Some minimum wage theory (Econ for poets)

On this blog, I have a bias toward highlighting center-right economic ideas and research, because most of my friends and most intellectuals have left-of-center inclinations, and I like to try to provide a helpful counterweight. But I am, consequently, left vulnerable to accusations of selection bias in the evidence I confront, and of providing a forum for ideas that is biased itself.

So in the spirit of guarding against that, here is a cool article in The Economist that highlights some recent economic research that defends the minimum wage. Now, as the article notes, until recently, the idea that the minimum wage did little to boost wages, and much to increase unemployment, was not even a center-right idea, but simply the consensus position in economics. In fact, in economic circles, the argument against the minimum wage is well-known, because it is used as an iconic example of how simple theory can show that government interference in markets (in this case, labor markets) has unintended consequences that hurt its intended beneficiaries. So, first, let me present the economic theory that explains the case against the minimum wage. (By the way, I should note that the word ‘theory’ should not be taken to mean ‘aerie speculation.’ ‘Theory,’ rather, is behind any causal claims about the world, and hence can be demonstrably true or false, and is also hence necessary for any policy recommendations. Indeed, any time you have ideas about the world that go beyond purely disjointed empirical observations — any time you even use the word ‘because’ — you have theory.)

Let’s start with a super simple model of a labor market, which consists of one person, a weaver, trying to get a weaving job. Suppose this weaver can, given access to a loom, produce fine linen worth $100 more than the cost of the raw flax, every day. This is her ‘marginal product.’ There are five weaving factories in town that have the looms our weaver needs.  Theoretically, every one of them should be willing to offer our weaver up to just around $100 a day to work there. If one factory offers her $85, another factory stands to make an extra $10 profit a day by making her a counter-offer of $90 a day. And so on. You get the picture. We all should make around our marginal product in labor markets — if we are making more than our marginal product, firms stand to profit by firing us; if we are making less than our marginal product, firms stand to profit by competing for our labor, bidding up our salary.

Now imagine in this world that a conscientious government decides it is unconscionable that a full day spent at the loom should yield only $100 in pay. It sets the minimum wage instead at $120 a day. What will happen to our weaver? The government wants to give her a pay boost, but in fact it will get her fired. She, necessarily, is now costing her firm $20 a day — they’ll bankrupt themselves if they make a practice of employing people at such a loss.

So, let’s generalize this model into an economic theory: In general, your pay should approximate your ‘marginal product.’ And, if the minimum wage sets wages below your marginal product, it doesn’t effect you at all. If it sets wages above your marginal product, then you should get fired, because your employer will be losing money every day she employs you. So a minimum wage, according to this economic theory, should have no benefits whatsoever, and its only effects should be to increase unemployment and make firms contract their output (because they have fewer workers). Economists thus generally prefer to help the poor through earned income tax credits, and other such incentives, which  increase the take-home pay of workers without reducing employer’s incentives to hire them.


Now, back to The Economist article. It reports that, “a pioneering case study by two noted labour economists, David Card and Alan Krueger, examined the response of fast-food restaurants to a rise in New Jersey’s state minimum wage. It found that this had actually increased employment.” Now, this research has faced some empirical contention. But the more immediate and important objection than that empirical research is the theoretical question — how could it possibly be the case that a minimum wage not only doesn’t decrease employment but actively increases employment? It doesn’t make any sense with the simple labor-market model we constructed.

Economists are theory-minded people, so surely they have a reply. The Economist gives its readers a brief hint: “economic theory allows for the possibility that wage floors can boost both employment and pay. If employers have monopsony power as buyers of labour and are able to set wages, for instance, they can keep pay below its competitive rate.”

Let’s unpack this in full. First, ‘monopsony.’ We know what a ‘monopoly’ is, and why it’s a problem. A monopoly, of course, happens when only one firm is selling a good. Because it has no competitors, the monopolist can sell the good for as high a price as it likes. Not only do the consumers thus face higher prices when they buy the good, some of them don’t buy the good at all — these are two forms of ‘welfare loss’, relative to what society could have gained if the good were sold in a competitive market. Under monopoly, society as a whole does not gain the benefits that, given its technology and resources, it really could gain from this product.

A monopsony is the opposite of a monopoly — it’s when there is only one person/firm/entity buying a good from many different suppliers. In the labor market this is like only one firm hiring (i.e, ‘buying’ labor) while thousands of people are searching for a job (i.e., hoping to ‘sell’ their labor). Just as a monopoly causes goods to be overpriced, because the supplier has all the power, a monopsony causes the good — in this case, labor — to be underpriced.

So let’s revise our model by fastforwarding in the history of our imaginary town. Suppose the textile industry is no longer expanding. A good weaver can still produce fine linen worth $100 per day. But there is now only one linen company in town, with space at its factory benches and looms for only one more worker. Because the long-term prospects of linen look grim, no more companies plan to make the big capital investment to establish new factories nearby,  nor does the one company plan to expand its own facility. So there’s only one weaving job available, and no hope for more in the future. Now, too, it’s a recession with widespread unemployment, so our weaver faces competition from twenty other prospective employees. Suppose the factory owner makes an offer to our weaver of $50 a day. This is an outrage — utter exploitation — but she has no choice. There are no other employment opportunities, so if she refuses this offer, one of the next 19 weavers will take it, and she could be out of work forever. (Indeed, in a perfect monopsony, the owner should be able to drive her wage down to next to nothing.)

So this model shows how under conditions of ‘monopsony,’ as when, for example, a labor market is dominated by a few enormous, consolidated firms, or in which a general recession yields high unemployment, such that there are many many applicants for every job opening, laborers actually do not get paid their marginal product, and get paid much less. In this situation, the government can improve general welfare by setting the minimum wage somewhere above people’s current, suppressed wages, but below their marginal product. In our new, revised, model, this means the government should set the minimum wage at, say, $90 a day. The factory will still employ our weaver, because it’s still making $10 a day profit off of her, and it would make $0 profit by firing her. And she would make an extra $40 a day. If the government raised the minimum wage to $110, it would cause her to get fired — but anything in the $50-$100 range is an improvement.

So now we have a theory that explains how, in economic conditions in which employers have monopsony power over their employees, raising the minimum wage can give workers a pay boost, without causing unemployment. But this still doesn’t explain how a minimum wage could also boost employment. How is that possible? Our revised model doesn’t quite explain it — higher labor costs, should not, in any simple model of rational economic actors, induce firms to use more labor. So what’s going on? The long and short of it is: this is where the model gets messy. But the basic idea is that in the real world, employers of low-skilled workers do have a lot of monopsony power that allows them to drive low-skilled wages below the workers’ marginal product, and it’s also the case that, due to welfare, unemployment benefits, the safety net, black markets, etc., some prospective workers can just leave the labor market altogether. They might, in outrage, refuse to work for excessively low wages. And so a minimum wage that raises their wages below a depressingly-low level, while keeping them below their marginal product, doesn’t cut any of them out of the labor market by making them an unprofitable hire, but it does give more of them a greater incentive to actually join the labor market in the first place. (This is like, our revised model, our weaver refusing to take the $50 offer — except, in the real world, labor markets are dynamic over the long run, so it’s not just as if she gets replaced right away, and permanently locked out of employment opportunities.)

The Economist goes into some other interesting effects, as well. Because we humans rely on ‘anchors’ in a lot of our decision-making, a minimum-wage hike also, it seems, can boost wages up the income and skill scale. The idea here is that your employer really doesn’t have a good idea of how to calculate your marginal product, or what other firms might pay to steal you away, and so in setting your wage, she’s actually thinking something like, “Well, hmm, well my Matthew must be worth at least twice as much as a minimum-wage burger-flipper.” So the minimum wage boosts your wage by boosting that salient anchor.


I thought it was fun to unpack this theory, and this was a useful exercise for guarding against libertarian economic triumphalism. And the evidence does seem to suggest that the ‘costs’ of the minimum wage are probably lower than traditional economic theory suggests, and so, at the very least, market libertarians should focus on other market-oriented reforms, such as decreasing the barriers to entry to costly and lucrative professions like medicine and the law. But I still honestly doubt that the minimum wage is the ideal policy for helping the poor. One thing even our revised economic theory does not comprehend is that every single employment situation is unique — while, no doubt, many people at the minimum wage are getting paid less than their marginal product, under their employer’s monopsony, there are no doubt other firms where the workers’ minimum wages are competitive with their marginal products, and so a hike in the minimum wage could cause them to lose employment. So even if it were true that the minimum wage increased employment and wages overall, there should be more efficient ways to do so. For example, larger negative-income taxes generally (like, for a specific example, the Earned Income Tax Credit in the U.S.) should theoretically have all the encouraging effects of drawing more people into the workforce with higher take-home pay, with none of the downsides of cutting some people out of the labor market altogether.

So, executive summary: The minimum wage isn’t as harmful as a lot of libertarians think, and may even be beneficial overall. But hiking the minimum wage would still not be as good a way to help the poor as, e.g., greater negative income taxes.


3 thoughts on “Some minimum wage theory (Econ for poets)

  1. I don’t see why you need to assume that there’s any monopsony power. Surely you only need that there are more weavers than are necessary to fully utilize the looms.

    If there are enough looms (owned by several competitive companies) to employ 24 weavers, then they need to offer only enough wages to lure the 25th most desperate weaver away from their best alternative; then if a weaver threatens to leave their job unless they’re offered a pay-rise, there’s another weaver ready to take the job, and the threat fails.

    If there are aren’t many other jobs available, and the weavers don’t have access to enough land to grow their own livings, then the owners of the looms might drive wages down very low indeed.

  2. Pingback: Complicating labor markets | This is your brain on economics

  3. Pingback: Research dump, 2/4/2013: | This is your brain on economics

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