The Marginal Product of Labor

In this set of lectures on labor markets, we'll be looking at questions, such as: How are wages determined? Why do Americans earn so much by global standards? What's human capital and how does it help us to increase wages? Do labor unions help workers? And if so, by how much? And how does discrimination affect labor markets? We're going to begin in this part of the lecture with the determination of wages.

In this set of lectures on labor markets, we'll be looking at questions such as How are wages determined? Why do most Americans earn so much by global standards? What's human capital? How does it help us in increased wages? Do labor unions help workers, and if so, by how much? And how does discrimination affect labor markets? We're going to begin in this part of the lecture with the determination of wages. What makes the demand for labor different than the demand for apples is that the demand for labor is a derived demand. Firms hire workers because the workers increase their revenues.

The key idea behind the demand for labor is the marginal product of labor, the increase in a firm's revenues created by hiring an additional laborer. And we're going to see several important things about this marginal product of labor. First, it declines as more labor is added. And this is because the first laborer goes to the most important task, the second laborer goes to the second most important task and so forth. Moreover, firms will hire workers, laborers, as long as the wage is less than the marginal product of labor.

Let's take a look at this in a table. This table shows how a restaurant like McDonald’s might think about hiring janitors. The first janitor is assigned to the most important task -- cleaning the restrooms once a day. That task adds $35 an hour to the firm’s revenues. Customers like restaurants with clean restrooms. The second janitor empties the trash, the third janitor hired will also be assigned to cleaning restrooms, now done twice a day -- and that use increases revenues by less -- by $24 an hour. The demand curve for labor is derived from the marginal product of labor. Notice that as the wage goes down, the firm will want to hire more and more janitors and as the firm hires more and more janitors, the marginal product of labor falls. So let's take a closer look at this derivation.

Here's the marginal product of labor schedule and here is the demand for labor derived from that schedule. Notice that if the wage were greater than $35 an hour the firm would demand no janitors. That's because the very first janitor adds $35 an hour to the firm's revenues. If the wage is higher than that, that janitor is not worth hiring. As the wage falls, however, more and more janitors become worthwhile to hire. If the market wage were $10, 7 janitors would be hired. If the market wage were $30, only 1 janitor would be hired. Now this is the demand for janitors from a single firm.

Now consider summing up the quantity of janitors demanded at each wage for all the firms in the market. That's how we get to the market demand for janitors. So let's go to the market demand. So here's the market for janitors in the United States. We have a demand curve derived from the marginal product of labor and a supply curve. The supply curve says that as the wage increases the quantity of janitors supplied will also increase. That's intuitive but I want to say a little bit more about the supply curve in a moment because there's one possible complication which we should discuss.

For now, however, let's focus on the main point, which is that the wage is determined as usual by the point where the quantity demanded is equal to the quantity supplied -- the intersection of the demand and the supply curve. In the United States, the wage for janitors is about $10 an hour and the quantity supplied is about 168 million hours per week. Overall, there are about 4.2 million janitors in the United States. So the key here is really that we can use our tools of demand and supply to understand the market for labor. So we can predict what will happen with an increased demand for labor or a reduced supply. Other factors which might influence the demand and supply of labor -- we now know how to analyze this market.

Let's add one qualification to the supply of labor. We need to make a distinction between an individual’s supply curve for labor and the market supply curve for labor. So let's suppose we have a janitor -- let's call him Joe -- and let's imagine that his wage is currently $16 an hour and he's working 40 hours a week. If the wage were to increase to $20 an hour, Joe decides he may work more, 50 hours per week, in order to take advantage of that higher wage. But now suppose that the wage increases even more to $28 an hour. Well, will Joe choose to work more at $28 an hour than he did at $20? Not necessarily. After all, there's only so many hours in the week. Anyway, Joe has other things to do with his time. Now that his wage is higher, Joe might want to take his family on a vacation. His income is pretty high as well now -- $28 an hour, 40 hours a week, Joe may decide he in fact would like to work a little bit less. He in fact would like to buy more leisure with the income which he is earning from his job.

So an individual’s labor supply curve could possibly have a backward bending component. There's nothing irrational or peculiar about that. Although it's possible for an individual to have a backward bending labor supply component, it's less likely for the market as a whole, because even as the wage for janitors increases and Joe works a little bit less, there are lots of other people -- Mary, and Jose and Rita -- who are currently employed, say waiting tables or as sales staff, who would be willing to work in janitorial services if the wage were higher.

So consider a wage of $20 an hour -- the market supply has 320 million hours of janitorial services. As the wage goes up to $28, well Joe works a little bit less, and maybe some of the other people in the industry work a little bit less -- people who are already in the industry -- but more people enter the market for janitorial services when the wage is $28 than when it was $20. So as the wage increases, the quantity supplied of janitorial services increases for two reasons. The people who are already janitors may work more, but even more importantly, as the wage for janitors increases more people enter the janitorial industry.

So what this means is that our labor supply curve will typically have our usual shape -- an upward sloped labor supply curve. Even when some individuals might have a backward slope over some portion of the curve, the market slope is going to have our typical shape.

So why do janitors in the United States earn more than janitors in India? After all, they're doing pretty much the same thing -- sweeping floors and so forth. It certainly isn't the case that janitors in the United States are sweeping more floors per hour or working so many more hours. If you answered demand and supply, give yourselves half points.

Let's go a little bit deeper. The demand for janitors is higher in the United States because the United States is a more productive economy than the Indian economy. There's more and better capital to work with, the office workers are more productive, and the American office produces a more valuable product. The result is that it's more valuable to keep a U.S. office building clean -- that's one of the reasons why American janitors earn more. The demand for their services is higher. This is a useful reminder -- you may have a number of valuable skills. Perhaps you're able to program a computer, or write a report, or motivate sales staff, and so forth. But your skills only have value within a given context. If you were transplanted to a different economy, your skills might be worth less -- maybe because your skills would be less useful, but also because other people might not have the money to pay for your skills. It's better to be a barber in a rich country than in a poor country, even when the same number of people need a haircut.

Okay. So that's one reason why janitors in the United States earn more. The demand for their services is higher because the United States is a more productive economy. Wages, of course, are about demand and about supply. So here's the other half -- India has more workers than in the United States, and in particular India has more low-skilled workers who eagerly compete for the job of janitor. A janitor could be a quite high paying job in India, a well-respected job in India. So Indian janitors earn less because U.S. firms are more productive, the demand for labor is higher and also because the supply of low-skilled workers is greater in India. Here's a graph summarizing what we just said. Here's the demand and supply of janitors in the United States with the wage of $10 an hour. And here's the demand and supply in India. The demand is lower, the supply is higher so the wage is lower.

Okay. Next time we'll be looking at some of the factors which can increase wages, particularly human capital, and then we'll turn to discrimination and other topics.