Factor markets worked example | Microeconomics | Khan Academy

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 can have a go at it before we do it together.

All right, now let's do it together. So we're going to do side-by-side graphs, one for the market and one for the firm, Epic Eats. 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. This is the market.

And then over here, I want to do 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. This is at 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 going to be a lot of labor demanded, and then as the wage goes down, more and more people are going to want to hire people.

This is the market labor demand curve. Demand curve, and then the supply curve is going to be upward sloping. At a low wage rate, not a lot of people are going to want to give their labor, but then as wages go up, more and more people are likely to enter and want to be part of the labor force.

So this is going to be the market labor supply, 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 firm that hires in a perfectly competitive labor market. So it's just going to 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 is for Epic Eats that it has some marginal revenue product at a certain quantity, and then as it hires more and more people, it tends to have diminishing returns.

So the typical marginal revenue product curve looks something like this, so that'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 could 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 for the firm is right over there.

So we did this first part, and the quantity of workers hired by the firm—what would be rational 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 W sub F because operating in a perfectly competitive 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 wages being the same, but they had a price increase, 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 going to have a situation where the MRP shifts to the right or right and up, and so you're going to have MRP 2. This is after the price increase, and notice now we intersect the MFC line at a higher point.

So what will happen to the number of workers hired? The 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 can answer that.

All right, so they give us a few things. So the marginal product of the last unit of capital, so we can say marginal product of the last unit of capital use (cap 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 last 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 over here. The rental rate of capital, you could 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 figure out 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 costs. One way to think about it is the number of units per dollar that the firm gets 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 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.

And then we just solve for this, so this will get us to—we're going to have 4,000, this is 4,000 units divided by 400. 400 is 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, yep, 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 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.