Say there are 2 countries:  Fredonia and Frodoland.
The both produce two products: consumer goods (butter) and military goods (guns).
Here are the (linear) p.p. tables for each one.

Fredonia:
 

	H	I	J	K
butter	45	30	15	0
guns	0	50	100	150

Frodoland:
 

	M	N	O	P
butter	90	60	30	0
guns	0	50	100	150

Initially both countries are self sufficient.  Fredonia is producing combo J and Frodoland is producing combo N.

Questions:
1. Is this a case where comparative advantage applies? Yes or No and why?
2. If the countries each specialize, will total output ("world output") increase?
3. What are the minimum requirements which Fredonia would need in a trading deal  (i.e., so much of one for some much of the other).  What are the minimum requirements for Frodoland?
4. Can you figure out trade terms ( a trading ratio) which would be good for both countries at the same time?  (how about 5 guns for 2 butter?)
5. Try to demonstrate that both countries can move outside of their production possibilities curves with an appropriate trading deal.

for answers: scroll down this page
 
 
 
 
 
 

answers:
1. yes -- Frodoland is better at both, but "more better" at butter, Fredonia is worse at both, but less worse in guns production.

2.yes -- without specialization, world butter production is 15+60=75
and world gun production is 100+50 =150

Then, after specialization butter production is 90 and gun production is 150.  This output is greater than before (it was 75 butter and 150 guns).  If the countries insist on an increase in guns as well as butter, Frodoland  will have to make a small amount of guns, leaving total butter at just short of 90 and total guns at more than 150 (an improvement in both areas).

3. Roughly speaking, Fredonia needs to get about 1/3 of a butter for each gun it gives up.
And, Frodoland needs to get a little less than 2 guns for each butter. We could also put this another way: they would give a little more than 1/2 a butter for each gun they got in exchange..

4.  The trade terms of 2 butter for 5 guns is acceptable to both countries, and it lies, sort of, mid-way between the requirements of the two countries.

5.  Using the pattern of 2 for 5, lets try a deal where 20 butter are exchanged for 50 guns (obviously the same ratio as 2 for  5).  Fredonia has all guns (150), and when they trade away 50 of them they have 100 guns left.  The get 20 butter. So, the combination 20 butter with 100 guns beats their original combination "J".

Frodoland was making only butter (90).  They give up 20 of the butter, leaving 70 for themselves. They get 50 guns back.  Their ending combination of 70 butter and 50 guns is better than their original combination "N".

Comment: don't be tempted to add each country's guns and butter together to see who "wins".  Actually the total is 120 for each of them.  It is not a meaningful comparison,  however.  I think you will agree that Frodoland has the better combination, which is not surprising since they are the superior producer.  If we are looking for winners, we have to say that both win because they both move outside of their production possibilities curves.