Which of the following is true of the relationship between marginal cost and marginal product?

Problem 34 Hard Difficulty

Answer

Marginal product is additional product produced because of one addition unit of input andmarginal cost is additional cost because of production of one additional unit of output. As per thegraphs in the text, it can be seen that marginal product and marginal cost are inversely relatedi.e. when marginal cost increases, marginal product decreases. This happens because whenmarginal cost i.e. cost of production is increasing then the capacity of production is decreasing sothe marginal product will decrease. The relationship between marginal cost and marginal productstands true for both long-run and short-run. (adsbygoogle = window.adsbygoogle || []).push({});

Video Transcript

in order to figure out the relationship between marginal product on marginal cost. Let's first graf thes curbs. So in the top over here, I have the marginal product curb and I have the quantity of an input on the, uh X axis and the marginal product on the right, the y axis. So the reason this is the case is because marginal product represents the additional output from hiring or the change in the total output from hiring one additional input that could be labor or capital. So in this situation, let's just think of labor. Okay, so my marginal product, I will have it increase, or I will have it decrease until some point. And then, at some point things were gonna become so crowded that it will start to fall again. Okay, so let's let's think about why this is the case. So this is how the curb will look and this is the maximum right here. Why would this be the case? Suppose you have a small room Three people that Max can fit into a small room When you have three people that Max thinks you're kind of crowded once you go from one person to person, you can become more efficient. You can produce more, um, input. Okay, but you'll produce less than the person before you because of diminishing marginal returns. And then the next person. That third person that high that's hired, produces or ads less than the second person but still, um, increases the total output. Now, when you hire 1/4 worker and struck to cram people into this room, things we're going to reverse, you won't be able to fit these people, and they will be less efficient than if you let them be as original. Now, when we're talking about marginal cost and the quantity of output. If we looked at our longer on average, cost Tripp or even are short on average Cost group, we always have this kind of curve where as quantity increases, we have economies of scale for a while, and we have conscience returns to scale. And then we have Disick on Ami's of scale, and because of this, we see that over here, the minimum and maximum of the minimum of the marginal cost curve and the maximum of the marginal product curve are at the same point. So what this tells us is that sorry? What this tells us is that these curves are inverse ery, inversely related. These are inversely related, so marginal product is equal to the wage. We're sorry the marginal cost marginal cost is equal to the price of labor, So we'll call that wage or in parentheses or rent for capital over the marginal product. And let's come up with a mathematical deprivation for why this might be the case. So the marginal cost is equal to the change in total cost over the change in quantity of output. Correct, and the change in total cost is always going to be equal to the change in variable cost. The change in total variable costs because fixed costs stay fixed and doesn't matter. So it's the total variable change in total variable cost over the change in quantity. The change in total variable cost. If we just assume labor labor equals of variable input, a variable input that means that it is equal to wage times the quantity of labor over the change in quantity. Why does this make sense? Because if our variable costs are only labor, then to pay to find the cost that's associated with labor is equal to however much you pay for labor times the number of laborers so marginal product. On the other hand, by definition, marginal product by definition is equal to the change in quantity over the change in labor. So how much do you get? How much What is the increase in your total output per additional worker hired? So now we see a relationship between, um, marginal product and ah, the marginal cost an inverse relationship. So we'll have this over here and if we take, um, one divided. But so this is equal to won over wage times change in labor over the change in quantity. So actually, let me change this up a bit. So we have We have changing labor over the change in quantity and that is equal to the inverse of the marginal product. So the change in labor over the change in quantity is equal to one over the marginal product. So we can substitute one over the marginal product in for the change in labor over the changing quantity. So the marginal cost is equal to wage times one over the marginal product which is equal to wage over the marginal product. So marginal cost and the marginal product have an inverse relationship, an inverse relationship. As one goes up, the other must go down.

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