How to draw a PPF (production possibility frontier) - FreeEconHelp.com, Learning Economics... Solved!

## 8/21/18

This post was updated in August of 2018 to include new information and more examples.

The idea of a production possibility frontier (PPF)--also sometimes called a production possibilities curve--can seem difficult.  However, if you understand the intuition behind the economics of the PPF it is really just a graphical representation of what a country or individual is able to produce with a fixed amount of inputs. For example, most people are able to spend their day working or sleeping. A PPF would show this relationship between work and sleep (with the constraint of time in a day).

This article will describe how to derive and draw a PPF given information from a table.  Sticking with the example of the United States producing broccoli and pizza from the prior lesson on PPFs, lets plot out the following PPF given the information from this table:

 United States Different Combinations Broccoli Pizza 6 0 100 5 5 80 4 10 60 3 15 40 2 20 20 1 25 0

You can see in the diagram below how we took the different combinations of goods
 Sample PPF with constant opportunity cost
(at each of the 6 different points) and plotted them to get a PPF curve.  Combination 1 is the choice of completely specializing in Pizza (producing 100 pizza and 0 broccoli), and point 2 shows that we give up 20 pizza in order to get 5 broccoli (which is why the PPF is downward sloping).

Points 3, 4, 5, and 6 continue this trade off of 20 pizza for 5 broccoli until we are completely specializing in broccoli (producing 25 broccoli and 0 pizza).

To summarize: In order to draw a PPF you take the numerical information from the table and use it to plot the individual points on a graph. You can then connect the points that were drawn to give you the complete PPF.

It really is the simple process of taking the information from the table and converting it into its graphical representation.  Remember, the PPF shows the frontier of what is capable for production given fixed inputs.  Anything inside the PPF is considered inefficient, and anything outside is considered unfeasible.

Now we will construct another PPF, one that has a bowed out shape, given new information:

 United States Different Combinations Broccoli Pizza 6 0 100 5 2 60 4 5 30 3 9 15 2 15 5 1 25 0

The information from this table translates into a PPF that looks like:

 PPF with increasing opportunity costs as more of a good is produced
Note that the bowed out nature of this PPF is due to increasing opportunity costs associated with specialization. Imagine a company that has fields and ovens. If the fields are used to grow broccoli and the ovens are used to cook pizza everything works well. However, ovens are pretty bad at growing broccoli, and fields are not very good at cooking pizza. This means that devoting all of your resources to the production of one good tends to reduce how good you are at doing it resulting in the bowed out PPF.

 United States Different Combinations Broccoli Diff Pizza Diff Opp cost Pizza Opp cost Broccoli 6 0 - 100 - - - 5 10 10 95 5 2 0.5 4 16 6 85 10 0.6 1.667 3 20 4 70 15 0.2667 3.75 2 23 3 40 30 0.1 10 1 25 2 0 40 0.05 20

We can use the information in the diff (differences) column to calculate the opportunity cost of switching between each of the different combinations (for example, switching from point 1 to point 2 gains you 10 broccoli, but you lose 5 pizza).  Using this information you can calculate the opportunity cost of pizza or broccoli.  So by moving from point 1 to 2, the opportunity cost of broccoli is 0.5 pizza, (likewise moving from 2 to 1, the opportunity cost of pizza is 2 broccoli).  The takeaway from this table is that specialization is bad, because the opportunity costs are rising as we specialize.  Choosing a mix of the two goods results in a lower opportunity cost for either good.

Remember:  PPFs are used to show the frontier of production possibilities for an economy.  The point is to tell if an economy is producing efficiently or not, at this point we are not able to make judgement on optimal allocations of goods production.  In order to do that we need to know more about consumer theory.

If you want help developing your intuition about PPFs or would like to see more example PPFs check out the video below: