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Current time:0:00Total duration:9:02
PRD‑4 (EU)
PRD‑4.A (LO)
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Video transcript

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 and the video we constructed it at this firm is a car wash and also how we can use this to think about what's a rational number of people for this firm to hire and 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 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 first person so what we could do is we can multiply the quantity of people which is 1 times the average times the average increment the average marginal product revenue that we get from one person or I should say the average we get going from zero to one person and the average is 25 the average is 25 and the reason why I set it that way is you can imagine a reality we're getting 1/10 of a person you get a value higher than 25 and you might say how do I get a tenth of a person well what if one person shows up every 10 days and then you get a little little less benefit as you get closer and closer to a whole person per hour but on average as we go from zero to one person we are getting 25 dollars of value or 25 dollars of marginal revenue per person per hour and 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 of 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 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 for Z between 0 and 1/2 is above this rectangle and between 1/2 and 1 it is below the rectangle and the area above is the same as the area below so $25 is also the area is also the area under under this curve and that's essentially how much benefit the firm is getting from hiring from going from zero to one person they're getting $25 of benefit now how much benefit they get going from one to two people well going from one to two our change in quantity of people per hour is one and then our average marginal product revenue going from one to two 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 hot what's the marginal product revenue we get going from 2 to 3 people well the average height here we'd essentially just say well 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 x 15 times 1 you get $15 $15 of benefit between 3 & 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 and 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 and I mentioned earlier that this is a competitive firm and 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 labour market so these are two different these are two different markets and I want to clarify in the car wash market in car wash market we are competitive we are a competitive supplier or I guess we could say we are seller of car washes in the labor market in the labor market our firm is a competitive is a competitive buyer now I'll do a little bit of an aside here because when we talk about suppliers we there's 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 so 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 doesn't you know you're not taken by surprise if someone says it just it means monopsony or the word is monopsony monopsony not relevant to this video we are the opposite of a monopoly in the labor market we there are we're assuming that we are 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 carwash market we're assuming that we are one of many competitive sellers monopoly means only one seller monopsony means one powerful buyer but the whole reason why I'm saying that it's 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 take that the market wage is going to be let's just say it is $10 per hour $10 per hour and given that what is a rational number of people to hire well that first 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 will just be my started will 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 two people the area would be between zero and two and under the curve which would be 20 or you could say the increment from going from one to two people is another $10 so we're going to two to three people this area right over here is another $10 if you go from three to four people this area under here is another $10 under this green curve so does it make sense to hire that first 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 so you definitely want to hire one person does it hire it make sense to hire that second person well the marginal product revenue is going to be $20 from that second person your marginal cost from that second person is $10 you're going to make $10 on that first on that second person so you should hire that second person the third person you're going to make $15 off them they're going to cost three they're going to cost you $10 so you're going to and this is all in a per hour basis you're going to make $5 so you should hire that the fourth person well now it's interesting the fourth person you're going to you're going to make $10 total off of the fourth person but you're not but you're also going to have to pay $10 for that fourth person so it doesn't make sense for you to hire a toll another total fourth 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 the net benefit we're going to get is going to be this area right over here so it would be rational to get them but what you're seeing is it makes sense to keep increasing the quantity demanded it keeps 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
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