The Production Function and Marginal Revenue Product

Alright guys, so now we're gonna start our discussion of the factors of production markets. Okay, So this is different than product markets and the factors of production markets. It's the firms that are demanding them, right? The firm's demand the factors of production so that they can produce and the individuals are the ones who provide it. Alright, let's check it out. So we've talked about factors of production in a bit more detail in another video, I believe it was just called factors of production. Right? So I'm just gonna go on a high level here and just mention what they are. Right? If you go to that video factors of production, you get a little more detail about each of these. But I think you'll get enough information just right here. Okay, so land is our first factor of production and land. It includes all natural resources. So it's not just the land itself. Right? It's gonna include things like forests, things like Oil deposits underground, right? These things are all in the land category. Alright, the next one is labor. So labor is a very important one. This makes up almost 70% of the money spent on factors of production. Okay, so labor is the big chunk here. And this is the physical and mental contributions of people in the production process. Right? So if you're hired by a pizza company to make pizzas, that's the labor right there. Okay, I'm just gonna note that we are going to spend our time in this chapter. Pretty much focusing on labor. Okay, so that's the factor of production. We're gonna focus on the other ones. A lot of our discussion goes over to them um But labor is going to be our focus. Okay, Physical capital, so this is gonna be things attached to the land that manmade, things attached to the land, like factories or any equipment that we use in the production process. Next is human capital. So human capital, it's it has to do with the productivity. So this comes from like training or education. Okay, so we're gonna say that um there's more human capital when people are more educated, right? So you can imagine that um people are more productive when they have a higher education and that comes from the human capital. Last one here is another type of of human capital in a sense, this is entrepreneurship, this is a little different. Okay, so this one, it's the resource that organizes, manages and a C assembles the other ones. Okay, so the entrepreneurship, they're the ones who have the ideas that put this all together, they bring this all to the table. Okay, so that's another factor of production, you need that entrepreneur to have those ideas to put this all together. Cool, Alright, so that's the factors of productions on a high level there. Um let's start diving in in the next video, we'll start with the production function. Alright, let's do that

Alright so now let's discuss the production function. This has come up before. We've had another video on this. I believe it was called production function. And diminishing returns. Um So if you just type in production function into that search bar you can get a little more detail. But we're gonna kind of go over here to. Okay so remember that the production function it's going to relate the amount of inputs. So in our case the amount of workers that we're putting in to the amount of output. Okay so how much are we getting out of each worker? Cool. So we're gonna talk about this concept the marginal product of labor. So remember marginal that's one more. Right? When we add one more, how much more does our labor produce? Okay so how much more? I like to think of it as the fruits of our labor? Right So the marginal fruits of our labor if we hire one more worker, how much more output are we going to get? Okay and when we talked about marginal product of labor we use M. P. L. Okay, marginal product of labor. Sometimes you see it mp with a little L. Here so it's the marginal product and it's of labor like that. Okay so either one is going to work for our case and then we're gonna talk now so this is the new part that we're adding into the production function. We're gonna talk about the value of the marginal product of labor. Okay so the value of the marginal product of labor is how much is that extra output? When we hire one more worker? How much is that extra output gonna bring into the firm in dollars. Right? How much extra dollars do we get? So what we're gonna do is we're gonna take that marginal product of labor and multiply it by price. Okay. So mpl times the price. Okay. So remember that that marginal product of labor is the additional that additional output that we're getting from hiring one more worker. Right? So, we take that extra output they get and we multiply it by what we would sell it for. And that's how much revenue we're going to get from that. Okay. So some books call it this value of marginal product of labor? V. M. P. L. But I don't really like this term and it doesn't seem to be as common as this other term. M. R. P. Which mrp that's the marginal revenue product. Okay, marginal revenue product. And this is what I'm gonna call it from now on through our lessons, is the marginal revenue product. And that that kind of makes a little more sense cause when we say value of the marginal, I'm not really sure what we're talking about as much, but here it's clear we're talking about revenue. How much extra revenue are we getting from this marginal product? Cool. Alright. So now that we've set the stage, let's pause real quick and then we'll do this example where we're gonna find out what the marginal product of labor is, marginal revenue product. And we'll see what that all means. All right, let's do that in the following video.

