What is the purpose of a Production Possibilities Graph?

Video transcript

Let's say you're some type of a hunter gatherer and you're trying to figure out how much of your time to spend hunting and how much of your time to spend gathering. So let's think about the different scenarios here and the tradeoffs that they involve. And just for simplicity we're going to assume that when you're talking about hunting, the only animal around you to hunt for are these little rabbits. And when we're talking about gathering, the only thing you can gather are some type of berries. That'll keep our conversation a little bit simpler. So let's think about all of the scenarios. So first, let's call this first scenario Scenario A. And let's say– so let's call this the number of rabbits you can get and then let's call this the number of berries. Let's do this column as the number of berries that you can get. So if you were to spend your entire day going after rabbits, all your free time out– making sure you have time to sleep, and get dressed, and all those type of things. Let's say that you can actually get five rabbits, on average, in a given day. But if you spend all your time getting rabbits you're not going to have any time to get berries. So you're going to be able to get 0 berries. Now let's say that you were to allocate a little bit more time to get berries and a little bit less time to get rabbits. So we'll call that Scenario B. We'll call scenario B the reality where you have enough time to get 4 rabbits on average. And when you do that, all of a sudden you're able to get 100 berries. And when we do these different scenarios, we're assuming that everything else is equal. You're not changing the amount of time you have either hunting or gathering. You're not changing the amount of sleep. You're not changing your techniques for hunting rabbits, or hunting berries, or you're not somehow looking to do other things with your time. So all other things are equal. And the general term for this, and it sounds very fancy if you were to say it in a conversation, is ceteris paribus. Which literally means– so any time someone says, oh ceteris parabus, we assume this variable changes or whatever else– they're saying we're assuming everything else is being held equal. So ceteris means all other things. You're probably familiar with et cetera. It's the same word, essentially. Other things in paribus, other things equal. So when you're going from Scenario A to Scenario B you're not changing the amount of time you're sleeping. You're not changing somehow the geography where you are in a dramatic way. You're not changing the tools you use or the technology. Everything else is equal. The only variable you're changing is how much time you allocate to finding rabbits versus finding berries. So let's do some more scenarios assuming ceteris paribus. So let me do Scenario C. You could, on average, have enough time to get 3 rabbits. But if you get 3 rabbits then all of a sudden you will to get– or if you're only getting 3 rabbits, you're now able to get 180 berries. And let's do a couple more. I'm going to do two more scenarios. So let's say Scenario D, if you reduce the amount of time you spend getting rabbits so you get 2 rabbits, now all of a sudden you have enough time on average to get 240 berries. And then, let's say you spend even less time hunting for rabbits, on average. Then you have even more time for berries. And so you're able to get to 180 berries and I'll do one more scenario here. So let's say Scenario F– and let's call these the scenarios. Scenarios A through F. So Scenario F is you spend all your time looking for berries. In which case, on average, you're going to be able to get 300 berries a day. But since you have no time for rabbits you aren't going to get any rabbits. So what I want to do is plot these. And on one axis I'll have the number of rabbits. And on the other axis I'll have the number of berries. So let me do it right over here. So this axis, I will call this my rabbit axis, rabbits. And we'll start. That will be 0. And then this will be 1, 2, 3, 4, and then that will be 5 rabbits. And then in this axis I will do the berries. So this right over here, let's make this 100 berries. This is 200 berries. And then this is 300 berries. And so this is my berries axis. Now let's plot these points, these different scenarios. So first we have Scenario A. Maybe I should've done all these colors in that Scenario A color. Scenario A, 5 rabbits, 0 berries. We are right over there. That is Scenario A. Scenario B, 4 rabbits, 100 berries. That's right over there. That's 100 berries. So that is Scenario B. Scenario C, 3 rabbits, 180 berries. 3 rabbits, 180. Let's see this would be 150. 180 will be like right over there. So 3, if you have time for 3 rabbits you have time for about 180 berries on average. So this is Scenario C. And then Scenario D we have in white. If you have time for 2 rabbits, you have time for 240 berries. So that is right around there. So this is Scenario D. Actually, a little bit lower. So this would be 250, so 240 is a little bit lower than that. So it'll be right over there. That is Scenario D. Scenario E, if you have time for 1 rabbit, you have time for 280 berries. So that gets us right about there. That is Scenario E. And then finally Scenario F. You are spending all of your time looking for berries. You have no time for rabbits. So all of your time for berries, no time for rabbits. 0 rabbits, 300 berries. That's right over there. So this is Scenario F. So what all of these points represent, these are all points– now this is going to be a fancy word, but it's a very simple idea. These are all points on you, as a hunter gatherer, on your production possibilities frontier. Because if we draw a line– I just arbitrarily picked these scenarios. Although I guess you could on average get 4 and 1/2 rabbits on average, on average get 3 and 1/2 rabbits, and then you'd have a different number of berries. So these are all points on the different combinations between the trade offs of rabbits and berries. So let me connect all of these. Let me connect them in a color that I haven't used it. So let me connect them. And do you see– this should just be one curve. So I'll do it as a dotted line. It's easier for me to draw a dotted curve than a straight curve. So this right over here, this curve right over here, represents all the possible possibilities of combinations of rabbits and berries. I've only picked certain of them, but you could have a scenario right over here. Maybe we could call that Scenario G, where on average the amount of time you've allocated, on average you would get 4 and 1/2 rabbits. So some days you would get 4 rabbits and every other day you would get 5 rabbits, so maybe it averages out to 4 and 1/2 rabbits. And then maybe it looks like you would get about 50 berries in that situation. So all of these are possibilities. You don't have to just jump from 4 rabbits to 5 rabbits. Or maybe in this scenario you're spending 7 hours and in this scenario you spend 8 hours. But you could spend 7 hours and a minute, or 7 hours and a second. So anything in between is possible and all of those possibilities are on this curve. So these five scenarios, actually these six scenarios that we've talked about so far these are just scenarios on this curve. And that curve we call, once again– fancy term, simple idea– our production possibilities frontier. Because it shows all of the different possibilities we can do, we can get. 3 rabbits, and 180 berries. 2 rabbits and 240 berries. What we cannot do is something that's beyond this. So for example, we can't get a scenario like this. So this right over here would be impossible Let me scroll over to the right a little bit. Let me scroll, see my scrolling thing. OK, so this right over here is impossible, this point right over here where I'm getting 5 rabbits and 200 berries. If I'm getting five rabbits, I'm spending all my time on rabbits. I have no time for berries. Or another way to think about it, if I'm getting 200 berries I don't have enough time to get 5 rabbits. So this point is impossible. This point would be impossible. Any point that's on this side of the curve is impossible. Now any point that's on this side of the curve, you can kind of view it as inside the curve, or below the curve, or to the left of the curve– all of these points right over here are possible. All of these points right over here are– these points, for example, it is very easy for me to get 1 rabbit and 200 berries. So that right over there is possible. Now, is that optimal? No, because if I were to really work properly, I could get many more berries. Or I could get more rabbits. If I have 200 berries, I could get more rabbits. Or if I'm concerned, if I only want one rabbit, I can get more berries. So this is possible. All of the points down here are possible. But they aren't optimal. They are not efficient. So the points in here, we'll say that they are not efficient. Maybe somehow I'm not using my resources optimally to do this type of thing, when I'm over here. Or maybe I'm just not being optimally focused, or whatever it might be. If you're talking about a factory setting, when you're talking about maybe deciding to make one thing or another, then maybe you just aren't using the resources in an optimal way. Now all the points on the frontier– these are efficient. You're doing the most you can do. Right now we're not making any judgment between whether any of these possibilities are better than any other possibility. All we are saying is that you are doing the most that you can do. Any of these things, you are making the most use of your time.


