What is the Production Possibility Frontier (PPF)?

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Definition:

The production possibility frontier describes all of the combinations of output that are possible given a constraint — like time, materials, capacity, or money.

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🤔 Understanding production possibilities frontier

A production possibilities frontier (PPF) is a microeconomic concept that defines all of the possible combinations of goods that a business can produce, given some finite resource. It can be used as a decision-making tool by managers. The concept can also be applied in macroeconomics as the limitations of output that a country can reach on its own, given its scarce resources. Any combination of products outside the PPF is unachievable without trade.

Example

Let’s say you were stranded on a deserted island, on which fish and coconuts were the only available food sources. Because there are only so many hours in a day, you must choose to allocate your time between fishing and foraging. Every hour you spend fishing is an hour you are not trying to get coconuts. Consequently, there is a trade-off to be made. Perhaps spending all day fishing yields two fish and spending all day gathering results in two coconuts. The limits of your production possibility frontier (PPF) include two fish and no coconuts, two coconuts and no fish, or one fish and one coconut. But, you could also choose to lay in the sun all day and get nothing done. So, no fish and no coconuts are also within your PPF.

Takeaway

A production possibility frontier is like the shelves in the grocery store...

The shelves provide a limit to what a company can display. It must carefully choose what to put on them. Every item that is displayed results in something else that cannot be seen by potential customers. If every inch of shelf space is used, that is one combination at the limit of all possible uses. There are nearly infinite other possibilities, some of which include leaving some space empty.

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How do you make a PPF?

The production possibility frontier (PPF) can be very complex when there are several items to choose between. For a country, there can be thousands of products that it can make and a near-infinite combination of production possibilities. It is easiest to understand the PPF by visualizing it in just two dimensions.

Let’s imagine a business that only makes two types of candy bars: milk and dark chocolate. For simplicity, let’s assume the company only has one machine that makes the candy bars. So, using the machine to make milk chocolate means that it is unavailable for dark chocolate ones. Let’s also assume that the machine makes one bar per minute, for a maximum of 1,440 bars per day. There is also a one-for-one trade-off for each candy bar. That is, the opportunity cost of making a milk chocolate bar is a dark chocolate bar.

With this framework established, we can plot all of the possible outputs in a day. If the company only made milk chocolate, there would be 1,440 of them and no dark chocolate ones. On the other hand, they could make 1,440 dark chocolate and no milk chocolate candy bars. Or, they could split the time in half, ending up with 720 of each. You could write this as an equation:

Dark chocolate = 1,440 – milk chocolate

The line that is generated from that equation is the boundary of the production possibility frontier. That means that if the machine is in constant use, the combinations on that line are the maximum possible output. However, nothing requires that machine to run 24 hours a day. So, every combination inside that line is also possible. That is what it means to have a frontier rather than an output equation. The frontier shows all possible combinations.

Why is the PPF curved?

Whenever you must choose between making one product or another, you bear an opportunity cost in the amount of the alternative you did not choose. If the cost were linear (making one milk chocolate bar implies making one less dark chocolate bar), then the boundary of the production possibility frontier would be a straight line.

However, the law of supply states that the marginal cost of production (the cost of increasing production by one unit) tends to increase as production increases. Therefore, there is not a set cost when choosing between two products. Let’s say that a business that makes chocolate bars has an increasing marginal cost of production — Imagine that sourcing the chocolate costs more as you try to increase production.

For example, the first 100 chocolate bars cost $25 to make. Each 100 increment increases the cost by one dollar. So, the second batch of 100 chocolate bars costs $26 to make. And so on. In this situation, the choice between products is not equal across all production levels. If you only produce dark chocolate bars, the 14th batch of 100 units would cost $38 ($25 for the first 100 plus $13 in escalating costs at a rate of $1 per batch). At that point (“Point A”), the decision is between the 14th batch of dark chocolate and the first batch of milk chocolate – which has a cost of just $25.

The situation is reversed at the other end of the PPF curve (“Point B”). Because the opportunity costs are changing at different combinations of production, the boundary of the PPF is not a straight line. Instead, it is curved. In this example, the company would maximize its profits by making an equal amount of each bar (“Point C”).

Why is the PPF concave?

The production possibilities frontier (PPF) is curved because the cost of production is not constant. If every trade-off were the same, it would create a straight line. But the direction that PPF is curved comes from the way that the trade-offs change. A concave curve is one that bends outward from the origin. It forms a shape that looks like a cave or a rainbow. If the curve bends inward, it will look more like a smile ⁠— That would be a convex curve.

A production possibility curve (PPC) is concave because the marginal cost of production increases as production increases. If you charge one price for all of your candy bars, you can see how increasing production leads to a smaller contribution to profits than previous production levels.

