Understanding Comparative Advantage: Opportunity Cost and the PPF

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At its heart, the theory of comparative advantage is not extremely difficult.  David Ricardo simply discovered that what matters is relative prices and productivity.  Absolute cost is unimportant.

But the implications are staggering.  Every individual, firm, nation, and (probably) not-for-profit organization has a comparative advantage at something.  This must be true due to the laws of algebra, laws which are much more reliable than the laws of economics.

Opportunity Cost

The idea of opportunity cost is central to comparative advantage.  The opportunity cost of any decision is the value of the next-best alternative.  In the case of individuals, it is the value to each person of what they gave up when they made a particular decision.

As individuals we face three important constraints:

  1. Our income, the annual amount we receive from all sources,
  2. Our wealth, the accumulation of past saving, and
  3. Our time, 24 hours per day.

The example I’ll use here is a very simple economy with no money and no financial system.  The sole constraint is time.  Let’s start by assuming each individual can work 12 hours per day.

On a Remote Island in the South Pacific

Robinson Crusoe finds himself stranded.  He is the lone occupant of the island.  He calls the island Zog because he likes that word.

Crusoe needs food and shelter.  Luckily the tropical Pacific waters are teeming with fish.  And there is a great supply of coconuts.  Add to that the vast quantity of bamboo for construction and he’s set. (Since he’s alone on the island clothing is a much lower priority than food and shelter.) Except that he only has 12 hours per day.

For the moment, let’s concentrate on keeping Crusoe alive.  Food is the most important item at the moment.  Ignore all that bamboo and assume he finds a dry, uninhabited cave where he can live.

How Much Food Can Crusoe Harvest?

If he spends all 12 hours fishing, he can catch 18 fish.  If he spends all 12 hours picking coconuts, he can pick 24.  In other words, the cost of one fish is 12 hours/18 fish = 0.75 hours.  And the cost of one coconut is 12 hours/24 coconuts = 0.50 hours.  But the true opportunity cost of one fish is the number of coconuts Crusoe must forego to catch that fish.  Thus the cost of one more fish is

Crusoes cost Understanding Comparative AdvantageMeasuring Cost

Notice that we’ve just calculated the opportunity cost of catching 1 more fish.  It’s 1.5 coconuts.  Therefore, the cost of one more coconut must be

Crusoes cost inverse Understanding Comparative AdvantageThe opportunity cost of gathering 1 more coconut is 0.67 of a fish. (For those who are OCD about arithmetic, technically the cost of 1 more coconut is 2/3 of a fish.)

Crusoe’s Taste and Preferences Are Important

It looks like the cost of coconuts is lower than the cost of fish.  Should Crusoe dine only on coconuts?  Probably not.  His tastes and preferences are important.  Suppose he spends half a day fishing and the other half picking coconuts.  He will have 9 fish and 12 coconuts.  Luckily he’s working pretty hard so he won’t gain weight from this particular diet.

Crusoe can harvest 1.5 fish per hour and 2.0 coconuts per hour.  Using this information we can construct his production possibilities frontier (PPF).  The PPF is a graph that shows the combinations of fish and coconuts Crusoe can harvest in one day.  Here’s Crusoe’s PPF:

Crusoe's PPF Understanding Comparative Advantage

(click for larger image)

Along the PPF

Let’s explore the PPF a bit more.  Suppose Crusoe develops a preference for fish.  Given his time constraint, he can, for example, consume 15 fish and 4 coconuts per day.  He will spend 15 fish per day/1.5 fish per hour = 10 hours per day fishing and 4 coconuts per day/2.0 coconuts per hour = 2 hours per day picking coconuts.

Crusoe develops a taste for fish Understanding Comparative Advantage

(click for larger image)

But after a few weeks, Crusoe is burned out on fish. He decides to increase his coconut intake.  He could, for example, consume 6 fish per day and 16 coconuts per day.  (Exercise: show that he will be able to do this in the allotted 12 hours.)

Crusoe develops a taste for coconuts Understanding Comparative Advantage

(click for larger image)

A Personal Example

An example will help.  I’m writing this article.  I will probably spend about four hours writing, putting together the numerical example, developing charts, and so on.  The cost to me is how much I value whatever I would have been doing had I decided not to write this piece.  In my case, I have a paying contract that I would have worked on.  The cost to me is the value I place on working on that contract.  (In reality, the value is lower than you might think.  (The project is off to a very slow start, so I haven’t really lost much by delaying my work four hours.)

Conclusion

In order to see the benefits of specialization and trade, we need a second person.  Joe Friday parachutes in during the next episode.  Part 2 will describe and discuss absolute advantage.  In Part 3 I will develop the idea of comparative advantage and see how welfare improves with specialization and trade,

 

 

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About Tony Lima

Retired after teaching economics at California State Univ., East Bay (Hayward, CA). Ph.D., economics, Stanford. Also taught MBA finance at the California University of Management and Technology. Occasionally take on a consulting project if it's interesting. Other interests include wine and technology.