PPF - Increasing Marginal Opportunity Costs and Allocative Efficiency - Online Tutor, Practice Problems & Exam Prep

Increasing marginal opportunity costs illustrate that as production of one good, like soy cheese pizza, increases, the cost of producing additional units rises. This is depicted in a bowed-out graph. Allocative efficiency occurs when marginal benefit equals marginal cost, indicating the optimal production mix. The marginal cost curve rises with each additional pizza, while the marginal benefit decreases. The efficient quantity is found where these curves intersect, demonstrating the balance between consumer preferences and production costs.

PPF - Increasing Marginal Opportunity Costs

So now we're going to continue with the discussion of increasing marginal opportunity costs. So when you look at a graph like you see on the left here, we've got the graph for Hipsterville, which I'm going to call here where they produce craft beer and soy cheese pizza. When we look at the graph, you see the graph has a shape that kind of bows outward, right? It's not this straight line just connecting these two points from one to the other. No. It's got this shape that bows outward, and the point of that is to describe this situation of increasing marginal opportunity costs. So the idea is that as we increase the production of one good, say soy cheese pizza, it's going to cost us more and more of the production of the other good. So the idea is as we increase the production of soy cheese pizza, it's going to become marginally more expensive.

Let’s look at this graph, and let’s see how that works here. The idea, remember when we're talking about marginal opportunity cost, what's the opportunity cost of one more? So what's it going to cost us for one more pizza in this case? So when we're at 0 and we want to move up to 1 pizza, well, when we have 0 pizzas we notice this graph goes up by 2, 4, 6, 8, 10. This spot right here is 15 on the graph, and when we move to 1, so when we create our first pizza, we are going to get less craft beer. Right? So when we had 0 pizza, we had 15 craft beers up there, and now it’s going to move us down to 14 craft beers here on the graph. So this is 6, 8, 10, 12, 14 and then 15 right there where it crosses. So what did we give up to get this first pizza? Right? We started at 15 and now we're at 14. We gave up one craft beer to get to that first pizza. Right? We had 15 craft beers, now we have 14 craft beers. The marginal cost is going to be one for that first pizza.

So now what about that second pizza? Now the marginal cost, remember it's how much for one more pizza. We already have one pizza, how much for that second one in this case? So here we started with one pizza, what happens when we move over to the second pizza? It looks like we lose two beers in this case, right. We had 14 beers, now we're down to 12 beers once we get to the second pizza. So the marginal cost of that pizza is going to be 2. When we've got one pizza, the marginal cost of the next pizza is 2.

Let’s do the same thing with the next one. So here we were at 12 beers and then we move down to this point right here which is in the middle of the graph, that's at 9 right there. So here we are giving up three beers, right. We were at 12. Now we are down to 9 beers once we have that third pizza. So our marginal cost when we have two pizzas of adding one more pizza is three beers. So that the third pizza, right?

Now let’s try the next one, right? Now we already have three pizzas, how much is that fourth one going to cost us? So we start here at 9. We’re going to find where it goes down to, and that’s right here in the middle again. Now we're at 5. So we had 9 beers, and we had to give up four of those beers to get that fourth pizza. So the marginal cost when we have three pizzas of the fourth pizza is going to be four beers in this case. Right? We had 9 beers, and we had to give up four of them to get to that fourth pizza.

And last but not least, what about when we want five pizzas? So we're at four, we want to have a fifth pizza, and the cost of that last pizza is going to be five. So notice we’ve got increasing marginal opportunity cost, right? The more we want of something, the more we have to give up. And if you were to do this the other way, you would see the same thing. We’d have to be giving up more and more pizza to get beers. Alright? Cool.

PPF - Allocative Efficiency with Marginal Analysis

Alright, so now let's see how this idea of increasing marginal opportunity cost relates to allocative efficiency. So remember, allocative efficiency, it deals with consumer preferences, right? It's a little more subjective in what is the right amount, how much craft beer should we have, how much soy cheese pizza should we have, and we have to find the right mix for that, for those consumers. So allocative efficiency is the mix of production where our marginal benefit equals our marginal cost. You guys remember this formula I told you was going to come up again? Marginal benefit equals marginal cost. Right? So the benefit of producing this much equals the cost of producing this much. That is where we're going to have the efficient point.

