Suppose a production possibilities frontier can be expressed as 9X² + Y² = 81 what is the opportunity cost of going from 2 units of X to 3 units of X (in terms of units of Y)? C) 1 D) 0

Question

Quizplus · Accepted Answer

To find the opportunity cost of going from 2 units of X to 3 units of X, we need to calculate the change in Y. We can rewrite the production possibilities frontier as Y = (81-9X)/12X, which gives us the equation for the slope of the PPF: dY/dX = -9/12 + 81/12X^2. 
If we plug in X=2, we get dY/dX = 3/4, which means that for every 1 unit increase in X, we give up 3/4 units of Y. Therefore, to go from 2 units of X to 3 units of X, we give up 3/4 units of Y per unit of X, for a total opportunity cost of 3/4 * 1 = 0.75 units of Y. Option B is the closest to this value.

Suppose a Production Possibilities Frontier Can Be Expressed as 9X2

Suppose a Production Possibilities Frontier Can Be Expressed as 9X²