Minimum wages in a monopsony

A well-known result in microeconomics is that a monopsony in a labor market produces a deadweight loss (assuming it does not wage-discriminate), leading to the counterintuitive result that some binding minimum wage levels might increase both employment and wages. 

A graph illustrating the welfare costs of a monopsony.
The deadweight loss of a monopsony. CC BY 2.5 (https://creativecommons.org/licenses/by/2.5/), SilverStar at English Wikipedia.

(I promise we won’t be talking about this graph at all. It’s just for the aesthetic.)

When initially learning economics, I found it hard to grasp this concept intuitively. I recently consulted Perloff (2020), Varian (2014), Landsburg (2013), and other textbooks searching for an answer that explained this without mathematics or graphs and didn’t find anything – so I thought I would try to articulate my understanding of this. I’m not sure this explanation is correct: it’s just my attempt at roughly translating the math to English, and I would appreciate if anyone could correct me on inaccuracies. 

A monopsonist is a single consumer of a good or service, often in a market with many suppliers. In a labor market, that is a single employer, with many workers willing to supply their labor. 

In a competitive market (i.e., many employers and prospective employees), standard economic theory suggests that imposing a binding minimum wage would decrease employment, because firms would lay off workers to compensate for the increased cost of labor. The empirical research is mixed on this question (and indeed, on the question of whether labor markets are competitive or monopsonistic/oligopsonistic). Here’s a good post on this subject by Trevor Chow.

A monopsonistic market – as you may have guessed – is more complicated. So let’s (re)build a model. I’ll outline some assumptions first. This is a single labor market – for example, a labor market in a particular type of worker (someone who does the same job). The employer pays every employee of this type the same wage. This seems reasonable – since workers do not have an incentive to accurately report their reservation wage (the lowest wage at which they are willing to work), a monopsonist does not have a metric by which to wage-discriminate. Furthermore, there are tangible barriers on many blue-collar employers from wage discriminating – including unions, legislation, fear of backlash, common labor contracts, and so on.

Back to a competitive labor market for a moment. In a competitive labor market, with many employers competing for workers and many employees competing for jobs, the wage in the market will end up (1) being the same and (2) equalling the marginal revenue product of labor (MRPL, which is the marginal increase in revenue from hiring an additional worker). (1) is true because if one employer pays a higher wage, every other employer will lose out on workers and be forced to raise their wages. If one employer pays a lower wage, they will either lose access to their workers (forcing it to raise its wage) or operate at a higher profit than others (forcing others to lower their wage). In the end, wages will normalize to be about the same. This is the Law of One Price. (2) is true because an employer is making a loss if the wage is significantly above the MRPL, while if the wage is significantly below the MRPL, the worker will find an alternative job (since there are many employers competing). 

This isn’t true in a monopsonistic labor market. If workers have no (or few) alternatives, then an employer will pay a wage less than the MRPL – because they can. This is a simple syllogism: the profit-maximizing wage for a firm with no competition is less than the profit-maximizing wage for a firm that does compete for workers, and we’ve established that the profit-maximizing wage is the MRPL for a firm that does compete. Now, remember: the MRPL is how much the firm values the worker (approximately) – it is how much a marginal worker would bring in. But a firm has chosen a profit-maximizing wage less than how much it values a marginal worker. That suggests that there are workers willing to work for a wage just incrementally below their additional revenue product, but who are not willing to work at the monopsonistic employer’s current wage. The monopsonist has a choice. Either they raise wages for everybody (since wages have to be the same, per our assumptions) to get these people to work, or they don’t hire some workers (hiring whom would give them a surplus) because it would mean raising the costs of keeping everyone else. Hence, many monopsonists would choose not to hire these workers.

This is a deadweight loss. There is a trade to be made that, on its own, would benefit both parties – the workers would get a job a bit above their reservation wage and employers would hire people a bit below how much they value their work. However, the implication it has for the wages of other employees (whom a monopsonistic employer can afford to pay below the MRPL) means the employer doesn’t maximize a profit when it hires everyone willing to work at below the employer’s value for a worker. 

You can now see how a minimum wage set at the MRPL would likely increase employment for such a monopsonist. If the government sets a binding minimum wage at the MRPL for each worker, then a monopsonist would have to pay all its existing workers the MRPL. That means hiring these new workers does not mean raising everyone else’s wage – so the monopsonist makes the decision on whether to hire a new worker solely on whether the wage they’re willing to accept is less than the value they offer the monopsonist. Since there are some workers who meet this condition who were not hired earlier, they are hired now.

