a. If Alpha produced 6 pearls and 15 pineapples while Beta produced 30 pearls and 8 pineapples before they decided to trade, how many pearls would each be producing after trade? Assume that the two countries specialize according to their comparative advantage.

A comparative advantage of a country is defined if the country is able to produce a product with the least opportunity cost than its trade partner countries.

So first we calculate the cost of producing each good for each of the countries.

For Alpha:

1 pearls = 15/6 pineapples

1 pearls = 2.5 pineapples

Similarly,

1 pineapple = 6/15 pearls

1 pineapple = 0.4 pearls

So for Alpha, the opportunity cost of producing one pearl is 2.5 pineapple, to produce 1 pineapple, Alpha has to sacrifice 0.4 pearls.

Opportunity cost for Beta:

1 pearls = 8/30 pineapples

1 pearls = 0.27 pineapples

Similarly:

1 pineapple = 30/8 pearls

1 pineapple = 3.75 pearls

So for Beta, the opportunity cost of producing one pearl is 0.27 pineapple, to produce 1 pineapple, Alpha has to sacrifice 3.75 pearls.

It can be seen that the opportunity cost of producing pineapples is least for Alpha, Beta has the lowest opportunity cost for producing pearls. So Alpha will export pineapples while Beta will export pearls.

Thus if both decide to trade produce only that good in which it has the opportunity cost, then Alpha's production of pineapple will be

15 + 2.5 X 6 = 15+15 = 30 pineapple

While Beta's production of pearls will be

30 + 3.75 X 8 = 30 + 30 = 60 pearls.

So Alpha will produce no pearls and Beta will produce 60 pearls, increasing the combined production from 36 pearls.