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The Costs of Production

1

Marginal Cost

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Alright. So now let's discuss the marginal cost what's gonna be marginal. Right? The additional cost from adding one more unit of output. Right? So what's the extra cost from one more unit of output. Let's check it out. So just here we've got that definition right? The additional cost from one more unit of output. Right? So we're gonna use um the acronym marginal cost M. C. We've used this before but here we're gonna dive into the topic a little more. Right? So we've got our marginal cost. Right? The the additional cost from one more unit. Well sometimes we are given right the one more unit as we've seen in our pizza example right? We add a worker and they add 30 more pizzas. 50 more pizzas. Right? They're adding more than just one pizza. So how do we get that one pizza? Well we're gonna kind of use an average kind of idea here. Right? Since we don't know what happens with one more pizza. We're gonna get this average from the quantity change. So what we're gonna use is this change in total cost over change in quantity. Okay. So what it's gonna tell us is that over this range? Right. From when we added one worker we added a bunch of pizzas but over that range. What's the marginal cost of one more pizza in that range? All right. So let's go ahead and calculate some marginal cost here. Um And we're gonna continue on that same example from the previous page. So what I've done is I've taken some of the information like on the on the previous page, we went ahead and we calculated total cost, right? We had we had a column for total cost and we were given total quantity, right? So what we're gonna do now is we're gonna use those numbers and we're gonna calculate our change in total cost and our change in quantity. And that's what we need to calculate our our marginal cost, Right? So let's go ahead and do that now. Um and see what the marginal cost is in all these situations. So, remember we had we were hiring workers right here, we had zero workers, one worker, two workers three workers four and five workers down there. Right? And that's what we're seeing um on the previous page. So let's go ahead and start calculating changes in total costs. Right? So let's start here. And the change in total cost is just gonna be what happens as we add workers here. Right? So here, we can't have a change when it's just the first one. So both of these are gonna be nothing. But let's go ahead and uh calculate the first one here. Right? So total cost was 100 when we had zero workers and it went up to 1 80. So what's happened is our total cost has increased by 80. Right? It was 100. Now it's 1 80. It's gone up by 80. Alright, let me fix that. Zero. And let's keep going here. Right, What happens when we add another worker, Right? We had total cost of 1 80 they went up to 2 60. Right? So, again to 16 minus 1 80. That's an extra 80 in cost. Right? And again, 3 40 -260. We're going to see that that difference is again, 80, right? So what are we seeing here in our changes in total cost? These are just the variable cost. Right? Every time we added a worker we had to pay them their wages, the wage was $80 per day. So, that's what we're seeing in the change in total cost, Right? Those fixed costs of the pizza ovens, They were 100 a day. That's not changing as we add more and more workers. That's not changing the cost. So, the only cost change we see here is from those extra workers. So, again, when we add 1/4 worker that 4 20 minus the 3 40. That's again, 80. Right? And this last one here, 500 -420. That's also 80. Right? So, our total cost has just been going up based on those variable costs. How about quantity? Well, we actually already calculated the change in quantity when we calculated the marginal product of labor, right? The marginal product of labor was our change in quantity, right? That was how we defined it as we add more and more workers. How much more output are we gonna get? So we've done this before, but let's do it right here again. Right? So the change in quantity, the marginal product of labor was 30 here in the first one, right? And then the next 1 80 minus the 30. Right? We already had 30 pizzas, and now we got up to 80. So that's gonna be uh 50 pizzas there that we changed in quantity. Right? We increased by 50. The next 11 50 minus 80. That's 70 more pizzas. Uh Now we have 100 80 pizzas minus the 1 50. That's gonna be 30 pizzas here, right? 30 right there behind me and the last one we've got 1 91 80 right? 