This also means a minimum wage set a bit above the MRPL has an ambiguous effect on employment. It has two counteracting effects – one increasing employment and one decreasing it, and which one of these effects dominates depends on how high the minimum wage is set. 

Beef bans likely reduce animal welfare

[Note: Beef bans probably significantly diminish human welfare, because, in some contexts, beef is a cheaper meat than many alternatives, because beef is a key export, and because beef bans are often targeted at particular minority communities, increasing resentment and legitimizing actions such as lynchings. This post, however, is not about human welfare—it looks at the very specific issue of how beef bans impact animal welfare.]

[Update below.]

Many Indian states and cities have implemented bans on the production and sale of beef (but not of other forms of meat), on predominantly religious (and majoritarian) grounds. Poorva Joshipura of the People for the Ethical Treatment of Animals argues in favor of these beef bans in India on the grounds that they advance the welfare of animals.

I disagree. I think beef bans, on net, diminish the welfare of farmed animals.

Why? Because beef is a substitute in consumption for other goods—including pork, goat, and chicken.

Much of Joshipura’s op-ed assumes that, in the presence of a beef ban, people will replace beef with vegan food. On an intuitive level, that seems unlikely. All else being equal, people who lose access to one good try to replace it with a good that’s a close substitute. Other meats are a closer substitute for beef than vegetarian and vegan food. When a beef ban reduces the quantity of beef supplied (assuming no black market formation, it reduces it to zero), the demand for other meats, which are often more common (e.g., chicken), increases, raising the equilibrium quantity.

There is empirical evidence for this as well. Reuters reports that many firms, anticipating bans on beef in Maharashtra, were considering increasing production by 5–8 percent back in 2015. By 2017, that change was far more substantial. According to The Hindu, the equilibrium quantity of chicken rose by 35–40 percent nationally in light of beef bans throughout the country.

On average, this reduces the welfare of animals. (Note that since the policy proposal here is a beef ban, we don’t have to take into account supply elasticities.) Two reasons. First, on a pound-for-pound basis, equal amounts of beef and chicken have vast disparities in terms of the number of animals that suffer and die. This is fairly intuitive. Cattle are larger than chickens. A single beef cow, on average, produces 212 kilograms in edible meat (out of a total weight of 544 kilograms), according to data from the 2017 version of this report. On the other hand, a single chicken raised for meat, on average, produces 1.35 kilograms of edible meat (out of a total weight of 2.5 kilograms). This needs to be adjusted for lifespan, however. Chickens farmed for meat, on average, live 42 days, whereas beef cattle live 395 days. Thus, per kilogram of meat, the number of days of life lost for a chicken is 42 * 0.74 = 31.08 days, whereas for a cow, it’s 395 * 0.0047 = 1.86 days. Since -31.08 < -1.86, ceteris paribus, eating beef is worse (unadjusted for (a) moral weight and (b) quality of life, both of which I’ll get into soon).

Second, the quality of life of smaller animals such as pigs and chickens are worse than that of cattle raised for beef. Joshipura’s article describes quite vividly the suffering beef cattle go through. It doesn’t match the suffering chickens go through. This paper makes some comparison. Brian Tomasik estimates that a chicken goes through 1.8 times more suffering than a beef cow, on average, even after adjusting for lifespan.  

There are two common objections to this. The first is that cattle have more moral relevance than chickens. This may well be the case, but it doesn’t seem intuitively true that one cow’s life is morally more relevant than 212/1.35 = 157 chickens. The differences in the extent to which these animals can experience suffering aren’t nearly as high. Brian Tomasik is more charitable—and more rigorous—than me, and says that only if you think a cow can experience more than forty times as much suffering as a chicken would the moral weight you assign to a cow relative to a chicken make a difference as far as maximizing animal welfare (measured in utilitarian terms) is concerned.

The second common objection is that beef farming is more environmentally harmful and that environmental harms increase animal suffering. Scott Alexander responds to this:

Some quick calculations: average American eats about 100 kg of meat per year. If that’s entirely beef, then that produces greenhouse gases equal to 8000 lbs CO2 (note unit conversion), which can be offset for $0.40 at carbon offset sites.

If it’s entirely chicken, then that adds up to about 100 chickens per year.

