Living Economics: Production Possibility Frontier (PPF)

*The game referenced in this article is ‘The Tribez‘ offered by Game Insight UAB.

The second major economic model after the Circular Flow Diagram (Link) is that of the Production Possibility Frontier (PPF).

The PPF is a simple graph of an outwardly curved line.

How the PPF Works

Assume for a moment that a company is interested in producing two products: Shirts (👚) and Shoes (👞).

Scarce Resources

The problem the company faces is that the resources available to use are scarce and there are not enough to produce infinite shoes AND shirts. The company is particularly concerned about its labor. Right now, the company has hired 10 workers . . . . it cannot afford to hire more workers because there is no money available to pay them.

The Trade-Off

The company discovers that in addition to having limited resources (maximum of 10 workers), these workers create a trade-off.

When a worker is creating shirts (👚), it is not possible for him to also be creating shoes (👞) simultaneously. The machines are different, the production is in different buildings, they take different amounts of time. . . . it is simply not possible for a worker to produce BOTH at the same time.

As a result, when the company sends a worker to create a shirt (👚), they lose one worker who could have created shoes (👞). When the company sends a worker to create shoes (👞), they lose one worker who could have created shirts (👚).

The PPF

The PPF is a model or graph demonstrating the possible production of two resources where resources are limited. It demonstrates the trade-off involved in changing production levels where all resources are already in use.


The Theory

The Horizontal (‘X’) and Vertical (‘Y’) lines each represents one of the resources being produced. In this example, X represents the quantity of shoes 👞 that the workers can produce and Y represents the quantity of shirts 👚 that the workers can produce.

The curved line represents the trade-off that evolves as we increase the production of one resource at the cost of producing the other. Each point on the line shows the Maximum Possible Combination of the Two Resources if All Resources Were Utilized

Notice that when we produce six shoes 👞, we can make a maximum of eight shirts 👚. We could obviously produce less, but because our workers are limited we cannot produce more. Remember the line shows the possible production if we maximized our resources. This means if all resources are being utilized and we can make at best a combination of six shoes + eight shirts = 14 Products

When we produce more shoes 👞 (9), the number of shirts 👚 that can possibly be produced declines (4). This is because we were already using all of our resources before . . . the only way to get more resources to produce shoes 👞 is by taking away resources that were producing shirts 👚.

A Couple Of Notes:

1) We can begin to see why this model is called the Production Possibility Frontier. . . the curved line represents the frontier or line between what is possible and what is impossible.

Consider the following chart:

According to this PPF model, when the company produces six shoes 👞, the maximum number of shirts 👚 that can be produced is eight.

Thus, Point A on the graph is the point at which the company maximizes production and is most efficient when producing six shoes 👞

Is Point B possible as well? At Point B, the company would produce the same six shoes 👞 but only four shirts 👚. Clearly this is possible. . . the problem with Point A is that the company could do better. If it uses the same resources to produce four shirts that it could use to produce eight shirts. . . the company is not practicing efficient resource management. Conclusion: Inside the PPF line, production is possible but not efficient.

If Point C possible as well? At Point C, the company would produce the same six shoes 👞 but would also produce twelve shirts 👚. Clearly this is not possible. . . the PPF is the maximum that is possible. The company can produce eight shirts 👚 but not more. Conclusion: Outside of the PPF line, production is impossible.

2) Why does the PPF curve downward?

The answer to this is related to the concept of Opportunity Costs (Link). Whenever a trade-off arises, so too do opportunity costs. These are the potential uses of a resource that are sacrificed in the decision made. In mathematical terms, the opportunity cost is calculated as the value lost from sacrificing the second-best alternative use of the resource.

In the case of the PPF, the opportunity cost is relatively clear. When we produce more Shoes 👞, we sacrifice the opportunity to use our materials to produce Shirts 👚. So the opportunity cost of producing the new shoes is the shirts sacrificed. When we produce more Shirts 👚, we sacrifice the opportunity to use our materials to produce Shoes 👞. So the opportunity cost of producing the new shirts is the shoes sacrificed. Conclusion: On a PPF Graph, the opportunity cost of producing more of Resource A is the quantity of Resource B that will be sacrificed.

There is an opportunity cost relationship between the horizontal axis (X — Resource A) and the vertical axis (Y — Resource B). Consequently, the result is that when the quantity of X increases (We produce more Shoes 👞), the quantity of Y decreases (We produce less Shirts 👚). And when the quantity of Y increases (We produce more Shirts 👚), the quantity of X decreases (We produce less Shoes 👞) This type of relationship between X and Y on a graph (X⬆ and Y⬇ . . . Y⬆ and X⬇) is known as an Inverse or Negative relationship and creates a line on the graph that slopes downward.

