Suppose goods X and Y are produced along a production possibilities frontier 4X² + Y² = 500 and they are perfect substitutes such that U = X + Y.The slope of the production possibilities frontier is .How much X should be produced?

Question

Quizplus · Accepted Answer

Since the goods are perfect substitutes and the utility function is U = X + Y, it means that as long as the sum of X and Y equals a certain value, the utility is constant. Therefore, the optimal choice would be at the midpoint of the production possibilities frontier, where X = Y.

The midpoint of the production possibilities frontier can be calculated as follows:

(1/2)(500) = 4X + Y 
250 = 5X 
X = 50

Since we want to produce half of X and half of Y, the optimal production of X is 5.

Suppose Goods X and Y Are Produced Along a Production