Production Possibility  Frontiers



So much of economics is about trade-offs: every choice made by an individual, a family, a company, or a government involves making a choice between alternatives.  How much of particular types of goods, such as cars, computers, bell peppers, etc, that a country can produce is the result of choices made by society -- often at the individual and firm level -- about how much of its scarce resources to allocate to producing each of the goods.


  Much of this course studies how markets help with this allocation, that is, to help coordinate all of the individual choices made by consumers and firms.  Before doing that, we first introduce the idea of trade-offs faced by countries through the use of the Production Possibility Frontier.

The interactive Production Possibility Frontier is at the bottom of the page.


Production Possibilities and Specialization

Goods are produced in economies through a production process that takes inputs and transforms them into output, i.e. goods.  There are many different types of goods, for example cars and bell peppers, and there are many different types of inputs, for example labor and machines.  Different goods are produced with varying amounts of each type of input.  Producing cars requires more machines than producing bell peppers, but agriculture is generally more labor intensive.  How much of each good that can be produced depends on the amount of each input that one has available.  

The lecture video titled "Gains From Trade" presented a simple example drawn from the movie Castaway.



In the example, Tom at first is the only one on the island and divides his time between catching fish and picking coconuts.  It was assumed that his labor meant that he could catch 6 fish/hour or 12 coconuts/hour.  In an 8 hour day that means he could catch 48 fish per day if all he did was fish, or 96 coconuts per day if all he did was collect coconuts, or some combination of fish and coconuts.  How much he fished versus collected coconuts depended on how much more he enjoyed fish to coconuts.


Choosing a simple example where there is a single input -- Tom's labor -- and two goods, allows us to come up with a graph that reflects the trade-offs faced by Tom.  This graph is called the Production Possibility Frontier.  

From the Production Possibility Frontier -- or in short hand the PPF -- we can also demonstrate another important concept: Opportunity Cost.


The Figure above is the PPF for the Castaway island -- consisting of only Tom at the moment.  The horizontal intercept is (48,0) which coincides with Tom only catching Fish, which means he can catch 48 fish a day.  Conversely, the vertical intercept is (0,96), which occurs when Tom only collects coconuts.  The bold orange line is the PPF, it gives all of the possible combinations of coconuts and fish that Tom can produce.  In fact, the shaded region are combinations of coconuts and fish that are feasible, but would only occur if Tom wasn't using all of his inputs, that is his 8 hour work day.  So Tom would always choose to be on the orange line, i.e. the PPF.  Outside the shaded region is the infeasible region.

What trade-offs does Tom face?  Tom has to decide how to allocate his 8 hour workday between fishing and collecting coconuts.  To make that decision wisely, Tom needs to know his Opportunity Costs.  

An opportunity cost is what is given up to acquire something.  In this example, there are only two goods, so the opportunity cost to Tom of acquiring another fish is the coconuts that Tom could have collected during that time he spent fishing.  Conversely, the opportunity cost to Tom of collecting an additional coconut is the amount of fish he could have caught during that time.  In this example from the lecture video, to get 1 additional fish his opportunity cost is 2 coconuts (recall in 1 hour, 6 fish or 12 coconuts, i.e. he is twice as productive collecting coconuts).  On the other hand, the opportunity cost of an additional coconut is 1/2 fish.  

Now continuing the example as in the lecture video, suppose that the Castaway island has another habitant in addition to Tom, call him Rob.  Rob has a different skill set than Rob and can catch 2 fish in an hour or collect 8 coconuts.  In this case, Tom has an Absolute Advantage since he can produce more of both fish and coconuts in an hour.  Does that mean that Tom should just produce as if he was the only person on the island?  Or, are there some gains from trade that would make both Rob and Tom better off by specializing in either fish or coconut production?  To see this, we can plot the PPF for the island as a whole.


