The Relationship Between Average Cost and Marginal Cost

10. The Costs of Production

The Relationship Between Average Cost and Marginal Cost - Video Tutorials & Practice Problems

On a tight schedule?

Get a 10 bullets summary of the topic

If marginal cost is above average cost, it will drive the average cost up. If marginal cost is below average cost, it will drive the average cost down.

1

concept

Average Cost and Marginal Cost

Video duration:

6m

Play a video:

Alright guys, now, I want to help you build a little intuition about marginal costs and average cost. Right? How are they related? Let's check it out. So what we're gonna see is that the average cost is gonna rise or fall depending on the marginal cost of the next unit. All right. So if we consider the marginal cost, that's gonna be the drive, the marginal cost is gonna be the driving force of the average cost. Right? It's gonna be what drives it up or down. Okay. So, I figured a great way to kind of bring this all together is to to talk about Gps for a second. Okay. So we're gonna instead of talking about costs, we'll think about your G. P. A. The semester G. P. A. As your marginal G. P. A. Right? What happens if I take one more semester of classes and your cumulative G. P. A. Right from every semester? That's gonna be your average G. P. A. All right. So let's go ahead and see what happens in this example. So here you go. You start freshman year in the fall, your party 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 G P. A yikes, right? And then in the spring you're like, you know what I'm gonna buckle down. I'm gonna do a great job and you end up pumping out a 3.0 G P A. 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? At 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 gps and the average G. P. A. Right? So the average is gonna be the total divided by the quantity, right? And in this situation it's gonna be the quantity of semesters. So we're not we're gonna see that you know the first semester your average G. P. A. Well you've only, excuse me, you've only had one semester of classes. So that is your average right? The G. P. A. That you got that first semester. That's your average G. P. A. Now what about after two semesters? Right in this situation uh We're gonna add your grades in both semesters and divided by the number of semesters. Right? We had two semesters in this case. So it's gonna be 1.5 plus two. Excuse me. Sorry 1.5 plus three divided by two. And there we go. There's our average G. P. A. Of 2.25. And that's gonna 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 a cumulative G. P. A. Here we're just gonna add all three semesters and divide by three. Right? And obviously this is a simplified example. Obviously G. P. A. 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 gonna take that total of three and divide it by three, right? We're gonna take those three semesters and divide by 31.5 plus three plus 2.8. And divide that by three. And we're gonna get I'm gonna round it to 2.43 right there as your G. P. A. And the last one is where we have one more semester, right? And you you started slacking off and you pulled off a 1.6. All right. So let's see what happens here. Now I'm gonna do it up here. We have some space. We're gonna add all the semesters, right? 1.5 plus three plus 2.8 Plus 1.6. Right? All the semesters and we're gonna divide by four because that's the quantity of semesters here. And let's see what that averages. We've got 1.5 plus three plus 2.8 plus 1.6 divided by four. And we're gonna get 2.23. I'm gonna round it off their 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 G. P. A. Falls a little bit right between spring and fall there. Your your marginal G. P. A. 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 average is only going to be driven based on the following semesters marginal. Even though that the marginal decrease 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. All right. And last one, here we see that again, your your G. P. A 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 gonna see that the cumulative G. P. A 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 gonna 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 G. P. A. Was greater than the average. Well it's going to increase the cost when we produce another unit. Right? That marginal cost is gonna drive up the average and the opposite right? When the marginal cost is less than average cost it's gonna decrease the average cost when we add another unit. Right? So that's gonna 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 gonna 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.

2

concept

Patterns of MC, AFC, AVC, and ATC curves

Video duration:

8m

Play a video:

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 gonna start with this information and let's go ahead and calculate our average fixed cost, our average variable costs and our average total cost um in each situation. Right? 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 gonna stay the same fixed cost but this denominator is going to increase and increase. Right? So what's gonna happen is we're gonna split up the same amount of cost between more and more units. So we're gonna 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 gonna be 100. Right? Um 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 gonna have 100 and fixed costs divided by 30 pizzas. Right? 100 fixed costs divided by 30 pizzas. And we're gonna get fixed costs of $3.33 there per pizza. Right? And let's keep going down 100 divided by 80 pizzas. Now it's a dollar 25. Right? So that same 100 is now split between 80 pizzas. So you can imagine now when we split the 100 divided by 100 and 50 pizzas, it's gonna be even less. We're gonna get down to 0.67 cents. Right, 67. I rounded it off there. Let's keep going. We had even more pizzazz divided by 1 80 Gets us down to 0.56 and last but not least 100 pizzas divided by 190. That gets us to zero, coming around it to 53 cents. 0.53. Right? And there we go. We saw it just decrease, decrease, decrease, decrease, decrease, right? Because 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 costs 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 160 in variable cost divided by 80 quantity? That gets us to $2 right? The next one, right? We're right here, this to 40 and this 1 50 so to 40 divided by 1 50 gets us to 1.6. Uh In in variable costs a dollar 60 output. And next we've got 3 20 divided by 1 $80.77. All right. And last but not least, we've got uh 400 divided by 1 90. And that gives us all round it to $2.11. Right? So last column here is gonna be our average total cost. Which is this total cost, column divided by quantity. Right? And in this first case I'm gonna do both. Well, do average total cost equals total cost divided by quantity. Or remember that it can also equal average fixed cost plus average variable costs. Right? So we can take those columns for A F. C. And a VC. And just add them together. Right? And that will get us to a T. C. So, let's confirm that in this first one. And then I'm just gonna use the A F C A V. C. Because addition seems easier. So in the first case we've got 180 total cost divided by 30 pizzas. Right? So 100 and 80 in total cost divided by 30 pizzas gives us $6. And what happens if we just add a. F. C. And A. V. C. $3.33 plus $2.67. There we go. We've also got $6. So both methods work. I'm just gonna add because I think that's easier. So I'm gonna add A. F. C. And A. V. C. To get to our A. T. C. Cool so dollar 25 plus $2. That comes out to 3 25 67 cents plus a dollar 60. That's 2 27 56 cents plus a dollar 77 to 33. And the last 1.53 plus 2.11 2 64. Right? And you can go ahead and confirm what we learned above right? That the marginal cost is gonna drive these averages up or down. Right? Now I want to know one thing that this marginal cost does not affect this. A. F. C. Right? The A. F. C. Is being driven down by the quantity, right? It's a fixed amount of cost and it's just gonna keep decreasing as quantity increases. But these other ones are gonna be affected. Right? We see that as the marginal cost here it was decreasing, right? And we saw that the 1.6 I'm gonna do it in a different color. This 1.6 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 1.6 was less and it drove it down to $3.25. Right? So same thing as we explored above. We're gonna see the same conclusions here. Right? Let's look at this last one here. Just to confirm, we had an average variable cost of a dollar 77 right? And our marginal cost was eight. It was way higher. Right? A higher marginal cost than the average variable cost. So, it's gonna drive it up and that's what we see happening, right? It goes up to 2 11. Same thing with total cost, It was 2 33. $8 is higher than 2 33. 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 gonna drive it up and if the marginal cost is less than that average right, it's gonna drive it down. Cool. So, let's go ahead and make some conclusions here about our four curves, right? Because these are the four curves that are going to be important. We're gonna see all of these on the graph, we're gonna see marginal cost, average fixed costs, average variable cost an average total cost. Right? So marginal costs. We've talked about it before, right? We saw that it falls just like we see it falling here, go back to read 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 gonna fall and fall and fall, right? It gets smaller and smaller because the the cost stays the same, but the quantity keeps increasing. Cool. How about variable costs? Well, we're seeing here that it decreases, decreases and then it increases. Right? So, it's gonna 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 three of our curves. Follow this philosophy, right. Falls and rises. Falls and rises. Falls and rises. So average fixed cost is the the odd one out here. Right? So, we would expect we could pick out our average fixed costs on a graph pretty easily, because it's gonna have a different shape. Right? The average fixed cost is just gonna keep decreasing and decreasing and decreasing as that output goes up. Alright, cool. Let's do some practice problems and then we're gonna go ahead and see all of this stuff on the graph. Alright, let's do that. Now

3

Problem

Problem

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.

4

Problem

Problem

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

5

Problem

Problem

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