Identifying the Opportunity Cost of X:

The downward shape of the PPF line reflects the opportunity costs realized by the company. Thus, we can identify the opportunity cost by studying the slope of the line.

For anyone who has perhaps been away from math for a while, a reminder that the slope of the line is the rate at which Y changes for one change in X. For example, the rate at which the production of shirts 👚 declines when we produce one additional shoe 👞 .

The formula of a line is

Y = MX + B

Where ‘M’ represents the slope of the line and B is the Y-Intercept (The Quantity of Y produced if we create no X).

The formula of ‘M’ is a ratio of the change in Y over the change in X

For simplification, let us assume for a moment that the PPF was a straight line.

Based on this chart, we can clearly see that if we devote all of our resources to producing shirts 👚, the maximum we can make is twelve (this is the Y-intercept). This suggests that we will never make more than twelve shirts unless something changes.

We can also see that if we devote all of our resources to producing shoes 👞, the maximum we can make is ten. This suggests that we will never produce more than ten shoes unless something changes.

We can also identify the slope of the line. Assume that we were originally producing 12 shirts 👚 but are now producing 10 shoes 👞 (we have moved from point A to point B). What was the slope of this line and what is the opportunity cost of this change?

Using the formula of the slope, we find that the slope is -1.2. The slope of the line also reflects the marginal opportunity cost of any increase in the production of X.

Identifying the Opportunity Cost of Y

Until now, we have assumed that we were increasing the production of shoes 👞 (X), but we might instead increase the production of shirts 👚 (Y).

Identifying the opportunity cost of Y is a relatively simple thing. . . it is the reciprocal of the opportunity cost of X.

Consider the following example, we can either start at Point A and increase our production of Shoes👞. Or we can start at Point B and increase our production of Shirts👚.

Point A ➞ Point B

(5👞,6👚) ➞ (10👞, 0👚)

If in increase the shoe production, the slope shows the marginal opportunity cost of X 👞

Point B ➞ Point A

(10👞, 0👚) ➞ (5👞,6👚)

In this case, you can still use the slope. . . just remember that it’s reversed this time and you’ve gained 1.2 👚 for each 1 👞 sacrificed.

Or use the reciprocal of the slope and find the exact marginal opportunity cost of Y👚

Marginal Opportunity Cost:

We can express the opportunity cost in two ways: Total Opportunity Cost and Marginal Opportunity Cost. In the example above:

  • The Total Opportunity Cost of producing ten shoes was twelve shirts.
  • The Marginal Opportunity Cost of producing each individual shoe was 1.2 shirts.

Some students can confuse Marginal and Average. Assume I have three workers . . . A produces 4 shirts per hour, B produces 3 shirts per hour, and C produces 2 shirts per hour. I move all three workers to the shoe factory. On Average I have lost approximately three shirts per worker (9👚/3👨🏻). Marginally, each worker is different. The Marginal cost of worker A was 4 shirts. . . the marginal cost of worker C was 2 shirts. Average considers the change on a total scale; Marginal looks at the exact loss created by a change of ONE unit.

In this example, the PPF is a straight line and straight lines have a universal slope — the slope never changes from unit to unit. This means that on a straight line PPF, the Marginal Cost of each new shoe produced is exactly the same for every shoe . . . -1.2 shirts.

We can use the equation of the line (Y = MX + B) to fill in the production chart.

We can then test our theory that the slope never changes by using two new points (X,Y). . . (9,1.2) and (5,6). What is the slope if we changed from producing 5 shoes to 9 shoes?

Again, we lost 1.2 👚 per shoe 👞 added. With a straight line PPF, the marginal opportunity cost of each new X produced is the same.

THE SITUATION IS DIFFERENT ON A CURVED PPF

Notice on the curved PPF two possible changes:

  • Shifting from Point A (0 Shoes 👞) to Point B (5 Shoes 👞)
  • Shifting from Point B (5 Shoes 👞) to Point C (10 Shoes 👞)

In both cases, I increase the shoe production by 5 Shoes. But the opportunity cost is not the same. The total opportunity cost of moving from Point A to Point B is approximately 2 shirts. The total opportunity cost of moving from Point B to Point C is approximately 10 shirts.

