In the last video for week one, we're still talking about chapter two, but we're going to talk about a case of non-linear PPFs. And the notes for this start on page six of the document here. So what do we mean by non-linear PPFs?
Well, the previous cases were all PPFs that are linear, meaning that the slope of the PPF didn't depend on the level of production. So the opportunity cost, the amount of, in the first example, say fish, they had to give up to increase coconut production, didn't depend on how many coconuts Hank and Tom were already producing. So if they wanted to go from one to two coconuts, they had to give up some level of fish production.
But if they wanted to go from two to three, they'd give up the exact same amount of fish production again. But we might think that... this isn't necessarily the most realistic model that we could come up with, although it does a good job, like we saw, of capturing this concept of specialization and trade.
We also might want to consider another scenario where the slope is not constant, and so the opportunity costs are also not constant, but they depend on the level of production. So why might this be a more realistic depiction of reality? Well, imagine, say, a group of people that are facing decisions about production of two different goods.
And I think some, it's probably relatively intuitive, but some resources might be better suited for production of certain goods than other goods. So In other words, not all land is good for growing corn, I guess is the way I like to say it, because in the example that we look at a little bit, we're going to talk about two goods, one of them being corn. And you might think that some resources that are really good for producing corn aren't necessarily good for producing other things.
And resources that are really good at producing other things might not be so good at producing corn. And so... We'll go over that example in a little bit, but first I'm just going to draw up a generic PPF that's not linear.
So we're going to have goods X and Y, and just kind of think about how this compares to the linear cases that we've looked at previously. So again, we're just going to start with a generic case here. So remember what the PPF tells us, it's the production possibilities frontier, which tells us the combinations of goods that are produced.
producer could feasibly produce. And so let's just kind of how we started this this chapter. Just draw up a PPF.
We have Y on the Y axis, X on the X axis. We're still going to think about this some intercept up here tells us the maximum amount of Y that they can produce. And this intercept down here tells us the maximum amount of X that they can produce.
But rather than just drawing a straight line between these two points, which is what we did before, we're going to think about a case where the slope changes and so the opportunity cost changes over the range of the DPF. So instead of a straight line, I'm just going to draw something that's bowed out like this. So that now the slope when we're producing a small amount of x and a lot of y is relatively flat.
But the slope when we're producing a lot of x and a little bit of y is relatively steep. So what exactly does that mean? I think it helps to consider two different possible changes that this producer is considering. So think about the case where they're producing a bunch of Y and just a little bit of X and they're considering increasing the production of X by a small amount.
So like we talked about earlier we could think about their cost of increasing the production of X. in terms of how much y they have to give up in order to increase x. Because the slope up here is so flat, That also means that the amount of y that they have to give up is very small to increase the level of x.
So they have to give up a small amount of y. So that's the same thing as saying that the slope up here is relatively flat. Now let's think about a second case.
This is just the change in x here. Think about a second case where this producer is producing a lot of x. And they're considering, we'll say that they're producing right here. It's a lot of x and less y than they were producing previously. And think about...
a scenario where this producer is considering increasing the level of x when they have this as the starting point. Again, we could measure their opportunity cost in terms of y, or their cost of increasing that level of x in terms of how much y they'd have to give up. And you can see that in the second case where the PPF is relatively steep, the producer has to give up a lot of y. in order to increase x by the same amount as they did in the last case.
So they give up a lot. So this is what we mean by a PPF that's not linear. And it's what we mean by the opportunity cost depending on the level of production.
So with this lower level of production amount. the opportunity cost is relatively small. Why might that be the case? Well, when they're producing at this point or these points all the way out here, they've devoted most of their resources to producing y and they're only using a little bit of resources to produce x. So the reason that we might have a scenario like this in reality where At this point there's a low opportunity cost of increasing X because some of those resources that they're using to produce Y might be not very productive in producing Y, but they might be really productive in producing X.
And so if we just shift some of those resources, we don't have to give up much Y in order to increase X by a decent amount. On the other hand, at this other level of production, where they're dedicating many more resources to producing X already, and not as many as they are to producing Y, It's no longer necessarily the case that they're allocating a bunch of resources toward Y that aren't good at producing Y. And so when they reallocate to increase the level of production of X, they're not getting the same bang for their buck, so to speak. So in our example here, we have some producer who is able to produce corn and haircuts.
And this table is just going to give us a bunch of different points. that are on their PPF. So the first option here that we'll fill in is that they could produce 1,000 pounds of corn.
