Economists Do It With Models

You guys, I love monopsonies…for starters, it’s a fun word to say, and it makes people do a double take when they initially think you said “monopoly.” Definitionally, a monopsony is a market with only one buyer- basically the economic counterpart to a monopoly, which is a market with only one seller. Not surprisingly, the buyer in a monopsony has all of the market power in much the same way that the seller in a monopoly does, and largely for a mathematically analogous reason.

Economists have been talking about monopsonies more than usual as of late, most often in the context of labor markets. In labor markets, companies are the buyers (or, perhaps more accurately given the 13th amendment, the renters) and people are the sellers of labor. When the number of employers in an area competing for workers is small, firms are generally thought to have “monopsony power.” This is a little different from literally being a monopsony, but you can think of monopsony power as the ability to act like a monopsony but to a lesser degree.

So what’s interesting about monopsonies in labor markets? Here’s a quick summary:

• In competitive markets, i.e. markets with large numbers of companies and workers, minimum wages are thought to decrease employment.
• If a labor market is a monopsony (or if employers have monopsony power), minimum wages could actually increase rather than decrease employment.

This distinction is obviously important from a policy perspective, since minimum wages look way more appealing if they don’t cause people to get laid off. Now, I could try to explain to you why minimum wages work this way using some fun graphs and whatnot, but I’ve come to learn that not everyone’s brain wants to operate at an abstract conceptual level, so let’s work through a simple example instead.

Ready? I’m gonna try to do this without using any econ-specific terms (they’re not as fun to say as monopsony), and we’re going to talk about a company that makes widgets- yes, I know this is a tired econ thing, but Widget is the name of my mom’s cat so I’m asserting it’s fair game.

First, here are some numbers on how many widgets workers can produce:

You’ll note that the “incremental widgets” numbers are decreasing as more workers are added- this is generally reasonable, since most production faces a diminishing returns or “too many cooks in the kitchen” problem. Now let’s say that the company can sell as many widgets as it wants at a price of $10 each- now we can see how much each worker would add to the company’s revenue (does revenue count as an econ term?)

If we want to figure out how many workers the company wants to hire, we need to know how much the workers cost. The thing about workers is that some of them will work more cheaply than others (even if they’re of equivalent quality), and this is relevant for a monopsony, since they’re not so small that they can increase their hiring without pushing up the going market wage. (In fact, this feature is the crux of why monopsonies look different from competitive labor markets!) Let’s assume the wage required to get each worker to work looks like this: (you can think of everything in per hour terms, per day, whatever, it doesn’t really matter)

We can now calculate how much it would cost to hire 1 worker, 2 workers, etc., and we can also calculate the incremental cost of each additional worker:

I feel like this requires some explanation since it’s not really intuitive…if you want to hire the first worker, things are pretty simple, but if you want to hire the second worker, you not only have to pay the second worker the $20 to get him to work, but you also have to pay the first guy $20 rather than $10- there are a number of reasons for this, but you can just imagine that the first guy will get really pissed if he makes less money than second guy for doing the same job. This means that the incremental cost of hiring an additional worker includes not only his wage but also the additional compensation that has to be given to everyone who came before. (This is seriously the most important point so keep staring at it until it sinks in. I’ll wait.)

So take a look at the relevant numbers so far- how many workers does the company want to hire?

Does the company want to hire the first worker? Sure, since that worker brings in $120 and only costs $10. (just assume that labor is the only cost of production) Does the company want to hire the second worker? Sure, since the second worker brings in an additional $100 but only adds $30 to the company’s costs. If we keep analyzing in this way, we can conclude that the company will want to stop hiring after it hires 3 workers. (and will pay a wage of $30)

Now how do things change if a minimum wage is imposed? Let’s assume that a minimum wage of $40 is set. (Now I look real generous to those people who interpreted the numbers as being per hour.)

Workers 1, 2, 3, and 4 are happy to work for the minimum wage, so the company can hire up to 4 workers at $40 each. After 4 workers are hired, however, things change dramatically- in order to hire the 5th guy, the company not only has to pay him $50 but also has to pay each of the 4 other workers $50 rather than $40. How many workers does the company want to hire now? (This is the last set of numbers, I swear.)

Now the company would find it profitable to hire the first 4 workers but not the 5th worker. BOOM- I just showed you a case where a minimum wage would increase rather than decrease the number of workers hired.

So why did this happen? Put simply, the minimum wage took away the “well if I hire you I have to pay everyone else more too” feature of the company’s analysis, at least for the first 4 workers. That said, the minimum wage still creates somewhat of a double-edged sword in terms of employment, since it also made it incrementally more expensive to hire the 5th guy than it was before. As a result, minimum wages placed on monopsonistic markets can both encourage companies to hire more workers and discourage companies from setting wages just above the minimum wage. (This is relevant for companies that pay just above what would be the minimum wage, since it could actually cause them to decrease wages!)

I’m not trying to convince you that minimum wages are good, I’m just walking you through some numbers so that you don’t do the “I took one econ class once and models of competitive markets are always applicable” thing that causes economists to call you an ass clown behind your back. One last thing- in case you (understandably) have the follow-up question of “how prevalent is monopsony power in labor markets?”, here’s some reading material for you to peruse. Spoiler alert: the answer is “too prevalent to ignore.”

Update: You can see a version of this story on Medium if you prefer.