That is called the law of diminishing returns, and it exists everywhere you look. Adding a second machine does not necessarily double production. Putting a fifth cook in the kitchen might not increase the amount of food that comes out. And studying for the 10th hour probably doesn’t do as much to improve your grade as the first hour of studying did.

This fact means that the opportunity cost of production decreases as you ramp up the production of one product versus the other. Making the 13th batch of dark chocolate versus the first batch of milk chocolate has a cost of $38 rather than $25. Dividing those numbers gives you a relative cost of 152%. But, if you slide down the graph line, trading the 12th batch of dark chocolate for the 2nd batch of milk chocolate has costs of $37 and $26 for a cost ratio of 142%.

This changing slope of the PPF implies that the boundary line is not straight. And, the decreasing nature of the change implies that it is concave.

What shifts the PPF?

Everything within the production possibility frontier (PPF) represents a combination of outputs that is possible with existing resources. In the case of a business, the PPF shows the limits of what can be done with the existing workforce, equipment, contracts, and money. If the business wants to expand, it will need more people, plants, machines, materials, or money.

When those limitations are lifted, the capacity of the company grows. That growth is represented by an outward shift in the PPF, signifying that more production combinations are now possible. Conversely, if something happens to contract the business operations, the PPF would cause an inward shift. That would mean that some combinations of goods that were available are now out of reach.

In the case of a country, it is the factors of production (land, labor, capital, and enterprise) available to that country that typically apply limits to what can be achieved. An increase in those available resources, or improved use of them, can lead to a shift in the PPF.

That could occur by increasing the population, either naturally or through immigration, so that more labor is available. On the natural resources front, it could mean discovering new deposits of natural resources. In terms of capital, encouraging more investment in businesses can lead to more output. In fact, the same is true with human capital. Investing in education and skills training can lead to more efficient use of labor, thus increasing output and shifting the PPF.

Finally, technology and process improvement can lead to a shift in the PPF. By finding ways to generate more output with the same amount of resources, the limit to what can be accomplished is lifted to a new level.

How does PPF show economic growth?

In the context of macroeconomics, the production possibility frontier (PPF) highlights the fact that an economy has limited factors of production. Because there are only so many people with labor to offer, so many businesses with capital to deploy, and a limited amount of natural resources to use, there is a limit to how much a country can produce.

Each country must decide how to use its factors of production in a way that makes the most sense for them. For example, let’s say there’s a country that can only produce pens or books. If all of the country’s resources are dedicated to making pens, there are no books. If they focus on books, there are no pens. The most likely outcome is something in the middle, but a trade-off always exists. When the country can use its resources in a way that generates the most value, it is called a “Pareto optimal outcome.”

If a country wants to do more of one without sacrificing the other, it needs more resources. With more resources, the combinations that are possible expand outward. That is how a shift in the PPF shows sustainable economic growth.

Not all increases in output are economic growth. First, a country might not always deploy all of its resources. During a recession, there is often labor, equipment, and money sitting idle. Therefore, the country is producing less than it could if everyone was working, and all the country’s resources were in use. When this occurs, the economy is producing inside the PPF.

Later, when the country recovers from the downturn, it might get back to the full use of its resources and reach a production level at the boundary of what can be accomplished. This is called a “Pareto efficient use” of its factors of production. Moving from inside the frontier to the boundary is an increase in output, but it is not economic growth.

It is possible to temporarily reach an output level beyond the PPF on its own. But, this can only be done by borrowing resources from the future, also known as taking debt, or by using labor beyond the natural rate of unemployment (enticing people that don’t really want to work into the workforce).

Increasing output through debt or overextending the labor force is not sustainable growth, and it does not shift the PPF. It is a temporary increase in output that will be met with a future return to sustainable levels.

The only way to increase productive output without increasing the PPF is through international trade. Because different countries have different comparative advantages (the relative cost of producing something is lower in one country than another), two countries can both improve their economic capacity through specialization and trade.

Take this simple example:

Country A is good at making cars, while Country B is good at making computers. Let’s say that it costs Country A $10,000 to make a car and $1,000 to make a computer. For country B, it cost them $12,000 to make a car and $500 to make a computer. For simplicity, let’s say that each country has $1B worth of resources to use.

This suggests that country A can make 100,000 cars, one million computers, or some combination of each. If they dedicate half their money to each, they can make 50,000 cars and 500,000 computers. For them, each car is worth 10 computers. So, they would gladly trade 1 car for 15 computers.

Country B would also gladly make that trade. For them, one car is worth 24 computers. If they can get a car for only 15 computers, that is a good deal. Now, if country A specializes in their comparative advantage, they can reach beyond their PPF. By making 100,000 cars, they can trade 50,000 of them to get 750,000 computers. That is an output level outside their PPF, which they could not reach on their own.

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