Interpreting the PPF

The PPF is graphically depicted as an arc, with one commodity represented on the X-axis and the other represented on the Y-axis. Each point on the arc shows the most efficient number of the two commodities that can be produced with available resources.

Economists use PPFs to demonstrate that an efficient nation produces what it is most capable of producing and trades with other nations for the rest.

For example, if a non-profit agency provides a mix of textbooks and computers, the PPF may show that it can produce either 40 textbooks and seven computers, or 70 textbooks and three computers. The agency’s leadership must determine which item is more urgently needed. In this example, the opportunity cost of producing an additional 30 textbooks equals four computers.

How Can the PPF Be Used in Business?

A PPF shows businesses a way to make sense of their production possibilities by charting out the opportunity cost of resource allocation, suggesting how to reach optimal allocative efficiency. With scarce resources, it tells us which products to prioritize and at what ratio, showing the maximum possible combinations of goods and services

But, for all of its utility, it is important to remember that the PPF is still a theoretical construct, not an actual representation of reality. It is important to remember that an economy only costs on the PPF curve theoretically; in real life, businesses and economies are in a constant battle to arrive at and then maintain optimal production capacity.

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How the Production Possibilities Curve Works

The production possibility curve portrays the cost of society’s choice between two different goods.An economy that operates at the production possibility frontier, or the very edge of this curve, has the highest standard of living it can achieve, as it is producing as much as it can using its resources. If the amount produced is inside the curve, then all of the resources are not being used. On the chart above, that is point E.

One possible reason for such an inefficiency could be a recession or depression. If that occurs, there is not enough demand for either good. Layoffs may occur as well, resulting in lower levels of labor being used and therefore lowered production.