1 91 80. I'm gonna go ahead and just get out of the way here. So I'm not dodging. And we'll calculate these marginal costs. So 1 90 minus 1 80. That gives us 10 for our final change in quantity there. Right. So let's go ahead and start calculating marginal cost per pizza. So we're not gonna have one there when we have zero workers, we don't even have any pizzas yet. So what about when we have one worker? Right, we've got 80 is our change in total cost and 30 is our change in quantity. So remember our marginal cost. Is that change in total cost over change in quantity? Right. So that's what we got here in the first one. We're just gonna be dividing the second column and the fourth column. Right? So when we got one worker change in total cost was 80 divided by 30. Change in quantity. That's gonna give us a marginal cost of 267 per pizza. All right. And how about at the second worker? The second worker, we've got a change in total cost of 80. Right, divided by a change in quantity of 50. So let's go ahead and calculate that 80 divided by 50. That's gonna give us 1.6 here. Right. A dollar 60 I guess I'll put a dollar 60. Um Next one right, 80 divided by 70 are changing quantity with 70 there and we're gonna get a dollar 14 all rounded off their dollar 14 per pizza and then 80 divided by 30. Well, we've done that one already. Right, We have the same one above 80 divided by 30. That's $2.67. And then last but not least 80 divided by 10. That's gonna give us $8 as our marginal cost for pizza there at the end. Right? So we've calculated all our marginal cost and I've gone ahead and I've graphed the marginal cost curve here on the graph. Right? So this is gonna be our marginal cost curve um noticed that on the X axis here we've got our quantity of pizzas and on the Y axis marginal cost. Right? So it's just a dollar amount on the on the on the Y axis here. So this is kind of follows the same graph we've always had right? We had price usually on that access. But this is the same thing, right? It's dollar amounts that's on that axis. So this is a very similar graph that we're used to. And here we go. We see the marginal cost, Right? And we see that it decreased to start and then it increased sharply, right? It increased really sharply. And you can expect this kind of shape every time you see a marginal cost curve, you're gonna see it take this shape or it decreases to a point and then it starts increasing sharply. Right? So this is gonna be our marginal cost curve. Right? And one last thing is I want to go ahead and compare um marginal product of labor, right? This was our change in quantity over here, marginal product of labor was the change in quantity with that marginal cost that we just calculated. Alright, let's go ahead and do that down here. So I'm gonna go ahead and fill it in with the numbers we had above. So the marginal cost was we didn't have one when there's zero workers. And then it went to $2.67 dollars, 60 dollars 14 and then to 67 8. Alright. So I'm just pulling down the numbers, we just calculated for marginal cost so that they're right here next to our marginal product. So this marginal product, $8. This marginal product, right? We calculated it in the previous videos, and we just kind of calculated again when we did our change in quantity. So let's go ahead and see the relationship here between marginal product of labor and marginal cost. Right? So, so we saw this with average costs as well. Um the idea here was that as the marginal product of labor was increasing. Right? So we saw here the marginal product of labor increase from 1 to 2 workers. And we saw an increase uh from 2 to 3 workers. Right? And what happened here to our marginal cost? Um Right here, the marginal cost went down right as our marginal product went up and again it went down, right? The marginal cost went down as our marginal product went up. And then we see the opposite once our marginal products starts decreasing from our diminishing returns right between three and four and four and five workers, that marginal cost increases again. Right? So notice when that marginal product got really small here at 10, that marginal cost sort up. Right? We got a really high marginal cost. Cool. So, let's go ahead and make these conclusions here. Uh so, when marginal product of labor is increasing, we saw that the marginal cost of output is decrease. Right? So they are inversely related right, as one goes up, the other goes down, So marginal product increase, marginal cost decrease and the opposite, right? As marginal cost, marginal product decreases, marginal cost increases. Right? So we're gonna see marginal cost increasing here when the marginal product of labor is decreasing. And just like we saw in the graph we saw that the marginal cost curve is initially gonna going to fall right, We're gonna see it falling at first and then it's gonna rise, right? And then it rises first, marginal cost initially falls and then rises and it's gonna form a U. Shape. Okay, So we're gonna use this to describe a few curves, the U shape, right? And that's what we see here is some sort of U shape where it falls and then rises. Cool. Alright, let's go ahead and move on to the next video.

2

Problem

Donny Saltlife shapes surfboards in Hawaii. He leases two production machines, paying $300 each per week. He cannot increase the number of machines he leases in his contract. He can hire as many workers as he wants at a cost of $400 per week. These are his only two inputs to produce surfboards. Fill in the remaining columns in the table below.

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3

Problem

A firm that sells headphones has the following average total cost schedule:The company currently produces and sells 600 units. A desperate customer calls and offers $550 for a pair of headphones. Should the company accept the offer?

A

Yes, because the offer is above average total cost

B

No, because the offer is above average total cost

C

Yes, because the offer is above marginal cost

D

No, because the offer is below marginal cost

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