Choosing inputs when factor markets are monopolistically competitive
A monopsonistic market for labor
- [Instructor] So let's continue with our conversation around factors of production for a firm, and we're going to focus on the labor market. And so we've already drawn axes like this multiple times, where our horizontal axis, this is the quantity, quantity of labor that's being employed by a firm. And then the vertical axis, this is our wage rate. And so this is, we're looking at the economics for a firm. And we're looking at how much labor is it rational for this firm to employ? And we've talked about the marginal revenue product multiple times. This is a view of how much incremental revenue can the firm get every time it brings on one more labor unit? And we've talked about that we typically see it like a downward-sloping line like this 'cause you have diminishing returns. Every time you add one more labor unit, the marginal revenue product of that labor goes a little bit down, and so that's when you have diminishing returns. So this is marginal revenue products, and I'll be very particular this time. This is of labor. We could do a similar marginal revenue product of other factors like land or capital. Now, to change things up in this video, we're not just going to talk about a firm that operates in a perfectly competitive labor market. If we did, then its marginal factor cost would be whatever the market wage rate would be, and it would be a horizontal line like this. So you would have a marginal factor cost of labor. But we're not going to talk about a firm that's in a perfectly competitive labor market. We're going to talk about a firm that is a monopsony employer, a very fancy word. So it is a monopsony, not a monopoly, a monopsony. Now, what does a monopsony mean? Well, you could almost view it as the reverse of what a monopoly is. A monopoly is you have one seller, so one seller, and many buyers, so many, many buyers. So that is a monopoly, monopoly right over there. A monopsony is when you have one buyer, so one buyer, and many sellers. And so you have many, many sellers. So this right over here is a monopsony firm, monopsony. And in the context that we're talking about, we're talking about labor markets. So this one, instead of saying one buyer, you could say this is one buyer of labor. So you could say one employer, one employer. And the sellers of labors, well, a seller of labor, well, these are many potential, potential workers, potential workers. And there is many real-world examples that approach monopsony employers. Let's say we're in a small town, and there's only one hospital, so they're going to be the monopsony employers of healthcare workers, of, say, nurses. And so what's interesting about a monopsony employer is they're not just going to take whatever the wage rate is, they have to essentially, they have a supply curve for labor in that market. And so, for example, in this market, when wages are low, there's going to be a low supply of labor. Not many people are going to wanna work for that hospital. And then as wages go up, more and more and more people are going to want to work for that monopsony employer. And so this is our labor, labor supply curve. Now, I'm gonna ask you a question. I'm gonna tell you right now, it is a trick question. What is going to be the rational quantity for this firm to hire? Now, you might be tempted to say, well, it's just the same thing. We would just want to keep hiring as long as our marginal revenue product of labor is higher than the cost of labor. And that would be true if you could afford to pay everyone a different rate. If this first unit of labor, you can pay someone this much, and then everyone that you hire, you have to just pay them a little bit more. But that's not the way that it typically works. In the real world, you often think about having to, whatever the wage is, if we decide that this is the quantity of labor that we wanna bring on, you wouldn't pay this wage just to that incremental person, you would have to pay that wage to everyone. And so to think about what is the rational quantity of labor to bring on for this firm, we would need to think, we need to calculate or at least visualize what the marginal factor cost of labor here, which is going to be different than our labor supply curve. And to help us visualize that, let me set up a little table here. So I'm just gonna make up some numbers. So look, we're going to think about the quantity of labor, so let's just go zero, one, two, three, four. And then let's think about the price of labor. And so let's say when the quantity of labor is one, the price of labor is three. And then it goes up as we, if we wanna hire more people, well, the price of labor goes up to four, goes up to five, goes up to six, keeps going. And then what would be the total cost of labor? So total labor cost, well, you could figure that out. If you hire one unit at $3 per unit, one times three is three. Two units at $4 per unit, remember, you're going to have to pay everyone the same amount. So it's not like you can just pay this first person $3 and only the second person $4, in which case, this would be seven. But if you're going to hire two units, you have to pay everyone $4. So your total cost is eight here, two times four. Three time five, your total cost is 15. Your total cost here is 24. And so now we could think about what is our marginal factor cost of labor? So when you bring on that incremental unit of labor, how much incremental cost are you taking on? Well, when you go from one to two units, your total cost goes from three to eight, so your marginal factor cost is five. This is plus five right over here. When you go from two to three, your marginal factor cost, you went from eight to 15. So eight to 15, you went up by seven. And once again, this is because when you wanna hire more people, you're going to have to pay more to track those incremental people, but then you have to pay that higher rate to everyone. And so you see that the marginal factor cost of labor is going up twice as fast as our labor supply curve. Our labor supply curve, every incremental unit, we're adding one. Here, every incremental unit, we're adding two. And we could see it again. To go from 15 to 24, you have to add nine, so our marginal factor cost of labor is nine. And so looking at this as an example, you see that your marginal factor cost of labor is going to go up at twice the slope of your labor supply curve. So your marginal factor cost of labor is going to look something like this. It's going to go up twice as fast, marginal factor cost of labor. And now this might be ringing a bell. This might seem like what we studied in the past when we looked at a monopoly or an imperfect competitor firm. And we talked about the demand for its goods, and we also talked about its marginal revenue. And the marginal revenue curve had twice the negative slope as the demand curve. And here, we see everything just flipped over. Because we're now not talking about revenue for the firm and marginal revenue for the firm, we are talking about costs for the firm. These are inputs for the firm. But now what would be the rational wage rate? And what's the rational quantity of labor for this firm? Well, now that we've done the marginal analysis, we would see that it's rational for the firm to keep bringing on more and more people as long as the marginal revenue product of labor for each incremental unit is higher than the marginal factor cost of labor for each incremental unit. And so we'd keep hiring until you get to this point right over here. So it would be rational for it to bring on this quantity of labor. And what would be the wage that it would pay? Well, you might be tempted to just go right over here and say it would pay this wage, but remember it doesn't have to pay this wage. At this quantity of labor, the labor supply curve tells us that the market wage would be right over here. So it would be paying, it would be paying this wage. It would be paying this wage right over here. So this is something for you to maybe ponder on a little bit more. But the big picture is, is when we're dealing with a monopsony firm, so it is the only person hiring in the market or something that's approaching a monopsony firm, it's going to have its own labor supply curve. And the way you think about what a rational quantity for it to hire is, you would think about the marginal factor cost of labor, which is going to go up at twice the slope. And where that intersects the marginal revenue product, well, that tells you the quantity, and then the labor supply curve will tell you the wage for that quantity.