In this article, we’re gonna talk about how to graph the marginal cost curve when you have a production possibilities frontier. So we use the following data in a previous article to create a production possibilities frontier and we assume that you and a group of friends were stranded on an island and all you could produce was food and clothing, so you had to make trade-offs think about how much food or clothing you could produce and we also graph the PPF.
We plotted each point so for example if you were to produce four units of food that would mean zero units of clothing. So four units of food zero units of clothing, three units of food would give you four units of clothing so these are the following combinations and we plotted them all out with our PPF.
We made our production possibilities frontier and then we introduced the idea that there’s an increasing marginal cost, right? and that actually explains why the PPF usually has this bowed-out shape. Instead of this PPF think about a PPF that could conceivably just look like a straight line but instead, we said usually the PPF has this bowed-out shape due to the fact that not all resources are equally productive.
So let’s take here we start with zero units of food we’re all starving and we say hey wouldn’t it be nice if we had food and so we decide okay well we’re gonna produce one unit of food we’re gonna go from zero to one unit of food and we give up one unit of clothing because clothing goes from ten to nine. We would say the marginal cost or the incremental cost of producing one unit of food is giving up one unit of clothing. So we’d say that the marginal cost of producing one unit of food when we start with zero units of food the extra one unit of food will gonna cost us one unit of cloth.
So that’s of marginal cost to produce that first unit of food but the marginal cost changes, it’s not constant. If it were a straight line then it’d just be constant but we said that the whole reason we’ve got this graph is the marginal cost is gonna be increasing. So let’s think about it, as we go from one unit of food and now we say you know what it’d be nice to have two units of food so we produce an extra unit of food. Now look we have to give up two units of clothing. If you go back to the numbers if we go from nine to seven units of clothing we give up this time to get an extra piece of food is two units of cloths. So now the marginal cost here would be two.
Now we think what if we wanted a third piece of food, what if we go from two units of food to three units of food? That extra one unit of food what is the cost of it? Now look it’s getting more and more of our cost, now our marginal cost is three. When I say marginal cost I mean the amount of clothing that we’re giving up to get that extra piece of food. Think about when we started with zero food and went to one it only costs us one piece of clothing but now we’ve got a marginal cost of three. Let’s go for the max let’s go for four units of food, from three to four. We’re getting one extra piece of food but we’re giving up four units of clothing.
So we can actually put all costs together in a little table and we say when we have one food the marginal cost was two, Then three and four. So we can just fill our table with marginal cost and now what we can do is we can graph this. We can graph this little table.
That’ll tell us something about our marginal cost which you probably already can see just from looking at the numbers. So I’ve got food here on the x-axis and the marginal cost on the y-axis. When we have want zero units of food the marginal cost of producing one unit of food is 1 so (0, 1) will be our first combination. Now one unit of food the marginal cost is two so that will give us the second combination. Here two units of food the marginal cost is three. Then when we have three units of food that make that extra last piece of food it will cost us four units of clothing. So we see that actually, this is our marginal cost curve.
and you see that the marginal cost is increasing. It’s an increasing marginal cost curve. So why is that? So again this idea that resources are not equally productive. So again let’s return to our example so we’re on an island, it’s a group of us we’ve been stranded due to a plane crash and we have to think about how much food and clothing to produce. Now some people are gonna be better at producing food and other people are gonna be better at producing clothing.
So let’s say there’s somebody on the island who is a tailor and then let’s say there’s somebody on the island who maybe was a chef. If when we’re producing zero food and ten clothing that means that the chef is being asked to make clothing. As everybody’s making clothing, right? Let’s have the chef he can go or she can go make some food, well maybe the chef wasn’t very good at making clothing. So we only really give up one unit of clothing. So our marginal cost is one when we want to get that first unit of food. The marginal cost is low there. Was somebody that maybe wasn’t even good at making clothes, to begin with, but as we get further and further along and we get to a point where to make that last unit of food to go from three to four, now we’re asking the Taylor, who makes clothes for a living and we’re asking them to make food.
So now we’re giving up four units of clothing to get that final piece of food. So that explains why we have an increasing marginal cost because as we move along the curve, not all resources are equally productive if we could equally trade-off resources. Let’s say hypothetically that we were in a world where we just everybody is equally good and making food and equally good at making clothing then the PPF wouldn’t look like that bowed-out shaped it would be like a straight line.