Production Possibility Frontier (PPF)

Before we start, it is important to note:

The Production Possibilities Frontier (PPF) is the same exact thing as the Production Possibilities Curve (PPC).

(Depending on the professor, they may call it different names.)

To understand what a PPF, is it is important to first understand a very key concept in Economics.

Scarcity which refers to the limited nature of society's resources. 

Our society does not have unlimited resources which means that we must make decisions with how limited resources are used. 

Here inlies the value of PPF curves…

A PPF is a line or curve on a graph showing the maximum attainable combinations of two goods that can be produced with resources and technology. 

Here is an example:

Say you run a local college bar and you have 2 drink specials on Thursday nights. It’s important to note: both specials use the same type of vodka, and we only have one handle left. You can either use all of the vodka to make 20 vodka sodas or use all of the vodka to pour 40 lemon drop shots.

In this case, the vodka is the limited resource: we only have 1 handle and now we are faced with the decision of how to use the vodka. A PPF graphs out this scenario and shows the different combinations of the two drinks that we can make. On each axis will be one of the drinks (the good we produce in this scenario). 

Creating a Production Possibilities Frontier (PPF) graph

It is alright if you are still confused, it makes more sense when you draw it out!

We’ll continue to use the example from above:

Say you run a local college bar and you have 2 drink specials on Thursday nights. It’s important to note: both specials use the same type of vodka, and we only have one handle left. You can either use all of the vodka to make 20 vodka sodas or use all of the vodka to pour 40 lemon drop shots.

Let’s start with a graph and label 20 on our y-axis as vodka shots and 40 on our x-axis as lemon drop shots. (Keep in mind: we could flip these. It doesn't matter which good you assign to which axis.)

Why are we putting these values on our x-axis and y-axis?

Because according to the prompt...

Say you run a local college bar and you have 2 drink specials on Thursday nights. It’s important to note: both specials use the same type of vodka, and we only have one handle left. You can either use all of the vodka to make 20 vodka sodas or use all of the vodka to pour 40 lemon drop shots.

...it’s the number of units we can get if we max out on any one of the given specials!

In other words, if we make 0 lemon drop shots, that means we can make 20 vodka sodas. On the flip side, if we make 0 vodka sodas, that means we can make 40 lemon drop shots.

Calculating opportunity cost using the Production Possibility Frontier (PPF) 

Using the example from above, let’s see how we can use a PPF to figure out the opportunity cost of each option using the same example. 

Say you run a local college bar and you have 2 drink specials on Thursday nights. It’s important to note: both specials use the same type of vodka, and we only have one handle left. You can either use all of the vodka to make 20 vodka sodas or use all of the vodka to pour 40 lemon drop shots.

Essentially, we need to determine how much of 1 vodka soda we'd have to give up in order to make "X" amount of lemon drops.

Whenever trying to understand the PPF at a given point, ask yourself: How many of good A you’d need to give up to get one of good B?

Considering that the PPF represents all the possible combinations of vodka sodas and lemon drop shots we can make, let’s use it to determine the opportunity cost of each drink.

Speaking in linear terms, we need to find the slope of our PPF line to determine the opportunity cost of each drink.

If you remember from mathematics, here's the equation for slope...

slope = (y2 - y1) / (x2 - x1)

For (x1, y1), we'll make this the point representing the max vodka sodas you could make. That occurs at (0, 20).

slope = (y2 - 20) / (x2 - 0)

For (x2, y2), we'll make this the point representing the max vodka sodas you could make. That occurs at (40, 0).

slope = (0 - 20) / (40 - 0)

When we solve this...

slope = (0 - 20) / (40 - 0) = -20 / 40 = -1/2

...we get a slope of -1/2.

What does this mean?

In relation to opportunity cost, we can understand it like so:

Opportunity Cost = What’s Lost / What’s Gained

So in our case...

Opportunity Cost = 1 vodka soda / 2 lemon drops

For example, if we lost one vodka soda (going from 20 to 19), that means we gain 2 lemon drops (going from 0 to 2)!

If we lost another vodka soda (going from 19 to 18), that means we gain 2 more lemon drops (going from 2 to 4)!

This process of losing 1 vodka soda for 2 lemon drops continues down the rest of our PPF line!

Inefficient and unattainable points on a PPF graph 

The scenario we just ran through with drinks assumes that our vodka is used efficiently. If our point of production (the combinations of drinks we make) falls below the line then that means our production is inefficient.

Here is an example using the same scenario.

Say we make 12 vodka sodas and 8 lemon drops. This point is plotted on the graph below. We see that it is inefficient because at those levels of production, we could be making more vodka sodas or lemon drops. 

If your point of production is below the PPF line, then your production is inefficient.

On the other hand, say we wanted to make 10 lemon drops and 22 vodka sodas. This point is plotted on the graph below. We see that it is unobtainable, because we physically cannot make those many drinks with one bottle of vodka.

If your point of production is above the PPF line, then your production is unobtainable.

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