The Relationship Between Average Cost and Marginal Cost: Videos & Practice Problems

Understanding the relationship between marginal cost and average cost is crucial in economics. Marginal cost influences average cost; when marginal cost exceeds average cost, it drives the average up, and vice versa. For example, average fixed cost decreases as output increases, while average variable cost and average total cost typically follow a U-shape, initially decreasing and then increasing. Key equations include average total cost (ATC) as total cost divided by quantity, and the relationship between marginal cost and average costs is essential for analyzing production efficiency and market dynamics.

Average Cost and Marginal Cost

All right, guys. Now I want to help you build a little intuition about marginal cost and average cost, right? How are they related? Let's check it out. So what we're going to see is that the average cost is going to rise or fall depending on the marginal cost of the next unit, alright? So if we consider the marginal cost, that's going to be the driving force of the average cost, right? It's going to be what drives it up or down, okay? So I figured a great way to kind of bring this all together is to talk about GPAs for a second, okay? So we're going to instead of talking about costs, we'll think about your GPA, the semester GPA as your marginal GPA, right? What happens if I take one more semester of classes? And your cumulative GPA, right, from every semester, that's going to be your average GPA. Alright? So let's go ahead and see what happens in this example.

So here you go, you start freshman year in the fall, you're partying way too much and you're failing all your classes, you're not even showing up for lecture, you end up with a 1.5 GPA, yikes, right? And then in the spring you're like, you know what, I'm going to buckle down, I'm going to do a great job and you end up pumping out a 3.0 GPA right there and then sophomore year comes around and you hit that sophomore slump, right? And your grades start decreasing again and in the spring you're back down to a 1.6 right? And that point is probably where you're like, maybe I should start using Clutch, right? So here we are now and let's see what happens with these marginal GPAs and the average GPA. Right, so the average is going to be the total divided by the quantity, right? And in this situation it's going to be the quantity of semesters.

We're going to see that in the first semester your average GPA, well you've only had one semester of classes so that is your average right? The GPA that you got that first semester, that's your average GPA. Now what about after two semesters, right? In this situation, we're going to add your grades in both semesters and divide it by the number of semesters. Right? We had two semesters in this case. So it's going to be 1.5 plus 3 divided by 2 and there we go. There's our average GPA of 2.25 and that's going to be what we put in here. Right? So let's go ahead and add another semester, right? So now sophomore year started and you got a 2.8. Well to find our cumulative GPA here, we're just going to add all three semesters and divide by 3. Right? And obviously this is a simplified example, obviously GPA has to do with credit hours and all of that, but let's just keep it simple right? Every semester you're taking the same amount of credits and they're all worth the same whatever. So it's been three semesters now, so we're going to take that total of 3 and divide by 3. 1.5 + 3 + 2.8 divided by 3 and we're going to get, I'm going to round it to 2.43 right there as your GPA, and the last one is where we have one more semester right and you started slacking off again and you pulled off a 1.6.

Alright, so let's see what happens here. Now I'm going to do it up here where I have some space. We're going to add all the semesters, right? 1.5 plus 3 plus 2.8 plus 1.6 right. All the semesters and we're going to divide by 4 because that's the quantity of semesters here and let's see what that averages. We've got 1.5 plus 3 plus 2.8 plus 1.6 divided by 4 and we're going to get 2.23. I'm going to round it off there. 2.23. Alright? So there we go. We figured out what those averages are based on those marginal. So let's go ahead and see how this marginal is driving the average. Right? So let's see what happens. In this semester the marginal went up, right? And when the marginal went up we saw the average go up, right? So we had a higher marginal cost than the average cost, right? And it brought the average up. But now notice what happens in the second semester, your GPA falls a little bit, right? Between spring and fall there, your marginal GPA, right, what you did in the semester went down, right? But it's still higher than the average. Even though the marginal cost fell, this marginal cost is higher than this average, right? So the previous is only going to be driven based on the following semester's marginal. Even though the marginal decreased, you did worse this semester than last semester, our average still goes up, right? And that's because the 2.8 is bigger than the 2.25, right? This semester you did better than your average so it's going to drive the average up, alright? And last one here, we see that again your GPA dropped, right? But this time it dropped below the average, right? The average in this case was the 2.43 and you only managed to pull off a 1.6 right? So look what happens, you're going to see that the cumulative GPA drops right? So it doesn't really matter the direction the marginal cost is going, what matters is whether it's higher or lower than the average right and that's what's going to drive the average cost up or drive the average cost down. So we saw that when the marginal cost is greater than the average cost, right, your marginal GPA was greater than the average, well it's going to increase the cost when we produce another unit, right? That marginal Cosby is going to drive up the average and the opposite, right? When the marginal cost is less than average cost, it's going to decrease the average cost when we add another unit, right? So that's going to be the relationship that we see there between the marginal cost and the average cost, right? So it depends if the marginal cost is greater than or less than the average and it's going to drive it in the direction of the marginal cost, right? Cool. Let's go ahead and pause here and then we'll continue on the bottom of the page.

