The Production Function and Marginal Revenue Product - Online Tutor, Practice Problems & Exam Prep

The factors of production include land, labor, physical capital, human capital, and entrepreneurship. Firms demand these inputs to produce goods, with labor accounting for nearly 70% of production costs. The production function relates input amounts, like workers, to output levels, focusing on the marginal product of labor (MPL). The value of the marginal product of labor (VMP) is calculated by multiplying MPL by the product's price, representing additional revenue generated. Understanding these concepts is crucial for analyzing market dynamics and optimizing production efficiency.

The Factors of Production

Alright, guys. So now we're going to start our discussion of the factors of production markets. Okay? This is different than product markets. In the factors of production markets, it's the firms that are demanding them, right? The firms 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. 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 going to 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 includes all natural resources, so it's not just the land itself, right? It's going to 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. Again, just going to 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 going to focus on. The other ones a lot of our discussion goes over to them but labor is going to be our focus, okay? Physical capital, so this is going to be things attached to the land that man-made 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 has to do with productivity. So this comes from like training or education, okay? So we're going to say that there's more human capital when people are more educated, right? So you can imagine that people are more productive when they have a higher education, cool? And that comes from the human capital. The last one here is another type 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 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 production on a high level there. Let's start diving in. In the next video, we'll start with the production function. Alright. Let's do that.

Marginal Revenue Product (Value of the Marginal Product of Labor)

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. So if you just type in "production function" into that search bar, you can get a little more detail, but we're going to kind of go over it here too. Okay. So remember that the production function is going to relate the amount of inputs, so in our case, the amount of workers that we're putting in, to the amount of outputs, okay? So how much are we getting out of each worker? Cool? So we're going to 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 marginal fruits of our labor. If we hire 1 more worker, how much more output are we going to get? Okay? And when we talked about marginal product of labor, we used MPL. Okay? Marginal product of labor. Sometimes you see it, MP with a subscript '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 going to talk now, so this is the new part that we're adding into the production function. We're going to talk about the value of the marginal product of labor. Okay, so the value of the marginal product of labor is how much extra output, when we hire one more worker, how much extra output is going to bring into the firm in dollars, right, how much extra dollars do we get? So what we're going to do is we're going to take that marginal product of labor and multiply it by price, okay? So MPL times the price, okay? So remember that the marginal product of labor is the additional output that we're getting from hiring 1 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 the value of marginal product of labor, V MPL, but I don't really like this term and it doesn't seem to be as common as this other term, MRP, which MRP, that's the marginal revenue product. Okay? Marginal revenue product, and this is what I'm going to call it from now on through our lessons is the marginal revenue product and that kind of makes more sense because 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 going to find out what the marginal product of labor is, marginal revenue product, and we'll see what that all means. Alright. Let's do that in the following video.