So if one chicken worth of animal suffering seems more than 40 cents worth of bad to you, you should go with beef.

I think it’s at least a bit weird to measure the extent of negative effects of pollution by the amount of money it takes to prevent it rather than the monetary loss it creates, since most people who eat beef aren’t spending money on carbon offset sites—but it does indicate that the environmental harm of beef doesn’t really stack up to the suffering this policy would induce on chickens, especially since chicken farming hurts the environment too.  

Some caveats:

(1) This does not take into account wild animal suffering at all, since the effects of meat consumption on wild animal suffering are deeply unclear.

(2) This analysis needs more rigor because it needs to take into account cross elasticities across beef and chicken—in other words, it needs more evidence on how much chicken production increases due to beef bans, and needs to factor that into the (implicit) animal welfare function I’m using.

(3) This analysis needs to consider non-chicken substitutes, such as pork and goat, but also buffalo meat.

(4) There is insufficient evidence on the extent of suffering the average chicken goes through in comparison to the average beef cow, especially since cattle have to live longer lives, on average.

(5) Further research into how much suffering the environmental impacts of beef would create when compared to the environmental impacts of other meats is necessary.

(6) This also doesn’t take into account negative effects on the cattle themselves. As Lewis Bollard briefly points out in his interview with Rob Wiblin, “[W]hat happens when these slaughter bans get passed at the same time as the Indian dairy industry is rapidly growing is huge numbers of surplus cows that can’t be legally slaughtered [are] either smuggled long distances to be slaughtered or they’re dumped in these sanctuaries where they will slowly die or won’t receive medical treatment.” I’m unclear about whether this outweighs the long-term impact of reduced beef consumption on the welfare of cattle.

(7) Lastly, most beef bans serve as bans on all cattle slaughter. This article doesn’t look at cattle slaughter and suffering in the leather industry, where there is no such substitution effect; but overall bans on cattle slaughter do have a substitution effect, so this doesn’t significantly adversely affect my argument.

However, on the margin, I think the evidence is fairly consistent with the notion that beef bans reduce animal welfare, measured in utilitarian terms, other things being equal.

Note that this should also affect your personal choices, in contexts where beef isn’t banned. Consuming chicken, pork, lamb, goat, farmed fish, or even eggs is likely worse—on a moral level—than consuming beef or wild-caught fish. While the ideal option may be to go vegan or lacto-vegetarian—I’m vegan myself—it would be prudent for people who consume meat to change their eating habits to make it more ethical.

Update (May 30, 2019):

I just discovered some further responses to the argument that beef production is worse for the environment. First, methane—the main source of environmental pollution unique to ruminant livestock such as cattle—is a short-lived greenhouse gas. This means that, in the long run, the effects of beef production on the environment significantly reduce. Second, Julian Baggini of The Guardian writes an article criticizing a proposed tax on red meat. There, they explain, “Most industrially produced meat is raised on imported feed made from crops such as soya, heavily dependent on commercial fertilisers and irrigation, often grown on woodland and forest cleared for cultivation. In contrast, properly pasture-reared animals feed on grasslands unsuitable for arable farming, watered by the clouds. These animals don’t depend on fertilisers further down the food chain, they actually provide manure for crops. If we were to tax red meat, many people would switch to more poultry, which is almost always reared on feed, adding to our burden on the planet.” This would apply to a ban on red meat such as beef as well.

Contra Mankiw on political philosophy

Harvard economist Greg Mankiw, someone I greatly respect, wrote an article for The New York Times a few years ago on the political philosophy of economists. The thesis of his piece is two-fold.

First, he says that any economist making a normative judgment—much like any normative judgment made by anyone else—is also assuming a particular political philosophy. Often, they look at what maximizes “social welfare,” measured in utilitarian terms. That’s a value judgment about political philosophy and not an assumption that can be taken for granted.

Second, he offers an alternate political philosophy which he calls a “do-no-harm principle” that is entailed, according to him, by epistemic humility. In his own words:

So, what is the alternative? At the very least, a large dose of humility is in order. When evaluating policies, our elected leaders are wise to seek advice from economists. But if an economist is always confident in his judgments, or if he demonizes those who reach opposite conclusions, you know that he is not to be trusted.

In some ways, economics is like medicine two centuries ago. If you were ill at the beginning of the 19th century, a physician was your best bet, but his knowledge was so rudimentary that his remedies could easily make things worse rather than better. And so it is with economics today. That is why we economists should be sure to apply the principle “first, do no harm.”

