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# Factor markets worked example

AP.MICRO:
PRD‑4 (EU)
,
PRD‑4.C.1 (EK)
,
PRD‑4.C.2 (EK)
,
PRD‑4.C.3 (EK)
,
PRD‑4.C.4 (EK)

## Video transcript

- [Narrator] We're told that Epic Eats is a perfectly competitive, profit-maximizing producer of stuffed sandwiches, and hires workers in a perfectly competitive labor market. Part A says, draw side-by-side graphs for the labor market and for Epic Eats and show each of the following. So pause this video and see if you could have a go at it before we do it together. All right, now let's do it together. So we're gonna do side-by-side graphs, one for the market, and one for the firm Epic Eats. So let me do that. So, this will be my market. This is my market graph. And so this is going to be quantity of labor. Quantity of labor. And then on the vertical axis, I have my wages, which you could view as the price of labor, the wage rate. And so this is the market. And then over here, I wanted it side-by-side. This is going to be the firm. This is going to be Epic Eats. Once again, I have quantity, quantity of labor. And I'm going to have the wage rate. And this is Epic Eats. That's the firm level. Now, they want us to show the market wage and the quantity of workers hired in the market. Well, to do that, we're going to have to think about the demand for workers in the market. Well, at a high wage rate, there's not gonna be a lot of labor demanded. And then as the wage goes down, more, more people are going to wanna hire people. This is the market labor demand curve. Demand curve. And then then supply curve is gonna be upward sloping. At a low wage rate, not a lot of people are going to wanna give their labor. But then as wages go up, people will, more and more people are likely do enter, want to be part of the labor force. So this is going to be the market labor supply curve. And then we have our equilibrium wage, which they want us to label W sub M. So that is going to be right over here. W, sub lowercase M. And then the quantity of workers hired in the market is going to be capital L, sub lowercase M. Capital L, sub lowercase M. So we did this first part, the fact part that focuses on the market. Then they want us to focus on the marginal factor cost curve labeled MFC. Well that's what it's going to cost Epic Eats to hire folks. And we're dealing with a, it hires in a perfectly competitive labor market. So which is gonna pay the market wages. So let me do that. So this is going to be the price it pays for labor which is its marginal factor cost curve, MFC, just like that. So I did the second part. The marginal revenue product, labeled MRP. Well the way you typically look at it, it is for Epic Eats that it has some marginal revenue product at a certain quantity. And then as it hires more and more people, intends to have diminishing returns. So typical marginal revenue product curve looks something like this. So it's MRP, did that part. The wage paid by the firm, labeled W sub F, and the quantity of workers hired by the firm, labeled L sub F. Well the wage paid by the firm, that's dictated by the market wage. So we can say that this is equal to the market wage, which is equal to the wage paid by the firm. And you could put this over here. The wage paid by the firm is right over there. So I did this first part, and the quantity of workers hired by the firm. Well what would be rational is, is that they would keep hiring people until the marginal revenue product is no longer higher than that marginal cost of hiring that extra unit of labor. So it's right at that point of intersection. And so that is the quantity of workers hired by the firm, so L. Now let's do the next part. It says, assume that there is an increase in the price of Epic Eats' stuffed sandwiches. In the short run, will the wage paid by Epic Eats be higher than, lower than, or equal to W, sub F? Explain. So pause this video and see if you can answer that. Well in the short run, Epic Eats, no matter how much it hires or doesn't hire, it's just going to pay the same wage. So we could say, it is going to be equal to. Equal, equal. So pay equal to WF because operating in perfectly competitive labor market. Labor market. In the short run, what will happen to the number of workers hired by Epic Eats? Explain. So in the short run, if the wage is being the same, but hey had a price increase. So that means that the MRP is going to shift to the right because per unit, they're going to be able to sell it for more, you're gonna a have a situation where the MRP switches shifts to the right, or right and up. And so you're gonna have MRP to, this is after the price increase. And notice, now we intersect the MFC line at a higher point. And so what will happen to the number of workers hired? So number of workers goes up because MRP shifts up due to price increase which causes it to intersect your marginal factor cost curve, MFC at higher quantity of labor hired. All right, now let's do part C. Epic Eats uses capital and labor in the production of sandwiches. The marginal product of the last unit of capital used is 4,000 units and the marginal product of the last unit of labor used is 3,000. If Epic Eats minimizes costs and the rental rate of capital is \$400, what is the wage rate? So pause this video and see if you could answer that. All right, so they give us a few things. So the marginal product of the last unit of capital. So you say, marginal product of the last unit of capital. I used K for capital even though I know it's... Not to confuse ourselves with something else. Although, you could argue to use C, but we'll use K to ease confusion. So the marginal product of the unit of capital is equal to 4,000 units. We know that the marginal product of the last unit of labor is equal to 3,000 units. And we could view this right of here. The rental rate of capital, you can view this as the price of capital. You could also view this as the marginal factor cost of capital, but I'll just call this the price of capital is equal to \$400. And they want us to get the wage rate.. So you could view this as the price of labor is equal to what? And they tell us that it's minimizing cost. And what we can think about it is, the number of units per dollar that the firm gets it on the margin, if they're able to get more units per dollar by switching, by putting that extra dollar into labor versus capital, or capital versus labor, they're going to do it. So what we would assume is, is that the number of units per dollar that they're getting at this point are going to be the same whether they invest in labor or capital. And so the number of units per dollar that they're getting from the capital is the marginal product of the capital divided by the price of the capital this is the number of units per dollar. And this needs to be equal to the number of units per dollar that they're getting from that last unit of labor. So that's the marginal product of labor. So the units they're getting from labor on the margin divided by the price of labor on the margin, and then we just solve for this. So this will get us to, we're gonna have 4,000, this is 4,000 units divided by \$400. It's going to be equal to 3,000 units divided by the price of labor. So you can manipulate this a little bit, you could divide both sides by 400. So this is going to be 10 units per dollar. So let me scroll down a little bit right over here. So we could, this is, let's see... Yup, this is going to be 10 units per dollar is going to be equal to 3,000 units divided by the price of labor. And so, you just do a little bit of manipulation, multiply both sides by the price of labor, divide both sides by 10. You do a little bit of Algebra. This gets you to \$300 per, for the incremental cost of labor. So this is going to get us to the price of labor is equal to \$300. And you can verify that, you could plug it back in if you like. And we're done!
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