The lower line (with the darker shading) is the PPF from above, i.e. it is the Tom's production possibilities without trading with Rob.  The outer line is the PPF for the island.  The horizontal intercept (64,0) assumes that both Tom and Rob only catch fish (=48+16), while the vertical intercept (0,160) occurs when they both only collect coconuts (=96+64).  The lightly shaded region then represents gains from trade.  Taking the example trade from the lecture video they would both be better off if they agreed to the following:

  • Rob only produces coconuts (=64 coconuts/day)
  • Tom divides between fish and coconuts, spending 6 hours fishing (=36 fish) and 2 hours collecting coconuts (=24 coconuts).
  • Rob gives Tom 28 coconuts in exchange for 10 fish.

With this trade, Tom ends up with 52 coconuts (24 he collects+28 from Rob) and 26 fish (the 36 he catches -10 he gives to Rob).  That is the blue dot in the figure above.  Notice that blue dot is beyond Tom's PPF in the gains from trade region.  So, even though Tom has an absolute advantage in producing both coconuts and fish, he can do better by specializing his time into catching fish and then trading with Rob.

This example illustrates the important idea of Comparative Advantage , that is the ability to produce at a lower opportunity cost than another producer.  In this example, Rob's opportunity cost of catching fish is 4 (recall he can catch 2 fish or collect 8 coconuts in an hour), while his opportunity cost of collecting coconuts is 1/4.  Tom's opportunity cost for catching fish is 2 and for coconuts it is 1/2.  So Tom has a lower opportunity cost in fishing, so he specializes his time in catching fish, while Rob has a lower opportunity cost in collecting coconuts, which is how he will specialize.  As the figure illustrates  above, by specializing in their comparative advantage and trading with each other, producers can be made better off.  Comparative advantage is the bedrock for trade, between firms, households and even international trade between countries.  It is one of the "big ideas" in economics, and a concept that we will return throughout the course.

Other Shapes for the PPF

In the examples above, the PPF is a straight line.  The slope of the PPF, at a given point, reflects the opportunity cost at that point.  When the PPF is a straight line, it means that the slope is the same at every point, i.e. the opportunity cost is the same for the economy regardless of whether it mostly produces fish or mostly produces coconuts.

In reality, it is unlikely that the PPF is a straight-line as there are very good reasons to think that the opportunity cost of producing goods depends on how much of a good is being produced.  For example, suppose an economy consists of two types of workers, computer programmers and celebrity chefs.  If society wants more and more computer software, such as smart phone app's, it will eventually run out of computer programmers and need to start hiring celebrity chefs to write computer code.  But, these celebrity chefs are not good at programming and so there will be large drop off in celebrity chef restaurants without much gain in software -- i.e. the opportunity cost becomes larger for producing software as the economy produces more software.  Conversely, an economy that wants many celebrity restaurants eventually has to hire computer programmers, who are terrible cooks.  So the opportunity cost rises as more celebrity chef restaurants are produced.  This makes the PPF take on a  "bowed-out" (concave in math-speak) appearance:

This, of course, is the picture from the top of the page.  Imagine that good A is computer software and good B is celebrity chefs.  As the economy goes to producing all computer software eventually there is no gain in software but a very steep drop in celebrity chef restaurants.  It is that increasing opportunity cost which gives the PPF a "bowed-out" appearance.

Interactive Practice with Production Possibility Frontiers

Now, practice what you've learned by playing around with the interactive production possibility frontier at the bottom of the page.  The best way to practice would be to also draw what happens in the interactive graph on a piece of a paper.  This way you can practice for the midterm exam.  

To test your understanding, use the interactive graph to answer the following self-check questions.

Self-check Quiz

Suppose that there is an increase in technology that affects the production of both goods equally. What happens to the production function?     Hint  |  Answer
shifts in
rotates out along the Good A axis
rotates out along the Good B axis
shifts out

Hint: try changing the maximum production of both goods equally..

Self-check Quiz

Suppose that there is a natural disaster that only affects firms producing Good A. What happens to the production function?     Hint  |  Answer
shifts in
rotates in along the Good A axis
rotates in along the Good B axis
shifts out

Hint: try changing the maximum production of both goods equally..

Self-check Quiz

In the above example, what do you think will happen to this country's trade in good A?     Hint  |  Answer
no change
lead to a balance of payments crisis.

Hint: try changing the maximum production of both goods equally..