Patterns of MC, AFC, AVC, and ATC curves

Alright guys, now let's go back to that pizza example, right. These are all numbers that we've calculated previously, Some of it was given to us automatically, right? We've got quantity of pizzas, the cost of the ovens, the cost of the workers, total cost, and marginal cost. Right? These are either things that were given to us or that we've calculated in previous videos. Right? So we're going to start with this information and let's go ahead and calculate our average fixed cost, our average variable cost, and our average total cost, in each situation. Alright? So let's go ahead and start here with fixed cost. Remember that fixed costs stay the same no matter how much we produce, right? So what would you expect to start happening with fixed costs? If the cost stays the same but the quantity keeps getting bigger and bigger, right? This numerator is going to stay the same, fixed cost, but this denominator is going to increase and increase, right? So what's going to happen is we're going to split up the same amount of cost between more and more units. So we're going to expect the average fixed cost to continue decreasing as output increases. Let's check it out. So we've got a fixed cost, right? It's always going to be $100, right? And our quantity is going to be over here, it's going to be changing as we increase our workers and increase our output. So let's go ahead and calculate the first one. We're going to have $100 in fixed costs divided by 30 pizzas, right? $100 in fixed costs divided by 30 pizzas and we're going to get fixed costs of $3.33 there per pizza. Right. And let's keep going down. $100 divided by 80 pizzas, now it's $1.25, right? So that same $100 is now split between 80 pizzas. So you can imagine now when we split $100 divided by 150 pizzas, it's gonna be even less. We're going to get down to $0.67, right? 67, I rounded it off there. Let's keep going. We add even more pizzas divided by 180 gets us down to $0.56. And last but not least, $100 divided by 190, that gets us to $0.53, right? And there we go. We saw it just decrease, decrease, decrease, right, cause the quantity keeps getting bigger, but the cost stays the same. Alright, let's try the next one. Variable cost, right? So now variable costs will be increasing, right? They don't stay the same. So as we add more and more quantity, we're expecting these variable costs to increase. So let's go ahead and calculate our variable cost divided by our quantity. Right? So here's our variable cost column and we just have to take that divided by our quantity. In the first case, we've got $80 in variable costs divided by 30 quantity. That gives us a variable cost of $2.67. How about the next one? $160 in variable costs divided by 80 quantity. That gets us to $2. Right? The next one, right, we're right here, this $240 and this 150. So $240 divided by 150 gets us to $1.60 in variable costs, a dollar 60 I'll put. And next we've got $320 divided by 180, dollar $1.78. Alright. And last but not least, we've got $400 divided by 190 and that gives us I'll round it to $2.11 cents. Alright, so the last column here is going to be our average total cost which is this total cost column divided by quantity, right? And in this first case, I'm going to do both. We'll do average total cost equals total cost divided by quantity or remember that it can also equal average fixed cost plus average variable cost, right? So we could take those columns for AFC and AVC and just add them together, right? And that'll get us to ATC. So let's confirm that in this first one and then I'm just going to use the AFC + AVC because addition seems easier. So in the first case, we've got $180 in total cost divided by 30 pizzas, right? So $180 in total cost divided by 30 pizzas gives us $6. And what happens if we just add AFC and AVC? $3.33 plus $2.67. There we go, we've also got $6. So both methods work. I'm just going to add because I think that's easier. So $1.25 plus $2. That comes out to $3.25. $0.67 plus $1.60. That's $2.27. $0.56 plus $1.78, $2.34. And the last one, $0.53 plus $2.11, $2.64, right? And you can go ahead and confirm what we learned above, right? That the marginal cost is going to drive these averages up or down, right? Now I want to know one thing that this marginal cost does not affect this AFC, right? The AFC is being driven down by the quantity, right? It's a fixed amount of cost and it's just going to keep decreasing as quantity increases, but these other ones are going to be affected, right? We see that as the marginal cost here, it was decreasing. Right? And we saw that the $1.60 was less than the $2.67, right, it was less than the average so it pulled the average variable cost down. Same thing here with the average total cost right? It was $6 the $1.60 was less and it drove it down to $3.25 right? So same thing as we explored above, we're going to see the same conclusions here, right? Let's look at this last one here just to confirm. We had an average variable cost of $1.78, right? And our marginal cost was $8. It was way higher, right? A higher marginal cost than the average variable cost, so it's going to drive it up and that's what we see happening, right? It goes up to $2.11. Same thing with the total cost, it was $2.34, $8 is higher than $2.34 and it drove it up to $2.64 right? So those are the conclusions we made above about marginal cost and average cost. When the marginal cost is greater than the average cost, the current average, right? It's going to drive it up. If the marginal cost is less than that average, right, it's going to drive it down. Cool? So let's go ahead and make some conclusions here about our 4 curves, right, Cause these are the 4 curves that are going to be important. We're going to see all of these on the graph, we're going to see marginal cost, average fixed cost, average variable cost, and average total cost, right? So marginal cost, we've talked about it before, right? We saw that it falls just like we see it falling here. Go back to red. It falls and then it starts rising, right? It had that U shape. Falls then rises. What about average fixed cost? Well average fixed cost, right, just as we discussed, as the output increases, it's just going to fall and fall and fall. Right? It gets smaller and smaller because the cost stays the same but the quantity keeps increasing. Cool? How about variable cost? Well, we're seeing here that it decreases, decreases, and then it increases, right? So it's going to have that shape as well, that U shape where it falls then rises. Last but not least, average total cost, same thing. Right? It's falling, falling, and then it starts rising again. So falls then rises. Look at that. 3 of our curves follow this philosophy, right? Falls then rises, falls then rises, falls then rises. So average fixed cost is the odd one out here, right? So we would expect we could pick out our average fixed cost on a graph pretty easily because it's going to have a different shape, right? That average fixed cost is just going to keep decreasing and decreasing and decreasing as that output goes up. Alright? Cool. Let's do some practice problems and then we're going to go ahead and see all of this stuff on the graph. Alright? Let's do that now.