Other reasons for an inefficient production can be a bit more complicated. An economy will fall within the curve when it ignores its comparative advantage. For example, Florida has the ideal environment to grow oranges, and Oregon’s climate is best for apples. Florida has a comparative advantage in orange production, and Oregon has one in apple production. If Florida ignored its advantage in oranges and tried to grow apples, it would create an inefficient use of resources. The U.S. economy would be operating within the curve, leading to a decrease in standard of living.

At the same time, any point outside the production possibilities curve is impossible. More of both goods cannot be produced with the limited resources. On the chart above, that is point F.

The Shape of the Production Possibilities Curve

The production possibility curve bows outward. The highest point on the curve is when you only produce one good, on the y-axis, and zero of the other, on the x-axis. On the chart, that is Point A, where the economy produces 140,000 apples and zero oranges.

The widest point is when you produce none of the good on the y-axis, producing as much as possible of the good on the x-axis. On the chart, that is point D: The society produces zero apples and 40,000 oranges.

All the points in between are a trade-off of some combination of the two goods. An economy operates more efficiently by producing that mix. The reason is that every resource is better suited to producing one good over another. Some land is better suited for apples, while other land is best for oranges. Society does best when it directs the production of each resource toward its specialty. The more specialized the resources, the more bowed-out the production possibility curve.


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Comparative Advantage and the Production Possibilities Curve

To construct a combined production possibilities curve for all three plants, we can begin by asking how many pairs of skis Alpine Sports could produce if it were producing only skis. To find this quantity, we add up the values at the vertical intercepts of each of the production possibilities curves in Figure 2.4 “Production Possibilities at Three Plants”. These intercepts tell us the maximum number of pairs of skis each plant can produce. Plant 1 can produce 200 pairs of skis per month, Plant 2 can produce 100 pairs of skis at per month, and Plant 3 can produce 50 pairs. Alpine Sports can thus produce 350 pairs of skis per month if it devotes its resources exclusively to ski production. In that case, it produces no snowboards.

Now suppose the firm decides to produce 100 snowboards. That will require shifting one of its plants out of ski production. Which one will it choose to shift? The sensible thing for it to do is to choose the plant in which snowboards have the lowest opportunity cost—Plant 3. It has an advantage not because it can produce more snowboards than the other plants (all the plants in this example are capable of producing up to 100 snowboards per month) but because it is the least productive plant for making skis. Producing a snowboard in Plant 3 requires giving up just half a pair of skis.

Economists say that an economy has a comparative advantage in producing a good or service if the opportunity cost of producing that good or service is lower for that economy than for any other. Plant 3 has a comparative advantage in snowboard production because it is the plant for which the opportunity cost of additional snowboards is lowest. To put this in terms of the production possibilities curve, Plant 3 has a comparative advantage in snowboard production (the good on the horizontal axis) because its production possibilities curve is the flattest of the three curves.

Figure 2.5 The Combined Production Possibilities Curve for Alpine Sports The curve shown combines the production possibilities curves for each plant. At point A, Alpine Sports produces 350 pairs of skis per month and no snowboards. If the firm wishes to increase snowboard production, it will first use Plant 3, which has a comparative advantage in snowboards.

Plant 3’s comparative advantage in snowboard production makes a crucial point about the nature of comparative advantage. It need not imply that a particular plant is especially good at an activity. In our example, all three plants are equally good at snowboard production. Plant 3, though, is the least efficient of the three in ski production. Alpine thus gives up fewer skis when it produces snowboards in Plant 3. Comparative advantage thus can stem from a lack of efficiency in the production of an alternative good rather than a special proficiency in the production of the first good.

The combined production possibilities curve for the firm’s three plants is shown in Figure 2.5 “The Combined Production Possibilities Curve for Alpine Sports”. We begin at point A, with all three plants producing only skis. Production totals 350 pairs of skis per month and zero snowboards. If the firm were to produce 100 snowboards at Plant 3, ski production would fall by 50 pairs per month (recall that the opportunity cost per snowboard at Plant 3 is half a pair of skis). That would bring ski production to 300 pairs, at point B. If Alpine Sports were to produce still more snowboards in a single month, it would shift production to Plant 2, the facility with the next-lowest opportunity cost. Producing 100 snowboards at Plant 2 would leave Alpine Sports producing 200 snowboards and 200 pairs of skis per month, at point C. If the firm were to switch entirely to snowboard production, Plant 1 would be the last to switch because the cost of each snowboard there is 2 pairs of skis. With all three plants producing only snowboards, the firm is at point D on the combined production possibilities curve, producing 300 snowboards per month and no skis.

Notice that this production possibilities curve, which is made up of linear segments from each assembly plant, has a bowed-out shape; the absolute value of its slope increases as Alpine Sports produces more and more snowboards. This is a result of transferring resources from the production of one good to another according to comparative advantage. We shall examine the significance of the bowed-out shape of the curve in the next section.

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