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

Question

Quizplus · Accepted Answer

To calculate the opportunity cost of going from 1 unit of X to 2 units of X, we need to look at the amount of Y that is given up. We can do this by finding the slope of the production possibilities frontier at the point where 1 unit of X is being produced.

The equation of the production possibilities frontier can be rewritten as Y = -9/12X + 81/12. Taking the derivative of this equation with respect to X gives the slope of the frontier, which is -9/12.

This means that for every 1 unit increase in X, we give up 9/12 units of Y. Going from 1 unit of X to 2 units of X means a 1 unit increase in X, so the opportunity cost is:

(9/12 units of Y given up) x (1 unit increase in X) = 9/12 units of Y

Simplifying, we get 3/4 units of Y. Therefore, the answer is C, which represents the difference in the amount of Y produced between 1 unit and 2 units of X, or 11ea6919_dd31_d1fe_80d0_7b8846f757b9_TB5165_11 - 11ea6919_dd31_d1ff_80d0_5bfc3561de94_TB5165_11 = 3/4 units of Y.

Suppose a Production Possibilities Frontier Can Be Expressed as 9X2

Suppose a Production Possibilities Frontier Can Be Expressed as 9X²