Question

1. Anne and Nancy are stranded on a deserted island where they survive by catching fish and picking mangoes. In one day, Anne can catch 4 fish or pick 12 mangoes and Nancy can catch 8 fish or pick 8 mangoes. When they are separated each chooses to spend half of their day on each good.

a. Draw the PPF for both Anne and Nancy combined. Label the slopes and intercepts and include a point representing the combination of fish and mangoes that they consume (combined) when they separated. Label this point “X.”

b. If Anne and Nancy are NOT separated and want to organize their labor in the most efficient way, and they want to keep getting the same number of fish as when they were separated, how many mangoes can they get?

Answer 1

a. The maximum amount of fish consumed by both Anne and Nancy is 4 + 8 = 12

The maximum amount of mangoes consumed by both Anne and Nancy is 12 + 8 = 20 mangoes

The production possibility frontier along with a consumption point is shown in figure.

b. If Anne and Nancy join together and want to maximize their combined production, they must specialize in the production of the good in which they have a comparative advantage that is good for which they have a lower opportunity cost in terms of the other good. The opportunity cost of producing one fish is 3 mangoes for Anne and 1 mango for Nancy. Therefore, Nancy has a comparative advantage in the production of fish and Anne has a comparative advantage in the production of mangoes. Suppose earlier Anne  had 2 fishes and Nancy had 3 fishes. Now Nacy produces the 5 fishes and anne produces 2×3 + 6 = 12 mangoes. So they consume 5 fishes and 12 mangoes together.