A firm is currently producing 100 units with an average total cost of $44 and a marginal cost of $32. If it were to increase production to 101 units, which of the following must be true?

• A. Average total cost would decrease.
• B. Average total cost would increase.
• C. Marginal cost would decrease.
• D. Marginal cost would increase.

Answer: (A)

The government imposes a $10,000 per year inspection fee on all restaurants. Which cost curves are affected?

• A. Average total cost and marginal cost
• B. Average total cost and average fixed cost
• C. Average variable cost and marginal cost
• D. Average variable cost and average fixed cost

Answer: (B)

A firm is producing 1,500 units at a total cost of $15,000. If it were to increase production to 1,501 units, its total cost would rise to $15,012. Which of the following is true?

• A. Marginal cost is $10 and average variable cost is $12
• B. Marginal cost is $12 and average variable cost is $10
• C. Marginal cost is $10 and average total cost is $12
• D. Marginal cost is $12 and average total cost is $10

Answer: (D)

Here’s what students ask on this topic:

What is the relationship between marginal cost and average cost?

The relationship between marginal cost (MC) and average cost (AC) is fundamental in economics. When MC is less than AC, it pulls the AC down. Conversely, when MC is greater than AC, it pushes the AC up. This relationship is crucial for understanding cost behavior in production. For instance, if producing an additional unit costs more than the average, the average cost will increase. Conversely, if it costs less, the average cost will decrease. This dynamic helps firms decide on the optimal level of production to minimize costs and maximize efficiency.

How do you calculate average total cost (ATC) and marginal cost (MC)?

Average Total Cost (ATC) is calculated by dividing the Total Cost (TC) by the quantity (Q) of output produced. The formula is:

$\mathrm{ATC}=\frac{\mathrm{TC}}{Q}$

Marginal Cost (MC) is the additional cost incurred by producing one more unit of output. It is calculated by the change in Total Cost (ΔTC) divided by the change in quantity (ΔQ). The formula is:

$\mathrm{MC}=\frac{\mathrm{\Delta TC}}{\mathrm{\Delta Q}}$

These calculations help firms understand cost structures and make informed production decisions.

Why does average fixed cost (AFC) decrease as output increases?

Average Fixed Cost (AFC) decreases as output increases because fixed costs are spread over a larger number of units. Fixed costs (FC) remain constant regardless of the level of production. The formula for AFC is:

$\mathrm{AFC}=\frac{\mathrm{FC}}{Q}$

As the quantity (Q) of output increases, the denominator in the equation increases, leading to a lower AFC. This spreading effect reduces the per-unit fixed cost, making production more cost-efficient as output grows.

What is the significance of the U-shape in average total cost (ATC) and average variable cost (AVC) curves?

The U-shape of the Average Total Cost (ATC) and Average Variable Cost (AVC) curves is significant because it reflects economies and diseconomies of scale. Initially, as production increases, costs per unit decrease due to efficiencies and better utilization of resources (economies of scale). This causes the ATC and AVC to fall. However, after a certain point, further increases in production lead to inefficiencies, such as overcrowding and overuse of resources, causing costs per unit to rise (diseconomies of scale). This results in the U-shape, indicating the optimal production level for minimizing costs.

How does marginal cost (MC) influence production decisions?

Marginal Cost (MC) plays a crucial role in production decisions. Firms use MC to determine the cost of producing one additional unit of output. If the MC is lower than the price at which the product can be sold, producing more units is profitable. Conversely, if the MC exceeds the selling price, producing additional units would result in a loss. Therefore, firms aim to produce up to the point where MC equals marginal revenue (MR), maximizing profit. Understanding MC helps firms optimize production levels and manage costs effectively.