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...

The PPF 1: Intro to The Production Possibilities Frontier (PPF) - Micro

The Production Possibilities Frontier or PPF is a very simply economic model, probably introduced to you during an introductory lessons of a microeconomics course. Whilst the model is very simply it does contain a wealth of information and is used to illustrate many important economic concepts.

Such concepts include scarcity, opportunity and marginal costs, productive and allocative efficiency as well as the effects of international trade. Indeed for a simple model it is rather rich, and the wealth of this model will be espoused in later posts, but for a simple introduction.

Building the  Model:

In order to set up (or build) this model it helps to imagine an extremely simple economy, one that is so simple that it can only produce two goods. Lets call these goods X and Y. In order to produce X and Y this very simple economy must use its available productive resources. Like all economies the availability of productive resources act as a constraint to how much can actually be produced.

Keeping things simple, we consider the resources available to our economy being just capital and labour (K and L). Capital is a very generic term that we use to describe all productive resources available to the economy apart from Labour, and therefore includes land, machinery, software, etc. Later, we will introduce technology and its affects on the economy as described by the PPF.

To draw the PPF we must assume that the economy is going to use all its resources to the best of its ability in the production of goods X and Y. Following this assumption we are presented with the PPF shown below.

If this economy decided to put all of its productive resources into the production of good Y, we can see by inspecting the PPF that a maximum of Y1 can be produced. Likewise, if the economy in question were to rather dedicate all of its productive capacity to producing good X, a maximum of X1 could be produced. X1 and Y1 hence represent the limits of production for these two goods.

Now say that the economy was producing at one of these maximum points. If it wanted  to change the productive mix present in the economy, that is produce a mixture of both X and Y , it will need to use some of its available resources to produce these other goods. It will have to sacrifice some production of one good in order to produce some of the other, there therefore exists a trade off.

If it were producing only X this economy would need to divert some of its resources away from the production of X and towards the production of Y, and vice versa. This would result in a movement along the PPF. The slope of the PPF represents all combinations of both X and Y that can be produced by this economy and are productively efficient. That is, the slope of the PPF represents all combinations of output that are obtainable give that its finite resources are being utilised to the full of their productive capacity.

All combinations of X and Y that are located within or along the PPF are obtainable but only those found along the PPF are productively efficient. All combinations found beyond the PPF are unobtainable as the economy simply does not have sufficient resources at its disposal to produce that combination.

What happens if the amount of resources increase?

If the amount of resources with the economy were too increase or say an increase in the level of technology increased thus enabling the current resources to be combined more efficiently, then the economy will be able to produce more combinations of X and Y.

Graphically this is illustrated as an outward shift of the PPF. All that the outward shift is illustrating is that there are now a whole host of output combinations that are now obtainable as well as there being a new set of combinations that are productively efficient. 

The PPF below illustrates a case where there has either been an increase in the amount of resources or an increase in the level of technology.

As you can see the diagram above illustrates an outward shift of the PPF. The new PPF is simply a larger version of the previous one give that the economy now endowed with more resources is also able to combine these additional resources to produce more output.

This concludes our introduction to the PPF. Future posts will look at some of the more interesting aspects of the model. Specifically we'll look at the concepts of scarcity, opportunity and marginal costs, productive (we touched on this in this post) and allocative efficiency as well as the effects of international trade.

Follow the links to part 2 and part 3 of the PPF series of posts.

 

The PPF 2: Productive Efficency (Microeconomics)

Productive efficiency simply implies that in the process of production all resources in the economy are used efficiently, such that given some production level of X and Y there are no resources left with which to produce more output. Drawing the PPF under this assumption also enables us to discuss scarcity as the PPF clearly illustrates combinations of output that are obtainable and unobtainable.

Productive efficiency and the PPF

Three output combinations have been highlighted on the PPF below, of these three output combinations only two are obtainable and of these only one is productively efficient, see if you can figure them out.

In the above PPF the three output combinations have been labelled A, B and C. Point A lies within the boundary drawn by the PPF, point B lies exactly on the PPF and point C is beyond the PPF. So which two are obtainable?

Remember that the PPF illustrates all combinations of production (of two goods) that are possible for an economy with a given set of resources, when these resources are combined in the most efficient manner. Therefore any point that lies within the PPF is technically obtainable, but is inefficient as producing at this level means that there is excess capacity. Output of X or Y could be increased without sacrificing the production of either. Hence there exists no trade off when increasing production from a point within the PPF as doing so requires only the employment of a previously underutilized resource endowment. All points along the PPF represent the combinations of output that are at the limits of the economy's productive capacity, and hence are productively efficient.

So both points A and B can be produced by this economy (with B being the productively efficient choice) leaving point C as a combination of output that is unobtainable.

C is illustrated as being unobtainable as it lies beyond the PPF, indicating that given the economy's current endowment of productive resources it is impossible for that specific combination of output to be obtained.

If the level of resources available within the economy were to increase or the technology with which these resources were combined improved, then we would observe an outward shift of the PPF. This outward shift of the PPF would result in more combinations of X and Y becoming obtainable and productively efficient. If the resource endowment or level of technology were to increase enough then it is possible that point C could come to represent a productively efficient level of output.

follow the links to visit part 1 or part 3 of the PPF series of posts