A few quick notes before we head to the graph down here, is the idea that marginal benefit is completely unrelated to the graph. It is not telling us anything about the marginal benefit. How much do people want soy cheese pizza? How much do people want craft beer, we can't derive that information from that graph. Alright? I'm going to have to give you that information separately about marginal benefit. Your teacher's going to have to give it to you. Right? You're just not going to be able to come up with it on your own.

So another note here, when we plot the marginal curve, or excuse me, the marginal cost curve, we're going to do it from the midpoint of each unit, and this goes back to that idea of the arc method of finding the slope on a curve. Since we don't have a straight line we would be using the arc method, and if you remember from the graphing review, basically we're finding the average slope, so we're going to do the same thing and we're going to take it from the average of the amount of pizzas. So instead of going from 0, 1, 2, 3, 4, we're going to go from the midpoint, from the half pizza, the 1.5, right? And that's because we're using the average slope, we're going to use the average on the graph as well. So we're going to go from the midpoint.

Alright, so here on the graph, it's a little different than the graph above. Above we had soy cheese pizza and craft beers. On the graph here we have soy cheese pizza and the marginal cost or marginal benefit in craft beer. So it's not the total amount of craft beers that we're going to be producing. We're talking about the marginal cost or the marginal benefit from this amount of pizza production. Right? So if we're going to produce this many pizzas, what's the marginal cost? What's the marginal benefit? Alright.

Let's start with the marginal cost curve, and then I'll give you the marginal benefit numbers, and we will plug it in there. So remember up above, we talked about the marginal cost of the first pizza. Right? When we've got 0 pizzas and we want the first pizza, that marginal cost is 1. So we're going to plot that here for our marginal cost curve, at 1, right, and we're going to do that for all the other ones too. Right? It went 1, 2, 3, 4, 5 as we moved along, and those were our increasing marginal costs. Right? That's why we see this number keep increasing here. So as we add pizzas so does our marginal cost increase.

And what I'm going to do is for our marginal benefit, we're going to describe this as the willingness to pay. Right? So the idea is that for that first pizza, they don't have any pizza yet. They're going to have a high willingness to pay. They really want that pizza. It's going to be worth a lot to them when they get the first pizza. So I'm going to put in some numbers here. I'm going to go 5 for that first pizza, 4 for the next one 3, 2, 1. Right. And the idea here is that as we get more pizzas, we don't get as much benefit out of them because that's how it works. The first ones are always worth more to us than future ones. Right? It's just like if you got your first Lamborghini, it's going to mean a lot more to you than when you have 10 Lamborghinis. Right? Once you're a professional microeconomist and you're making all that money, you're going to really cherish that first Lamborghini then that tenth one.

So let's go ahead and put these on the graph. We've got soy cheese pizza on the x-axis, our marginal cost, marginal benefit in craft beers on the y-axis. So let's go ahead. So for 0.5 pizzas, so that's right here in the middle of 0 and 1, we're going to have let's start with just the marginal cost. We are going to have a marginal cost of 1, and for the next set of pizzas and remember we're using the average here, right? We're going in the middle because it's the average slope and it's the average distance from 0 to 1, so we're going to start in the middle. From 1 to 2, we've got 2. 3, we go 3, 4, 5 here along the side. 4 and then 5. So here were our 5 points for our marginal cost curve, 1, 2, 3, 4, 5, and I'm going to go ahead and connect those right now. So we've got a marginal cost curve looks something like that. I'll put marginal cost out there.

Notice how it goes up as we increase our soy cheese pizza production. Let's do the same thing with marginal benefit. I'll get back out of the way so we see the numbers. So our marginal benefit remember, I just gave these to you. You can't derive these marginal benefits from anywhere. They have to be given or else you won't be able to figure this out. So at 0.5 pizzas, I'm going to use blue for our marginal benefit. We've got 5 is our marginal benefit here. So that means we really value that first pizza because we don't have any yet and the idea is the less of something we have, the more we value it. So the next one here is 4 when we have between 1-2 pizzas, and then right here notice what just happened. Right? I just bubbled on top of another bubble. You might think of what that point is going to be. So continuing on, marginal benefit of 3 when we have 3.5 and then at 4.5 marginal benefit of 1.

