The existence of the monopsony model does not imply a minimum wage is optimal

Most people support a minimum wage for rather stupid reasons. There’s the people with money — there’re the people without — simply make them be paid more. That it might have unintended consequences hardly crosses their mind. We should expect that declaring the price of anything to be beyond what the market will bear to reduce its utilization, all else being equal. There are much more theoretically sound reasons to support a minimum wage, such as the monopsony model, but I would submit that some of those who believe the monopsony model describes the world made their mind up first on the necessity of the minimum wage, and only then proceeded to finding reasons to support it. I believe that the monopsony model is applicable to the real world, but that does not logically proceed to support for a minimum wage, nor should it.

i. The case for the minimum wage

Perhaps I should have defined what I am attacking before I started. The monopsony model describes the inverse of a monopoly — instead of only a single seller, there is a single buyer. In this case, the monopsonist is buying labor. In a perfectly competitive world, the labor supply curve is flat. There are always more workers available at a given price (in the language of economics, the supply is perfectly elastic). Thus they hire until the cost of hiring one more worker precisely equals the additional production they will bring. (Or, where the demand curve crosses the supply curve.) For the monopsonist, however, the labor supply curve is upward sloping. If we presume they pay the same wage to all workers, then the only way to hire an additional worker is to increase the wages paid to all workers in the enterprise. Under such a condition, the marginal cost (this is the cost “on the margin”; the cost of additional unit) of hiring labor advances considerably quicker than the supply curve. It now crosses the demand sooner than before, and so the firm does not hire as many workers as a firm in a competitive environment would.

 

A picture is helpful. MC is the marginal cost of hiring one more worker, S the supply of labor, and MRP the marginal revenue product from hiring another worker. In the competitive world, the firm hires out to L’ and the wage is at W’ — if they didn’t, another firm would. In a monopsony, where they are the only buyer, they hire out to L, but price down where it crosses the supply line — not marginal cost. In this way, profits are maximized. The case for a minimum wage is that by raising the wage rate to W’, the firm will hire more, not fewer, workers. While the monopsonist is worse off, the gains to everyone else exceed their losses.

That there is only one buyer is patently unrealistic, but the monopsony model does not require that per se. All that it requires is that labor supply curves, from the perspective of an individual firm, slope upwards. This is not remotely unrealistic. Indeed it is more realistic to say that all firms have some amount of market power. It is costly to change jobs, you don’t know what it’s like until after you start, and so on and so on. Any amount of distortion opens the possibility for government intervention to be improvement — if the government could tell precisely how much they were deviating by.

ii. But, no: the case against

Yet, I think this case fails. The first is that it is frankly impossible to tell what the supply and demand curves are at any given moment. We can observe where they cross, of course, but to fill out other values requires heroic imputations, or an assumption that nothing has changed since the last time you had some natural experiment to measure it. It is striking how econometrics, in particular the natural experiment, was developed largely to identify supply and demand schedules. That to determine the approximate position of some parts of the supply and demand lines takes a substantial statistical effort and fortunate luck should go some way to explaining the impossibility. It brings to mind how Vickrey’s 1961 classic paper introducing the second-price auction starts by examining the idea of “counterspeculation” — the government making payments whenever outcomes deviated from competitive outcomes to make trades occur — was dismissed at totally infeasible.

Moreover, there would have be different minimum wages for every single firm. Firms do not hire all from the same pools of labor, but a minimum wage affects all of them. The minimum wage is only beneficial so long as it is raising it to W’ — beyond that unemployment results. A rise in the minimum wage would sweep many industries beyond their personal W’. It would not do to try and be more realistic in allowing for firm market power, and then salvage the policy prescription with an unrealistic denial of labor heterogeneity!

Moreover the fitting of a monopsony model to low wage labor is plainly tendentious. Who goes to a strip mall and thinks to themselves, “ah yes, this looks like one buyer to me”. I do not. Nor do stories of conspiracy make sense, for it fails to consider their own self-interest. (People are not at all motivated by their class interest). 

There have been numerous studies empirically measuring the effect of the minimum wage. The classic which kicked off the literature is Card and Krueger, 1994, which found that the minimum wage actually increased employment. This was contradicted by Neumark and Wachser, 2000, who used payroll-tax data instead of telephone surveys for data collection, and found that the positive effect was purely due to inaccurate data. The method they used, and which has been used repeatedly since, is called a “difference-in-differences”. Suppose the minimum wage is raised in New Jersey, but not in Pennsylvania (as with Card and Krueger). You can compare employment in the counties which border each other — the assumption being that their proximity is controlling for a lot of unobserved confounders. It would be inappropriate to compare New Jersey and Wyoming, because they’re very different, but the hope is that New Jersey and Philadelphia are all part of the same labor market. The vulnerability of this is other changes which affect one state only, or affect one more than the other. Imagine if New York City was undergoing a boom, causing more people to move to New Jersey, and for relative prices to rise. You could not meaningfully control for this, but there it would be, mucking up your data.

The consensus is that an increase in the minimum wage does indeed cause a small increase in unemployment, as well as a reduction in hours worked (for those studies which measure hours). The empirical literature goes on forever, but is stunningly well-covered at the Wikipedia page on the minimum wage. If you are interested in reading the back and forth, go check it out there.

One should remember a few things. The first is that elasticities are greater in the long run than in the short run, but we can only really measure the short run. You should expect disemployment to increase over time from the minimum wage — employers don’t like firing people, but they might choose to not rehire over coming years. Second, the minimum wage should be seen as a transfer policy. It may be beneficial to have, but it’s always going to be kludgier than just sending people money. Third, your model of the world should follow the facts, not the policy you want. Do not tendentiously fit everything into whatever model justifies the policy you wanted all along.