Marginal Revenue Product

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. It tells us that a local pizza shop leases 2 pizza ovens for a total daily cost of a hundred. So, if you remember these pizza ovens, this is going to be like capital, right, physical capital, and this is going to be the fixed cost of the firm right here. These pizza ovens, we're going to have to pay for those anyway, right? No matter how many pizzas we make, they're always going to be there, causing fixed costs. But then, the company is going to decide how many employees it wants to hire, and that's at a wage of $80 per day, right? So that wage is going to be our variable costs, right? Because this is going to change based on how many pizzas we want to produce. If we want to produce a lot of pizzas, we're going to need a lot of people making those pizzas, alright? So we've got fixed costs of $100 a day, and then the employees will be $80 per day. We're not going to worry about the cost of ingredients; that's just going to add a layer 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 the marginal product of labor before, let's go ahead and just do it again. So remember, the marginal product of labor is how much additional are we getting by hiring 1 more worker. So when we had 0 workers, there were 0 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 0 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 3rd worker? Well, we already had 80 pizzas, and we're getting up to 150. So the 150 minus the 80 we already had, that's an extra 70 pizzas. Keep going, the fourth worker, 180 minus 150. That's again another 30 pizzas there, and then the last one, 190 minus 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 we are 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 fourth, fifth, 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, the marginal revenue product that's going to be the P times MPL, right? And this P was the $5, right? P was $5. They told us in the question each pizza sells for $5. So that's easy enough. The marginal revenue product, so when we hired the first worker, right, we got 30 extra pizzas, and those 30 pizzas we're going to sell for $5. So essentially, this first worker is worth $150 to us, right? He produced an extra 30 pizzas that we sold for $5, and he brought in a $150. Now let's go on to the next one. So the second worker, 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 going to sell for $5. 50 times $5, that gets us $250 from the second worker. How about the third worker? The third worker brought us an extra 70 pizzas. So we're going to 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 pizzas, 30 times $5, 150. See? None of this is too crazy yet. Right? And the last worker, right, he brought in 10 extra pizzas that we're going to 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 going to be our marginal cost, in this case. It's the marginal cost because if we want more pizza, we're going to 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 ovens stay 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 1 worker, well, our marginal cost was 80, right? We went from having 0 workers to 1 worker, so we had to pay an extra $80. So our wage here, our marginal cost is 80. How about the second worker? So you might be thinking that we would put a $160 in this box, right? Because there are 2 workers now each earning $80. Remember, we're talking about the marginal cost. We already had 1 worker earning $80 now we're hiring 1 more who's also going to earn $80. So our marginal cost is just 80, right? We already spent 80, we're going to spend 80 more. So our wage here again, the marginal cost is just the wage, and the same thing with 3 workers, right? We already had 2, we're going to hire 1 more, so we're going to spend an extra $80. So all the way down here, we're going to put $80. Each time we're hiring 1 more worker, that costs 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 going to get by hiring that worker, and the wage is the marginal cost, right? So we're going to think that the marginal profit is going to be that marginal revenue right, and I'm going to put the marginal revenue 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 a $150 minus the $80 we had to pay him. Well, 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 $250, but we only had to pay him $80. So the $250 minus the $80, well, that gives us $170 there. The same thing with the third worker, right? He brought in an extra $350, but we only had to pay him $80. So $350 minus $80, that's $270. Moving right along here, the fourth worker brought in a $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 brings in 10 extra pizzas, right, that we can sell for $50, but we have to pay him $80. So we're going to have a negative marginal profit in this case, right? The marginal profit is going to be negative $30, the $50 minus the $80. So we end up with a negative profit in this case, a loss by hiring a fifth 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 4 workers, right? Because the first worker is bringing in extra money, the second worker is bringing in extra profit, right? Third worker extra profit, the fourth worker extra profit, but then that fifth worker is not bringing in extra money, we lose money by hiring him; so we're not going to hire him. Alright? So let's go down here before I come back in. 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 4 workers because if we went to that 5th worker, right, in this fifth worker, well here, the marginal revenue product is less than the wage. Right? The wage is higher so we don't want to hire that worker, we want to stop when we get to 4 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 going to be the profit-maximizing point. So one last thing and we're going to talk about this more in the next video. I'm going to come back in. I think I fit here. Hey, guys. Alright. So, one last thing here is that this MRP curve, so when we go ahead and we graph the MRP curve, well, this is going to 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 were $200, we wouldn't want to hire that fourth worker, right, because at that fourth worker, the MRP would be less than the wage. Cool? So you're going to see that that MRP curve, that is our demand curve because based on that curve is how many workers we are going to want to 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.

Here’s what students ask on this topic:

What are the factors of production and why are they important?

The factors of production are the inputs used to produce goods and services. They include land, labor, physical capital, human capital, and entrepreneurship. Land encompasses all natural resources, labor refers to the physical and mental contributions of people, physical capital includes man-made objects like machinery, human capital involves the skills and education of workers, and entrepreneurship is the ability to organize and manage these resources. These factors are crucial because they determine the quantity and quality of output a firm can produce, influencing overall economic growth and efficiency.

How is the marginal product of labor (MPL) calculated?

The marginal product of labor (MPL) is calculated by measuring the additional output produced when one more worker is added, holding all other inputs constant. Mathematically, it is expressed as:

$\mathrm{MPL}=\frac{\mathrm{\Delta Q}}{\mathrm{\Delta L}}$

where $\mathrm{\Delta Q}$ is the change in output and $\mathrm{\Delta L}$ is the change in labor. This helps firms understand the productivity of their workforce and make informed hiring decisions.

What is the value of the marginal product of labor (VMP) and how is it different from MPL?

The value of the marginal product of labor (VMP) represents the additional revenue generated from hiring one more worker. It is calculated by multiplying the marginal product of labor (MPL) by the price of the output:

$\mathrm{VMP}=\mathrm{MPL}\times P$

where $P$ is the price of the product. While MPL measures the additional output, VMP translates this output into monetary terms, helping firms assess the financial benefit of hiring additional workers.

What is the marginal revenue product (MRP) and how is it used in decision-making?

The marginal revenue product (MRP) is the additional revenue a firm earns from employing one more unit of labor. It is calculated as:

$\mathrm{MRP}=\mathrm{MPL}\times P$

where $P$ is the price of the output. MRP helps firms determine the optimal number of workers to hire by comparing the MRP to the wage rate. If MRP exceeds the wage rate, hiring more workers is profitable. Conversely, if MRP is less than the wage rate, reducing the workforce may be necessary.

How do firms use the production function to optimize production?

Firms use the production function to understand the relationship between inputs (like labor and capital) and output. By analyzing this relationship, firms can determine the most efficient combination of inputs to maximize output. The production function helps identify the marginal product of each input, guiding decisions on resource allocation. For example, if the marginal product of labor is high, a firm might hire more workers. Conversely, if the marginal product of capital is higher, investing in machinery might be more beneficial. This optimization ensures that firms produce at the lowest cost and highest efficiency.