This principle suggests that when people have voluntarily agreed upon an economic arrangement to their mutual benefit, that arrangement should be respected. (The main exception is when there are adverse effects on third parties — what economists call “negative externalities.”) As a result, when a policy is complex, hard to evaluate and disruptive of private transactions, there is good reason to be skeptical of it.

He then proceeds to apply this principle to the Affordable Care Act and the minimum wage:

As I see it, the minimum wage and the Affordable Care Act are cases in point. Noble as they are in aspiration, they fail the do-no-harm test. An increase in the minimum wage would disrupt some deals that workers and employers have made voluntarily. The Affordable Care Act has disrupted many insurance arrangements that were acceptable to both the insurance company and the insured; these policies were canceled because they deviated from lawmakers’ notion of the ideal.

I agree with him that anyone making normative judgments is assuming a certain political philosophy. Notice that his “do-no-harm” principle is also a political philosophy—and not one that’s somehow less controversial than utilitarianism. For one, it isn’t prima facie clear to me that people should be allowed to make decisions that hurt themselves. In fact, whether the state should legislate to prevent self harm is a key source of debate among political philosophers.

For another, the fact that a contract exists and was signed by both parties does not necessarily make it truly voluntary. For a truly free choice to exist, I would argue that certain conditions must be met.

First, I think that, for a choice to be truly free, people should be given access to full information. If there’s a significant information asymmetry, then a person is making a choice without knowing what options exist and what the implications of their choice are. That sounds, intuitively to me, like a coerced choice. And there are good reasons to believe that the market for health insurance. In fact, Professor Mankiw made this argument about health insurance himself:

Consumers often don’t know what they need. In most markets, consumers can judge whether they are happy with the products they buy. But when people get sick, they often do not know what they need and sometimes are not in a position to make good decisions. They rely on a physician’s advice, which even with hindsight is hard to evaluate.

And consumers are often unaware of the possibility that they might get sick. In fact, people are empirically really poor at making long-term calculations. Here’s some research to prove it. And here’s a meta-analysis of the literature. And often, information about the likelihood of getting specific illnesses—and the question of whether those illnesses are covered by insurance—exists with insurers but not with consumers. That’s an Econ 101 case of asymmetric information that renders free choice not truly free.

Second, people should have access to many options—or at least, more than a few bad options, at least if this is possible or if government intervention can cause this to occur. If they don’t have options, then them choosing the only option they have available is certainly not ideal—the state should seek to expand the options they have. The labor market is a good example for this. A person chooses to work a low-wage job because that’s the only option they have available—they’d rather a higher wage job. A minimum wage opens this option up to them and doesn’t force them to rely on a $3/hour wage.

Now, Mankiw would likely object to this in two ways. First, he could say that both the suppliers and the demanders should have their choices maximized—a minimum wage removes the freedom of employers. The problem with this is that it potentially doesn’t take into account imbalances in power. Minimum wages often exist in industries where the demanders—employers—have substantial market power. Here, trades between workers and employers aren’t as free as they could be, and minimum wages can help make them free in that context. Second, he could say that minimum wages reduce the options available as firms simply reduce the number of workers available. I agree that that’s a possibility—but now that becomes an empirical question, and not one of political philosophy. My point is simply that a “do-no-harm principle” doesn’t necessarily entail the abolition of the minimum wage.     

In short, I don’t think Mankiw’s proposed political philosophy is any more obvious than utilitarianism, and doesn’t necessarily entail opposition to Obamacare or the minimum wage. Economists do use political philosophy in making normative judgments—I think that’s true and is entailed by the definition of a “normative judgment”—and I agree that we need to be more cautious about assuming the truth of utilitarianism. What I disagree with is his proposed alternative, which seems (at least to me)—and I may very well be wrong here—to run into the very same problems he critiques in his op-ed: assuming a debatable political philosophy without much justification.

Hello

I’ve blogged before. So, the point of this new blog is for me to blog with a bit more epistemic humility – and being a bit more willing to question my own opinions. That’s pretty much it. 

I wrote a longer version of this earlier, but it seems to have been deleted. In any case, I’m going to be try to be regular with posts (and to remember to always write them in Google Docs so I don’t lose them).

In other news, here’s a TED talk by Julia Galef that I found interesting.