On a production possibilities frontier, 500 kilograms of apples and 1200 kilograms of bananas can be produced while, at another point on the same frontier, 300 kilograms of apples and 1300 kilograms of bananas can be produced. Between these points, what is the opportunity cost of producing a kilogram of bananas?

Question

Quizplus · Accepted Answer

To calculate opportunity cost, we need to identify how much of one good we must give up to produce more of the other good.

Between the two points on the production possibilities frontier given, we can see that to produce an additional kilogram of bananas, we must give up a certain amount of apples.

At the first point (500 apples and 1200 bananas), if we increase banana production by 1 kilogram, we must decrease apple production by 100/3 (since the slope of the production possibilities frontier is -300/500 = -3/5, meaning we give up 3/5 of an apple to produce 1 banana). Therefore, the opportunity cost of producing 1 kilogram of bananas at this point is 100/3 apples per kilogram of bananas.

At the second point (300 apples and 1300 bananas), if we increase banana production by 1 kilogram, we must decrease apple production by 200 (since the slope of the production possibilities frontier is -1000/300 = -10/3, meaning we give up 10/3 apples to produce 1 banana). Therefore, the opportunity cost of producing 1 kilogram of bananas at this point is 200 apples per kilogram of bananas.

Since the opportunity cost of producing 1 kilogram of bananas is higher at the second point than at the first point, we must choose the point where the opportunity cost of producing bananas is lower. Therefore, the answer is D) 2 kilograms of apples, which corresponds to the first point where the opportunity cost of producing 1 kilogram of bananas is 100/3 apples.

On a Production Possibilities Frontier, 500 Kilograms of Apples and 1200