Suppose you are stranded on an island. Luckily, this island is rich in clams and mangos. If you devote all of your time to harvesting clams, you can get 100 clams in a week. If you us all of your time to collect mangos, you can find 200 mangos in a week. Assume it is possible to collect fractional amounts of both goods and draw a sketch of your production possibility frontier for a week. (Place mangos on the x-axis and clams on the y-axis.)
Calculate the opportunity cost of each good. (Use a straight-line PPF for this question because the opportunity cost is constant - it doesn't change)

a. See the attached photo for the sketched PPF.

b. We have:

Opportunity cost of a clam = 2 mangos

Opportunity cost of a mango = 0.5 clam

Explanation:

a. Assume it is possible to collect fractional amounts of both goods and draw a sketch of your production possibility frontier for a week. (Place mangos on the x-axis and clams on the y-axis.)

Note: See the attached photo for the sketched PPF.

In the attached PPF, Point A indicates when you use all of your time to collect mangos and find 200 mangos in a week; while Point B shows when you devote all of your time to harvesting clams and can get 100 clams in a week. Since it assumed that it is possible to collect fractional amounts of both goods, Point C indicates when you use half of your time to find 100 mangos and harvest 50 clams in a week.

b. Calculate the opportunity cost of each good.

If you devote all of your time to harvesting clams or to collect mangos, we have:

100 clams = 200 mangos ................. (1)

Dividing both sided of equation (1) by 100, we have:

Opportunity cost of a clam = 2 mangos

Dividing both sided of equation (1) by 200, we have:

Opportunity cost of a mango = 1/2 clam, or 0.5 clam

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