The PPF 3: Increasing Opportunity and Marginal Costs

One of the most important features of the Production Possibilities Frontier (PPF) is that it can be used to illustrate the concepts of opportunity and marginal costs. This section will look at both these concepts in turn as well as illustrate them on the appropriate diagrams.

Opportunity Costs

An opportunity cost is simply the value of the best alternative that is forgone when a decision is made. In terms of the PPF, where you only have two products, your best alternative is simply the other good. If you choose to increase the production of X, the opportunity cost of doing this  equal to the quantity of Y that must be forgone.

Marginal Costs

The concept of marginal costs is closely related to that of opportunity costs, however it is a somewhat more precise concept. Marginal cost can be defined as the cost associated with a one unit change in production. So the marginal cost of increasing the production of X is the fall in the production of Y when the production of X is increased by one unit.  Just as with opportunity costs, as you continue to increase the output of a good so  more of the alternative good must be sacrificed.

Marginal and Opportunity Costs along the PPF

You probably remember it being said in class or elsewhere on this blog that the bowed out shape of the PPF illustrates that opportunity and marginal costs  increase as the production of a good increases. That is, as you choose to produce more of good X, larger amounts of the alternative good (good Y) must be given up each time.

Try identify this relationship yourself quickly by sketching a quick PPF and seeing what happens to the amount of Y you give up as you increase the amount of X that you produce.

*Quick tip: Increase X by the same amount each time. By keeping as many things the same as possible we can better identify relationships. If you increase X by a single unit each time you will be working out the marginal cost of producing more X in terms of the amount of Y that is given up. So MC=OC when you vary output by a single unit.

Look at the PPF drawn below where the above exercise has been carried out.

You'll notice that each time we increase along the X axis so the amount of Y that is given up increases. 

Increasing the production of X from zero to one only cost half a unit of Y. Moving one to two units of X cost 1.5 units of  Y with the next increases in X costing 3 and 5 units of Y respectively/

This sacrifice is the opportunity cost of producing more X, and you'll notice that the further you are along the X axis the greater these opportunity costs are, and hence there is an increasing opportunity cost associated with increasing the production of X.

Now because we only increased the production of X by a single unit each time, in this this instance the opportunity costs are equal to the marginal costs. 

This increasing opportunity cost is illustrated graphically by the slope of the PPF; notice how the slope becomes steeper as the upper bound of X is  approached.

Graphing Marginal Costs

We can now use the data from the PPF above to graphically represent the marginal cost of increase the production of X. To do this sketch a pair of axes with the Y axis represent the change in Y (the cost of producing X) and the X axis is simply representing the amount of X produced.

This diagram shows that the first unit of X cost o.5 units of Y to produce, the second costs 1.5 units of Y, with the third and fourth units of X costing 3 and 5 units of Y to produce respectively.

Why do Opportunity/Marginal Costs Increase?

To understand why opportunity and marginal costs increase as we increase the production of a good we need to think about resources a little bit. The are many different types of resources that can be used in production, such as land, technology and human capital. These terms are very generic, but the reality is that resources vary greatly. Consider land for example, is all land equally suited to growing fruit or building houses upon? Likewise consider your classmates, do you all possess the same talents and proficiencies? Because of the heterogeneous nature of resources some resources are better suited to some tasks rather than others.

With this in mind turn back to the PPF above. Now when the economy is only producing good Y it is committing all of its productive resources to producing this good, even those resources that are not that suited to the task. When you no look to increase the production of X, what resources should you sacrifice? Well those that are least suited to producing Y of course. Doing this minimise the opportunity cost associate with increasing X. However as more and more of X is produced so the resources that have to be diverted to the production of X become those that were actually better suited to producing Y. Because these resources were better at producing Y we observe larger and large drops in the production of Y for a given increase in the production of X.

This is why the opportunity/marginal cost of production increases as you move along the slope of the PPF and hence why the PPF is drawn with its bowed out shape.

What would happen to opportunity and marginal costs if the PPF were drawn with a straight line? This will be covered next time...