So I'm going to connect these dots to make our curve here, and that is our marginal benefit curve, and what were we talking about, right? We were saying that the allocative efficiency is where the marginal benefit equals the marginal cost. Can you find that here on the graph? That is going to be this point right here and that is when we are producing 2.5, 1,000,000 pizzas, right? So what is the allocative efficiency quantity? We know that 2.5 pizzas is the correct amount, but this graph right here, it doesn't tell us anything about the amount of craft beers that we want, right? So in this box at the bottom, we want to know the efficient quantity of pizza and the efficient quantity of craft beers as well. So we do know that the soy cheese pizzas was 2.5, but we need to go back up to the graph to find out how many craft beers we make when we got 2.5 pizzas, right. That other graph isn't telling us anything about the total amount of craft beer, so we're going to go to 2.5 here. Go up to the graph, and we're going to see that we're going to want, let's say that's 10 right there. Right? So 2.5, 1,000,000 pizzas and 10 craft beers. That is going to be our efficient quantity right there. Our allocated efficient quantity. Notice that that's also productively efficient, right, because we are on the graph there. We are on the line. So that's productively efficient and it's also allocatively efficient based on our marginal benefit and our marginal cost. Cool. Let's move on.

Chuggy wants to earn a high grade in his microeconomics class, but also loves going to parties and binge drinking. The first graph illustrates Chuggy's PPF. The second graph denotes his MB curve from binge drinking. What is Chuggy's marginal cost of binge drinking if he parties for three hours a week?

• A. 1 percentage point
• B. 1.5 percentage point
• C. 2 percentage point
• D. 3 percentage point
• E. 5 percentage point

Chuggy wants to earn a high grade in his microeconomics class, but also loves going to parties and binge drinking. The first graph illustrates Chuggy's PPF. The second graph denotes his MB curve from binge drinking.  If Chuggy achieves allocative efficiency, how many hours does he spend binge drinking per week?

• A. 3 hours
• B. 4 hours
• C. 5 hours
• D. 6 hours
• E. 7 hours

Chuggy wants to earn a high grade in his microeconomics class, but also loves going to parties and binge drinking. The first graph illustrates Chuggy's PPF. The second graph denotes his MB curve from binge drinking. What is Chuggy's economics grade when he achieves allocative efficiency?

• A. 60 percent
• B. 70 percent
• C. 76 percent
• D. 82 percent
• E. 85 percent

Here’s what students ask on this topic:

What is the concept of increasing marginal opportunity costs in a PPF?

Increasing marginal opportunity costs refer to the phenomenon where producing additional units of one good requires giving up increasingly larger amounts of another good. This is depicted in a Production Possibility Frontier (PPF) that bows outward. For example, if a society produces more soy cheese pizza, it must sacrifice more and more craft beer. This occurs because resources are not perfectly adaptable to the production of both goods, leading to inefficiencies as production shifts. The bowed-out shape of the PPF graphically represents this increasing cost.

How does the shape of the PPF illustrate increasing marginal opportunity costs?

The shape of the PPF illustrates increasing marginal opportunity costs through its bowed-outward curve. As production of one good, such as soy cheese pizza, increases, the opportunity cost in terms of the other good, like craft beer, also increases. This is because resources are not equally efficient in producing both goods. Initially, the opportunity cost is low, but as more resources are allocated to producing one good, the cost of forgoing the other good rises, creating the bowed-out shape.

What is allocative efficiency and how is it determined on a PPF?

Allocative efficiency occurs when the mix of goods produced represents the combination most desired by society. It is determined on a PPF where the marginal benefit (MB) of producing a good equals its marginal cost (MC). This point is found where the MB curve intersects the MC curve. For example, if the MB of producing soy cheese pizza equals the MC at 2.5 pizzas, this is the allocatively efficient quantity. This balance ensures that resources are used in a way that maximizes societal welfare.

How do you calculate marginal opportunity cost from a PPF graph?

To calculate the marginal opportunity cost from a PPF graph, you need to determine the amount of one good that must be given up to produce an additional unit of another good. For example, if moving from 1 to 2 soy cheese pizzas reduces craft beer production from 14 to 12 units, the marginal opportunity cost of the second pizza is 2 craft beers. This process involves examining the slope between points on the PPF, which represents the trade-off between the two goods.

What is the relationship between marginal benefit and marginal cost in achieving allocative efficiency?

The relationship between marginal benefit (MB) and marginal cost (MC) is crucial for achieving allocative efficiency. Allocative efficiency is attained when MB equals MC, meaning the value consumers place on a good (MB) matches the cost of producing it (MC). For instance, if the MB of producing an additional soy cheese pizza is 3 craft beers and the MC is also 3 craft beers, the production level is allocatively efficient. This balance ensures that resources are optimally allocated to maximize societal welfare.