Marginal Cost - Online Tutor, Practice Problems & Exam Prep

Marginal cost (MC) represents the additional cost incurred from producing one more unit of output. It is calculated using the formula: (Change in Total Cost)/(Change in Quantity). As marginal product increases, marginal cost typically decreases, reflecting economies of scale. Conversely, diminishing returns lead to rising marginal costs. Understanding these relationships is crucial for optimizing production and achieving efficient market outcomes while managing variable and fixed costs effectively.

Marginal Cost

Alright, so now let's discuss the marginal cost. What's going to be marginal, right? The additional cost from adding 1 more unit of output, right? So what's the extra cost from 1 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 going to use the acronym marginal cost, MC. We've used this before but here we're going to dive into the topic a little more, right? So we've got our marginal cost, right? The additional cost from 1 more unit, well sometimes we aren't 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 1 pizza. So how do we get that one pizza? Well, we're going to kinda use an average kind of idea here, right? Since we don't know what happens with one more pizza, we're going to get this average, from the quantity change. So what we're going to use is this change in total cost over change in quantity, okay? So what it's going to tell us is that over this range, right, from when we added 1 worker we added a bunch of pizzas, but over that range what's the marginal cost of 1 more pizza in that range, right? So let's go ahead and calculate some marginal cost here, and we're going to 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 previous page we went ahead and we calculated total cost, right? We had a column for total cost and we were given total quantity, right? So what we're going to do now is we're going to use those numbers and we're going to calculate our change in total cost. So let's go ahead and do that now, and see what the marginal cost is in all these situations. So remember, we were hiring workers. Right? Here we had 0 workers, 1 worker, 2 workers, 3 workers, 4 5 workers down there, right? And that's what we were seeing on the previous page. So let's go ahead and start calculating changes in total cost, right? So let's start here and the change in total cost is just going to 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 going to be nothing but let's go ahead and calculate the first one here, right? So total cost was 100 when we had 0 workers and it went up to 180. So what's happened is our total cost has increased by 80, right? It was 100, now it's 180, it's gone up by 80, right? Let me fix that, 0. And let's keep going here, right? What happens when we add another worker, right? We had total cost of 180 and it went up to 260, right? So again, 260 minus 180, that's an extra 80 in cost, right, and again 340 minus 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 costs, right? Every time we added a worker, we had to pay them their wage, right? 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 a 4th worker, that 420 minus the 340, that's again 80. Right? And this last one here, 500 minus 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 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 going to 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 one, 80 minus the 30. Right? We already had 30 pizzas and now we got up to 80. So that's going to be, 50 pizzas there that we changed in quantity, right, we increased by 50. The next one, 150 minus 80, that's 70 more pizzas. Now we have 180 pizzas minus the 150. That's going to be 30 pizzas here. Right? 30 right there behind me, and the last one we've got 190, and 180, right? 190 minus 180. I'm going to go ahead and just get out of the way here so I'm not dodging and we'll calculate these marginal costs. So 190 minus 180 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 going to have one there when we have 0 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 going to be dividing the 2nd column and the 4th column, right? So when we got one worker, change in total cost was 80 divided by 30, change in quantity. That's going to give us a marginal cost of $2.67 per pizza. Alright? And how about at the 2nd worker? The 2nd 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 going to give us $1.60 here. Right? A dollar 60. Next one. Right. 80 divided by 70. Our change in quantity was 70 there and we're going to get $1.14. I'll round it off there. A 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 going to give us $8 as our marginal cost per pizza there at the end. Right. So we've calculated all our marginal costs and I've gone ahead and I've graphed the marginal cost curve here on the graph. Right? So this is going to be our marginal cost curve. Notice 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 y-axis here. So this is kinda follows the same graph we've always had, right? We had price usually on that axis 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 going to see it take this shape where it decreases to a point and then it starts increasing sharply, right? So this is going to be our marginal cost curve, right, And one last thing is I want to go ahead and compare 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 going to go ahead and fill it in with the numbers we had above so that the marginal cost was we didn't have one when there's 0 workers and then it went to $2.67, $1.60, $1.14 and then $2.67.8. 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 oops, $8 This marginal product, right, we calculated it in the previous videos and we just kind of calculated it again when we did our change in quantity. So let's go ahead and see the relationship here between 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 it increase, from 2 to 3 workers, right? And what happened here to our marginal cost? 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 product starts decreasing from our diminishing returns, right, between 3 and 4 and 4 and 5 workers, that marginal cost increases again. Right? So notice when that marginal product got really small here at 10, that marginal cost soared up, right? We got a really high marginal cost. Cool? So let's go ahead and make these conclusions here. Whoops. So when marginal product of labor is increasing, we saw that the marginal cost of output and the opposite, right? As marginal cost marginal product decreases, and the opposite, right? As marginal cost marginal product decreases, marginal cost increases, right? So we're going to see marginal cost increasing here when when the marginal product of labor is decreasing. And just like we saw on the graph, we saw that the marginal cost curve is initially going to, going to fall. Right? We're going to see it falling at first and then it's going to rise. Right? And then it rises. 1st, marginal cost initially falls and then rises and it's going to form a U shape. Okay, so we're going to use this to describe a few curves, the U shape. Right? And that's what we see here. It's some sort of U shape where it falls and then rises. Cool? Alright. Let's go ahead and move on to the next video.

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.

