statistical resolution necessary to advance a policy that can change the lives of many individuals.