Notice also that the marginal opportunity cost is increasing (this is known as the law of diminishing marginal returns). The loss of producing the first shoe was miniscule. . . almost unnoticeable. The loss of producing the tenth shoe is significant. . . almost 5 shirts. Why this happens is for another article. Nonetheless, if we calculated the slope of this line you would find it is constantly changing.

Conclusion: On a Straight Line PPF, the marginal cost is constant and the slope is the same regardless of which points are used in the calculation. On a Curved Line PPF, the marginal cost increases as production of X increases, and the slope changes.

Finding the Ideal Production Point:

It is clear from the PPT that the total cost in resources of producing any combination of shoes and shirts along the PPF line is the same. This is because the PPF already assumed that we have a limited quantity of resources and all resources are employed (the cost is the same no matter what we do).

In this case, we will be using the same amount of labor (and paying the same wages) whether we produce 12 Shirts or 10 Shoes.

So finding the ideal production level requires more than a simple comparison of costs. It is not cheaper to produce one point on the production line compared to others.

Instead companies will need to take other factors into consideration including but not limited to:

  • The Retail Price of Shirts and Shoes . . . if Shirts sell for $20 and Shoes sell for $80, clearly that would be significant. Profits = Revenue – Cost. If the Cost is the same no matter what, consider the Revenue.
  • The Overall Output Levels. It is true the cost is the same . . . but we produce more products overall if we make 5 Shoes and 6 Shirts (11 Products) than if we produce just 10 Shoes.

How the PPF is Key to Resource Allocation Decisions

Consider the following example:

The company currently has 12 Workers available for producing and packaging Turtles or Birds for pet shops. When a worker is assigned to package and ship Turtles, he will not have time or ability to handle birds and vice versa.

Based on the chart above,

  • One Turtle requires Two Workers
  • One Bird requires Four Workers

So the company (along a PPF) can produce the following combinations of Birds and Turtles with 12 Workers:

  • 6 Turtles + 0 Birds = 12 Workers
  • 4 Turtles + 1 Bird = 12 Workers
  • 2 Turtles + 2 Birds = 12 Workers
  • 0 Turtles + 3 Birds = 12 Workers

One might be tempted to believe that because all animal combinations cost the same in terms of labor, they are all equally acceptable. Wrong.

Consider the Financial Opportunity Cost of each decision.

  • 6 Turtles = $60 Profit
  • 3 Birds = $90 Profit

The Marginal Opportunity Cost of producing one turtle is 0.5 Birds = $15 Profit sacrificed.

The Marginal Benefit of producing one turtle is $10 Profit.

The Trade Off Formula =

Marginal Benefit – Marginal Opportunity Cost = Marginal Return.

  • When the Marginal Return is Positive — This Production is Acceptable
  • When the Marginal Return is Negative — This Production is Unacceptable

So let’s calculate the production of Turtles

Marginal Benefit – Marginal Opportunity Cost = Marginal Return
+10 Profit – $15 Opportunity Cost = -$5 Marginal Return

Choosing to produce Turtles is profitable. . . . it’s not like the company will lose money overall by producing Turtles and go bankrupt. Every turtle they produce will create $10 Profit for the firm.

STILL, THEY COULD DO BETTER!

By producing a turtle instead of birds, the company is sacrificing the opportunity to create an additional $5 in profit MORE with birds. This is not a practical decision for a firm to take.

Changing the PPF:

Assume that for once, we want to accomplish the impossible. What can we do to obtain Point C levels of shirts and shoes, which is currently not possible with our resources available?

In General, there are three ways to increase the output available to us:

  1. Increase the Level of Resources Available ⇨ If you want to increase your production possibility, hire new workers and buy new supplies. With more resources available you can expand your PPF.
  2. Improve Technology and Decrease the Marginal Opportunity Cost ⇨ If the company were to become more efficient at producing products with the same resources, they would be able to produce more with the same labor or materials. Training the workers, encouraging specialization, building better and faster tools can all help a company to produce more with the same supplies.
  3. Specialization and Trade ⇨ There is an important concept known as Comparative Advantage which we discuss more in detail later. But the basic concept is that production increases when a company or person specializes (focuses on one specific product / industry). This is because that person is able to devote all their time and energy to mastering that one style of production, become faster and more effective at producing it (see #2 above). This allows the company to produce more using the same labor as that labor improves. However, to capitalize on this means the company will only be producing shoes OR shirts, not both. In order for the company to also have the other resource to sell. . . it will need to trade with other companies who are specializing in the other goods. The fundamental theory here is a combination approach: two companies cooperating can bring together a expanded resource base (1) and then by specializing, each improves its efficiency and decreases the opportunity costs (2).

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