How to Graph or Draw the Production Possibilities Frontier (PPF)? Overview & Explanations

In this article, we're gonna discuss how to graph the production possibilities frontier which is also known as the PPF. Let's say that you and a group of friends are stranded on a deserted island after a plane crash and you have to make decisions about how much food to collect and how much clothing to produce. So your production decisions are about food and clothing and so you can have a number of different combinations that you can produce four units of food and zero units of clothing, you could produce three units of food and four units of clothing, etc.

So we've got these different combinations running the PPF. Remember we have seen in the PPF article that, it's just a graph of the different combinations of goods or services that could conceivably be produced. We're gonna have a curve and along with that curve, there's gonna be all the maximum points that we could have of food and clothing.

So let's graph this out so we're gonna start and I'm just gonna draw a simple graph here so in our graph I'm gonna put food on the y-axis and then we're gonna put clothing on the x-axis and I'm making the x-axis a lot longer because we're gonna go from 0 to 10 of clothing.

So here's our clothing over here, the food we've said could go it could go from 0 up to 4, so that's how you just map out on the axis one of the goods. So what we're gonna do now is we're just gonna plot the points. So our first combination is, four units of food & zero units of clothing, so we can plot that we can say okay four units of food and it's gonna be right here

Then we've got point (3,4). So three units of food is going to correspond to four units of clothing and then two units of food if we look up is gonna correspond to seven units of clothing. As we give up some food, we're able to get more clothing.

So now one unit of food will be nine so that would be right here and then if we produce no food at all and just decide to starve we could have ten units of clothing and won't we be happy.

Now what we can do is we can just we can draw our curve right so we can draw our curve through those points. This is our PPF, this is our production possibilities frontier. This tells us that, each of these points it's telling us the maximum amount of goods and services we're able to produce given our current level of resources. Remember we have limited resources so we have to make trade-offs

Opportunity Cost:

Now if we add zero units of food for us to go to one unit of food, how much clothing do we give up? You can see you can look at the table if you want or you can look at the graph so look at the table, from zero to one which is our first combination, if we produce no food and we're like "hey we're starving let's produce some food" and we go to one unit of food we will give up one unit of clothing.

So we could say that the marginal cost of one unit of food is 1 unit of clothing. So we give up one piece of clothing to get one piece of food but then to get the second unit of food we give up two units of clothing. Then to get the third unit of food so assuming we have two units and we give up three units of clothing. So we give up one piece of clothing to get the first food, we give up two clothing to get the second food three pieces of clothing to get the third piece of food, and then if we want to go from having three food to four food we give up four units of clothing.

So that's why the PPF as we've drawn it out here that's why it has this bowed-out shape, it has this bowed-out shape because of increasing opportunity cost or increasing marginal cost. 

Why is the PPF bowed outward?

When we're producing no food at all and we're just dedicating everyone on the island to producing clothing we say well "Let's just have one unit of food to get that we don't give up that much clothing here we only give up one unit" but then when we go for that last unit of food we give up a lot of clothing and why might that be the case?

That's because resources are not equally productive. So we might have somebody in our group that may be a professional tailor and they're really good at producing clothing but there are other people who don't know anything about making clothing. So if we do nothing but make clothing or our entire group and we say "let's produce some food here" and we go to one unit of food, we don't give up that much clothing. Because maybe someone in our group really was terrible at making clothing but they're good at collecting food. 

So we only give up one piece of clothing we only give up one unit of clothing to get one piece of food. As we go along this curve we see that we have this increasing marginal cost of what we're giving up to get that last unit of food to go from three to four units of food, we give up four units of clothing, and we do it because maybe that person who's a tailor and that's their specialty is making clothing maybe they're a lot better at making clothing than they are collecting food. So we'll see this bowed-out shape.

Now it does not have to be that bowed-out shape if resources were equally productive. Let's say that it substituted one unit of food for one unit of clothing or something like that, then you could just have a straight line PPC. For example that it was the case where we could either produce four units of clothing and no clothing in for new units of food. You could have a straight line in that case and say to give up one unit of food we would get one unit of clothing and vice versa.

So the PPF could be drawn in a number of ways but in an economics textbook and stuff basically, you're going to see this bowed-out shape, and now because I had ten items here for clothing and only four for food, it looks a lot longer than you see if you've got an economics textbook. Because resources are not equally productive as we produce more and more of a good as we produce more and more food to get that last unit of food we're giving up a lot more clothing than we did to get that first unit of food and we'll talk about that more in the articles to come.

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