Calculating the opportunity cost in a gains from trade example - FreeEconHelp.com, Learning Economics... Solved!

## 6/15/11

Look at table 1 again,
 Mexico U.S. Papayas Apples Papayas Apples 0 12 0 63 8 9 7 42 16 6 14 21 24 0 21 0

you can see that Mexico can either produce 24 papayas in one day, OR 12 apples.  Imagine they were producing all papayas, in order to make 1 apple, they would need to give up 2 papayas.  How do I know this?  You can either refer to table 2 to see the amount of time it takes to make an apple (2 hours, which would require giving up 2 papayas), or you could divide the maximum amount of papayas they are able to produce by the maximum number of apples they are able to produce.  Here it would be 24/12 or 2.  So the opportunity cost of an apple is 2.  Here is a mathematical example, since the opportunity cost is a ratio, we need to solve for a ratio, and we want to solve it so that the opportunity cost for an apple is in terms of a papaya.

Begin with what the maximum amount of each good is:

12 apples = 24 papayas, now add in the opportunity cost so:

The opportunity cost of 12 apples  = 24 papayas, now divide both sides by 12 so:

The opportunity cost 1 apple = 24 papayas/12 = 2 papayas.

So the opportunity cost of 1 apple is 2 papayas.  Do this again for papayas.

The opportunity cost of 24 papayas = 12 apples.

The opportunity cost of 1 papaya = 12 apples/24.

The opportunity cost of 1 papaya is .5 apples.

Notice anything?  You are right, the opportunity costs of the different goods are inverses of each other, meaning that if the opportunity cost of one good is 2, the opportunity cost for the other is ½.  If it is 3 for one, it is 1/3 for the other.  If 5 for one, 1/5 for the other and so on.

So now we have the opportunity costs for Mexico, we need to find out the opportunity costs of the goods for the US.  Using the method described above we get:

The opportunity cost of 63 apples = 21 papayas.
The opportunity cost of 1 apple = 21 papayas/63.

The opportunity cost of 1 apple is 1/3 papaya, so the US has to give up 1/3 of a papaya in order to get an apple.  Because of the inverse rule, we know that the opportunity cost of a papaya is 3 apples.

We can also solve for opportunity cost by looking at the slopes of the PPFs for each of the countries.