Alright, let's try this practice. Donnie Salt Life shapes surfboards in Hawaii. He leases 2 production machines paying $300 each per week. He cannot increase the number of machines he leases in his contract, so he's stuck with that amount of machines. 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, all right? So they gave us some information, right? They told us as he hires more and more workers, he's going to have certain quantities that are going to be output there. Cool, so let's go ahead and start here with our fixed cost. What do you think our fixed costs are going to be? They told us 2 costs in this problem. They told us he has 2 production machines at $300 per week and he's got laborers that he's going to hire for $400 per week. So the fixed cost is going to be those production machines, right? And he's got 2 production machines each at $300, right? And the reason these are fixed is that no matter how many surfboards he makes, he's going to have this same cost, right? This $300 each per week is not going to change no matter how many surfboards he makes. So we're going to see the fixed costs are going to be those $300 times 2, right, because he's got 2 machines and they're each $300. So the fixed cost, it's always going to be $600, right? $300 times 2, no matter how many surfboards he shapes, the fixed cost will always be $600, alright? Let's go about the variable cost. So now variable costs are going to change with output, right? So the more output we make, the more we expect to spend in variable cost. So we had 2 costs in this problem. We already said that the production machines were going to be our fixed cost, right? Because that's not going to change with output, but the workers are going to change with output, right, as we want to make more and more surfboards we're going to need more and more workers. So let's calculate our variable cost as the number of workers times the wage they're going to get, right? This is going to be our variable cost in this situation. So let's go ahead and start. At first, we've got 0 workers so 0 workers are going to get $0. How about 1 worker? When we've got 1 worker, he's going to earn the wage of $400, right? So it's going to be 1 times the $400 wage and we're going to have a variable cost of $400 there. How about 2 workers? Well now we're talking about 400 times 2, right? 2 workers so it's going to be $800 and moving right along, 3 workers, it's going to be $1200 right? That's $400 times 3. 4 workers is $400 times 4 which is $1600 and last but not least, 5 workers times $400. That's going to give us $2,000 in variable cost. Right? 5 times $400. So total cost, right, total cost is just going to be our fixed cost plus our variable cost, right? That's how we define total cost. So let's go ahead and just add across here, right? We've got our fixed cost, we've got our variable costs. Let's do it. $600 plus 0, I can do that in my head. That's $600, right? How about $600+$400, that's going to come out to $1000. $600 +$800 is going to be $1400. $600 +$1200, that's $1800. $600+$1600, that's $2200 and last but not least, $2000 +$600, that's $2600. Cool? Alright. So we've filled in quite a bit here. Now we just have to calculate average total cost and our marginal cost. So let's start here with average total cost, right, and that's just going to be that total cost. Right? Anytime we want an average cost, we just divide by quantity, right? So it's going to be that total cost divided by quantity. So let's start here. In the first case, we've got $600 total cost but no surfboards, right? So we can't calculate an average there, we didn't produce anything. How about when we've got one worker, we produce 8, right, where our quantity is 8. So we're going to take our total cost of $1000 divided by the 8 quantity and we're going to get a $125. Right? So it's going to be a $125 per surfboard there, average total cost. Next one, $1400 total cost divided by, what did we get there? 20 surfboards. Right? $1400 total cost divided by 20. That's going to get our average total cost down to $70 there, right? And continuing, we've got $1800 in total cost divided by 25 surfboards this time. That gives us a total cost of $72 and let's keep it going. We've got $2200 in total costs divided by 28 and I'll round this off here to $78.57. Cool. And last $2600 in total cost divided by 30 and that's going to give us an average cost here of $86.67. Alright. Rounding it off there. Cool. So there's our average total cost just taking that total cost column divided by the quantity for that row. Alright? Let's go ahead and finish up here with our marginal, our marginal cost, right, and that's going to just be the change in total cost over the change in the quantities, right? So we're going to need the change in total cost

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

Here’s what students ask on this topic:

What is marginal cost and how is it calculated?

Marginal cost (MC) represents the additional cost incurred from producing one more unit of output. It is calculated using the formula:

ΔTCΔQ

where ΔTC is the change in total cost and ΔQ is the change in quantity. This formula helps businesses understand the cost implications of scaling up production. For example, if the total cost increases by $80 when producing 50 more units, the marginal cost per unit is $1.60.

Why does marginal cost initially decrease and then increase?

Marginal cost initially decreases due to economies of scale, where increasing production leads to more efficient use of resources, lowering the cost per unit. However, as production continues to increase, diminishing returns set in. This means that adding more inputs (like labor) results in smaller increases in output, causing the marginal cost to rise. This relationship creates a U-shaped marginal cost curve, where costs decrease to a point and then increase sharply.

How does marginal cost relate to marginal product of labor?

Marginal cost (MC) and marginal product of labor (MPL) are inversely related. When MPL increases, indicating that each additional worker produces more output, MC decreases because the cost of producing each additional unit is lower. Conversely, when MPL decreases due to diminishing returns, MC increases as each additional unit of output becomes more costly to produce. This inverse relationship helps businesses optimize labor and production costs.

What factors can cause changes in marginal cost?

Several factors can cause changes in marginal cost, including changes in variable costs (like wages and raw materials), production efficiency, and technology. For instance, an increase in wages will raise the marginal cost, while improvements in technology can lower it by making production more efficient. Additionally, the law of diminishing returns plays a significant role; as more units are produced, the marginal cost eventually rises due to less efficient use of additional inputs.

How is marginal cost used in decision-making for businesses?

Businesses use marginal cost to make informed production decisions. By comparing marginal cost to marginal revenue (the additional revenue from selling one more unit), firms can determine the optimal level of production. If marginal revenue exceeds marginal cost, increasing production is profitable. Conversely, if marginal cost exceeds marginal revenue, reducing production is advisable. This analysis helps businesses maximize profit and allocate resources efficiently.