## 6/23/11

### How to draw a PPF (production possibility frontier)

Sometimes drawing the production possibility frontier can seem difficult.  However, if you understand the intuition behind the economics of the PPF it is simply a graphical representation of what a country or individual is able to produce. This article will describe how to derive and draw a PPF given information from a table.  Sticking with the broccoli and pizza example from the prior article on PPFs, lets plot out the following PPFs given the information from the tables:

 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
(at each of the 6 points) and plotted them to get a PPF curve.  Combination 1 is the choice of completely specializing in Pizza, 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.

So all we have done is taken the information from the table and converted it
into its graphical representation of a PPF.  Remember, the PPF shows the frontier of what is capable for production.  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:

 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:  PPF's 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 judgements on optimal allocations of goods production.  In order to do that we need to know more about consumer theory.