Alright, so let's dive into this example right here, and this is the same example that we used when we first studied the production function. Now, we're just adding that extra layer where we talk about the marginal revenue product. Cool. Let's check it out. So it tells us that a local pizza shop leases two pizza ovens for a total daily cost of 100. So, if you remember these pizza ovens, this is going to be like capital, right? Physical capital. And this is gonna be fixed costs of the firm right here. These these pizza ovens, we're gonna have to pay for those anyways, right? No matter how many pizzas we make, they're always gonna be there causing fixed costs. But then the company is gonna decide how many employees it wants to hire and that's at a wage of $80 per day. Right? So that wage is gonna be our our variable costs, right? Because this is gonna change based on how many pizzas we want to produce. If we want to produce a lot of people or if we wanna produce a lot of pizza, we're gonna need a lot of people making those pizzas. All right, So, we've got fixed costs of $100 a day and then the employees will be $80 per day. We're not gonna worry about cost of ingredients. That's just gonna add a layer. We don't need we don't need to worry about But we've added this here that each pizza sells for $5. Okay, So now we've got a price for the pizzas, right? This $5 That is our price. Okay, That is the price. So let's go ahead and start filling this out. We've done marginal product of labor before. Let's go ahead and just do it again. So remember marginal product of labor, is how much additional are we getting by hiring one more worker? So when we had zero workers, there were zero pizzas, right? The ovens are just sitting there, no pizzas being made. But then once we hire that first worker, right? When we hire that first worker, we had zero pizzas and we went up to 30 pizzas, Right? So there's an additional 30 pizzas made. How about the second worker? We already had 30 pizzas from the first worker and it brought us up to 80. Right? So we're getting an extra 50 pizzas, the 80 minus the 30. So there's an extra 50 pizzas when we hire a second worker. And then let's do the same thing all the way down. How about the third worker? Well, we already had 80 pizzas, and we're getting up to 1 50. So the 1 50 minus the 80 we already had. That's an extra 70 pizzas keep going. The fourth worker, 180 minus 1 50. That's again, another 30 pizzas there. And then the last 1, 1 90 -180. Well, that gets us an extra 10 pizzas. And this brings back that idea of diminishing returns. Right? So there were a few workers. The first few workers were getting bigger marginal product, right? Because we only had one guy, so he had to do everything. The second guy, they were able to specialize a little bit third even more specialization. But then by the 4th and 5th, they're kind of stepping over each other's toes. Maybe the pizza ovens are full of pizza. They start to get restricted, right? And they have less marginal product. Cool. So now let's go here to the marginal revenue product. So remember marginal revenue product, that's gonna be the P. Times M. P. L. Right? And this P. Was the $5 right? P. Was $5. They told us in the question, each pizza sells for five. So that's easy enough. The marginal revenue product. So, when we hired the first worker, right? We got 30 extra pizzazz and those 30 pizzas, we're gonna sell for $5. So essentially this first worker is worth 100 and $50 to us. Right? He produced an extra 30 pizzas that we sold for five bucks and he brought in 100 $50. Whoops. Let's try that again. $150. All right, now let's go on to the next one. So, the second worker, he he added an extra 50 pizzas. Right? When we hired the second worker, it brought us up from 30 to 80. So we got 50 extra pizzas that we're gonna sell for $5.50 times $5. That gets us $250 from the second worker, right? How about the third worker? The third worker brought us an extra 70 pizzas. So we're gonna do the mpl of 70 times the $5. Well that third worker brought in an extra $350. Go on to the fourth one. Now we're back to 30. So he brought in 30 extra pizzazz 30 times $5 150. See none of this is too crazy yet. Right? And the last worker right? He brought in 10 extra pizzazz that we're gonna sell for $5. So he's only bringing in an extra $50 in revenue. Right? So we hired him and we earned $50 extra in revenue. Cool, now let's go on to the next one. The wage. So remember the wage was $80 a day per employee. Right? So this wage, it's really gonna be our marginal cost in this case it's the marginal cost because if we want more pizza, we're gonna have to hire more workers. Right? So what's the only cost that changes here. We didn't have to buy more ovens. Right? The oven state constant. The only cost that's changing is how many workers we have, how much extra wages we're paying. Right, So let's go ahead and check this out when we had one worker. Well, our marginal cost was 80, right? We went from having zero workers to one worker. So we had to pay an extra $80. So our wage here are marginal cost is 80. How about the second worker? So you might be thinking that we would put $160 in this box, right? Because there's two workers now each earning 80 bucks. Remember we're talking about the marginal cost? We already had one worker earning $80. Now we're hiring one more, who's also gonna earn $80. So our marginal cost is just 80, right? We already spent 80. We're gonna spend 80 more. So our wage here again, the marginal cost is just the wage and the same thing with three workers, right? We already had two. We're gonna hire one more, so we're gonna spend an extra $80. So all the way down here, we're gonna put $80 each time we're hiring one more worker that cost us an extra $80. Cool. So let me get out of the way for this marginal profit. The big payoff here. What we've been talking about leads to this. Okay, So we've got our marginal revenue product and our wage, which is our marginal cost. So, if you think about it, this marginal revenue product, this is our marginal revenue, right? This is the extra money that we're gonna get by hiring that worker and the wage is the marginal cost, Right? So we're gonna think that the marginal profit is gonna be that marginal revenue, right? And I'm gonna put marginal revenue of the product minus the marginal cost, which is the wage, right? So the marginal revenue product minus the wage there. So let's see what we get when we hired that first worker, he brought in 100 and $50 minus the $80. We had to pay him what we came out on top $70 right? We came out on top $70 because he brought in more than we had to pay him. The same thing with the second worker he brought in to 50 but we only had to pay him 80. So the 2 50 minus the 80. Well, that gives us 1 70 there. Same thing with the third worker, right? He brought in an extra 3 50 but we only have to pay him 80. So 3 50 minus 80 that's $270. Moving right along here. The fourth worker brought in 150 but we only had to pay him 80. So we got an extra $70 by hiring him. But what about the last worker now the last worker only brightens in 10 extra pizzazz, right? That we can sell for 50 bucks, but we have to pay him $80. So we're gonna have negative marginal profit in this case, right? The marginal profit is gonna be negative $30 the 50 minus the 80. So we end up with a negative profit in this case a loss by hiring 1/5 worker. So just by seeing this chart, you could probably make a good conclusion about how many workers to hire, Right? So in this case it's probably pretty clear that we want to hire four workers, right? Because the first workers bringing in extra money, the second workers bringing in extra extra money, extra profit, right? Third worker extra profit. Fourth worker extra profit, But then that fifth workers not bringing in any extra money, we lose money by hiring him, so we're not gonna hire him. All right, So, let's go down here before I come back in. Um Let's go ahead and make these conclusions. So, a competitive profit maximizing firm will hire workers up to the point where the marginal revenue product equals the wage. Notice in our example, there was no situation where the marginal revenue product equaled the wage, right? They were never the same. But what you never want to be is in a situation where you're paying a higher wage than the marginal revenue product. So we stopped at four workers, because if we went to that fifth worker, right, in this fifth worker, well, here, the marginal revenue product is less than the wage, right? The wages higher. So we don't want to hire that worker. We want to stop when we get to four workers. In all those cases, the marginal revenue product was greater than the wage. And ideally we could stop when the marginal revenue product equals the wage. Okay, And that's just the idea of marginal revenue equals marginal cost, right? We've talked about that before and that is gonna be the profit maximizing point. So, one last thing and we're gonna talk about this more in the next video, I'm gonna come back in. I think I fit here. Hey guys. All right, So, one last thing here is that um this mrp curve? So when we go ahead and we graph the mrp curve, well, this is gonna be the demand curve for the firm, the demand curve for labor. Okay. So the firm is going to demand based on their mrp and you could think about that, right? If the wage was different, say the wage was $50 instead of 80 we would have hired that fifth worker, right? Because the marginal revenue product would equal the wage, right? And what if the wage was $100 right? That would also change our situation, or if the wage was, you know, $200 if the wage was $200 we wouldn't want to hire that fourth worker, right? Because um at that fourth worker, the mrp would be less than the wage. Cool. So you're gonna see that that mrp curve, that is our demand curve, because based on that curve is how many workers were gonna wanna hire. Cool. So in the next video, we'll see some graphs and we'll see the demand curve there on the graph. Alright, so let's go ahead and do that now