And this point A corresponds to the point where they're dedicating all their resources to corn production. And so they would end up with zero haircuts. In each of these points, they're going to give us a different point of the PPF. If they produce a little bit less corn, we'll say 800 pounds, 800 pounds of corn, they're going to end up with 300 haircuts. So this is the scenario where they're relatively, they're at a point where they're producing a relatively small amount of haircuts, low number of haircuts, but a bunch of corn, and so when they decrease their corn production a little bit, they can get a lot of haircuts in exchange.
And we're going to continue going on here. If they produce 600 pounds of corn, they will end up with, we'll say, 500 haircuts. If they decide to produce 400 pounds of corn, we'll say that they'll end up with 600 haircuts.
If they decide to produce 200 units of corn, they could also produce 650 haircuts. And the final point F here is the other extreme case where they're producing zero pounds of corn but they're getting 675 haircuts. So you can notice from looking at the table, as we decrease the level of corn production, I fixed the change in the level of corn from 1,000 to 800, 600. So it's decreasing by 200 pounds of corn between each point.
But you'll notice that when corn production is really high and we decrease production by 200 pounds, we get a lot of haircuts. We get 300 haircuts. One reason we might get a lot of haircuts is that At point A, we're using all of our resources to produce corn, so that means we have all of our barbers who aren't very good farmers actually producing corn. They're much better at producing haircuts, and so when we reallocate some of those resources to our haircuts, we can get a lot of haircuts.
And as we move down these points, so think between C and D, for example, instead of getting 300 haircuts when we go from point C to point D, We only get 100 additional haircuts. So we've already reallocated all of our best barbers toward cutting hair and now we're getting into reallocating resources that are not necessarily near as productive for producing haircuts as the first barbers that we moved over to cutting hair. And so as we move across to different levels of production, another way to think about this or what I'm trying to say is that the opportunity cost or what we get out of reducing corn production changes and it's decreasing as we decrease corn production here and I think it may even become more clear if we draw this up in a figure so let's do that next. So let's draw the figure that we just um or that we outlined in the table here it's going to look pretty similar to what we just drew earlier for a nonlinear PPF.
And in this example let's put a corn on the y-axis and haircuts on the x-axis. And we're just going to plot out the different points and see what that, see what the resulting PPF looks like. So at this y-intercept here we can produce 1,000 pounds of corn and zero haircuts.
And so this point all the way up here corresponds to point A in the table. If we reduce our production to 800 pounds of corn, we would end up with 300 haircuts. So all the way up here. If we reduce our corn production further to 600 units, we would also be able to produce a total of 500 units of corn. And these points correspond to B and C on the table.
If we reduce corn production to 400 units, we would end up with 600 and... 600 units of corn. If we reduce corn production, sorry that's 600 haircuts.
If corn production is 200, we'd have 650 haircuts and at corn production zero we'd have 675 haircuts. So these correspond to points E and F. And if we connect the dots here, sort of, a little bit of imagination, you can see that this PPF, the slope of this PPF, depends on the level of production.
So when we move from point A to point B, for example, we're decreasing corn production by 200, but we're gaining. 300 haircuts. On the other hand when we go from 200 units of corn to zero we're also decreasing by 200 but we're only gaining 75 or sorry 25 actually 25 haircuts.
So another way to say this, there are two questions at the bottom of the example, which ask, what is the opportunity cost? What is the opportunity cost of increasing corn by 200 pounds? And I ask at two different points.
So at point B. is the first one. So if we're at point B and we want to increase corn by 200 pounds, how many haircuts would we have to give up?
And that tells us the opportunity cost. So to do that we have to give up 300 haircuts. We're just moving the other direction here. So at that point it's relatively expensive in terms of haircuts in order to increase corn production.
and that corresponds to this relatively flat slope here. And then I also ask, what about at point E? So if we're at point E, we're all the way out here, and if we decide to increase corn production by 200 units, we'd be going from 200 to 400, and to do that, we'd have to give up 50 haircuts. So at point B the opportunity cost is $300. At point E the opportunity cost is only $50.
That corresponds to this relatively steep slope over on this portion of the PPF. So even though the opportunity cost changes depending on the level of production. We can still think about it as being related in the same way to the slope of the PPF. It's just that the slope is different depending on the current level of production.
And that's what this is meant to drive home here is that in both cases we're talking about 200 pound increases in the level of corn production but we have to give up very different amounts in the level of haircut production. in order to obtain those. And so the opportunity costs, in other words, are very different. So this is the last video or last example for chapter two and we'll pick back up next week starting talking about a combination of chapters three and four.