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How many people to hire given the MPR curve

Given that hiring more workers gives more revenue, but also has additional cost, what is the optimal amount of labor to hire? We begin thinking about this as well as briefly discuss another type of competition: monopsony labor markets.  Created by Sal Khan.

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Video transcript

Voiceover: What i want to do in this video is dig a little bit deeper in this marginal product revenue curve, and really make sure we understand what it's telling us, that it really is the marginal benefit curve for this firm. In the video we constructed, this firm is a car wash. Also, how we can use this to think about what's a rational number of people for this firm to hire? Just as a reminder, this horizontal axis here, this is a quantity of labor per hour, so this is people per hour that are working at the firm. People per hour. And the vertical axis here, the marginal product revenue, that you could view as the marginal dollars, or the incremental dollars that you're getting per person, per hour. Per person, per hour, per hour. And to just verify that it's telling us the same thing visually that this table told us right up here, we can think about what is the marginal, how much incremental revenue do we get from hiring that 1st person. What we could do is we could multiply the quantity of people, which is 1, times the average, times the average increment, the average marginal product revenue that we get from 1 person, or I should say, the average we get going from 0 to 1 person, and the average is 25. The average is 25. The reason why I said it that way, is you could imagine a reality where getting a tenth of a person, you get a value higher than 25. You might say, how do I get a tenth of a person? Well, what if one person shows up every ten days? Then you get a little less benefit as you get closer and closer to a whole person per hour. But on average, as we go from 0 to 1 person, we are getting $25 of value, or $25 of marginal revenue per person per hour. So if you wanted to figure out what's the total marginal revenue that we got from this person right over here, the total incremental revenue that this is allowing us to get, well, it's the one person times the average marginal product revenue, which is 25, so that would give us the area of this rectangle right over there, which would be $25. Now, and you would really have to do a little bit of calculus to fully appreciate it, but I think you can look at it geometrically, that also happens to be, given that this is a line, that our curve, our marginal product revenue is a line right over here, that the area under this rectangle is going to be the same thing as the area under the orange curve. The orange curve, between 0 and ½ is above this rectangle and between ½ and one, it is below the rectangle. The area above is the same as the area below. So $25 is also the area, is also the area under this curve. That's essentially how much benefit the firm is getting from hiring, from going from 0 to 1 person. They're getting $25 of benefit. Now, how much benefit do they get going from 1 to 2 people? Well, going from 1 to 2, our change in quantity of people per hour is 1, and then our average marginal product revenue going from 1 to 2 people is $20. So, it is $20, and so the area is 1 times 20, and that's also going to be the same as the area under the curve. So the area under the curve right over there is going to be 20. Likewise, the area under the curve, if we want to say how much ... What's the marginal product revenue we get going from 2 to 3 people? Well, the average height here, we'd essentially just say, "What is the area between 2 and 3?" And we can figure out that area by saying, "Well the average height, The average height is 15. Multiply 15, so this height, the average height is 15. Multiply 15 times 1. You get $15, $15 of benefit. Between 3 and 4, the average height is 10. The average height is 10, so you get 10 times 1. You get $10 of benefit, would be the area under the curve right over here. $10 of benefit. Then the area under the curve there, by the same argument, is $5. Is $5 of benefit. Now, we've ... Given this, this is just telling us the revenue we're getting, but it's really not telling us, it's really not telling us what is the optimal, or the rational number of employees to hire? To do that, we have to think about the cost per employee, the marginal cost that we are actually incurring. I mentioned earlier that this is a competitive firm. When I mentioned it before, I talked about it being competitive in terms of the car wash market, so it was a competitive supplier, but let's assume that it is also a competitive buyer in the labor market, so these are two different, these are two different markets, and I want to clarify. In the car wash market, in the car wash market, we are competitive, we are a competitive supplier, or I guess we could say are a seller of car washes. In the labor market, in the labor market, our firm is a competitive, is a competitve buyer. Now, I'll do a little bit of an aside here, because when we talk about suppliers, there's the competitive suppliers, where there's many undifferentiated people who are supplying some type of good or service and the opposite of that was a monopoly, so a non-competitive, non-competitive. As a seller, we call that a monopoly. If we had a non-competitive buyer, so if you had many sellers but only one big buyer that could have a lot of market influence, and we haven't done a deep analysis of that yet, that word, just so you know it, and you're not taken by surprise if someone says it, it means monopsony, or the word is monopsony. Monopsony. Not relevant to this video. We are the opposite of a monopsony in the labor market. We are assuming that we are a competitive buyer. There are many, many, many, many, many buyers here, so we essentially just have to take the market wages, and we are also the opposite of a monopoly in the car wash market. We're assuming that we are one of many competitive sellers. Monopoly means only one seller, monopsony means one powerful buyer. The whole reason why I'm saying that we are competitive in the labor market is I'm assuming that we're just going to have to take the market wages, so the market wage for the type of labor we're hiring, so the market wage, and we're just going to have to take that. The market wage is going to be, let's just say it is $10 per hour. $10 per hour. Given that, what is a rational number of people to hire? Well, that 1st person we hire, we're getting $25 of benefit. The marginal cost of them, and we can actually draw a marginal cost curve. The marginal cost curve will just be flat right here at $25. It'll just be, sorry, it'll be flat here at $10. That's how much it costs us. If we hire one person, it costs us, the area would be $10. If we hire 2 people, the area would be between 0 and 2, and under the curve, which would be 20, or you could say the increment from going from 1 to 2 people is another $10, or going from 2 to 3 people, this area right over here is another $10. If you go from 3 to 4 people, this area under here is another $10, under this green curve. Does it make sense to hire that 1st person? Sure, you're going to get $25 in revenue, and you're going to have $10 in wages, so you're going to have $15 of benefit. You definitely want to hire one person. Does it make sense to hire that 2nd person? Well, the marginal product revenue is going to be $20 from that 2nd person. Your marginal cost from that 2nd person is $10, so you're going to make $10 on that 2nd person, so you should hire that 2nd person. The 3rd person, you're going to make $15 off them, they're going to cost you $10 dollars, so you're going to, and this is all on a per-hour basis. You're going to make $5, so you should hire that. The 4th person, well, now it's interesting. The 4th person, you're going to make $10 in total off of the 4th person, but you're not, but you're also going to have to pay $10 for that 4th person, so it doesn't make sense for you to hire another total 4th person. Now, if you could, it could make sense for you to hire another half person, maybe someone who shows up every other day, if this still holds, or maybe someone who shows up for half an hour, or maybe someone who is doing this job and also operating the cash register, and they're kind of going in between. Because for a half-person, it does make sense. A half-person is going to cost $5, and their marginal benefit is going to be the area under the curve between this point and this point, and so we get, so the profit from that person, the net benefit we're going to get is going to be this area right over here. It would be rational to get them. But what you're seeing is, is it makes sense to keep increasing the quantity demanded. It makes sense to keep hiring more and more people until the marginal benefit, or another way of saying, the marginal product revenue curve is equal to the marginal cost curve. After that point, the person's costs are higher than their benefits, and you wouldn't want to hire them.