A country produces two goods X and Y. Its production possibility frontier is given by the equation. Y = 100…

Question

A country produces two goods X and Y. Its production possibility frontier is given by the equation. Y = 100 − 20X What is the opportunity cost of producing one more unit of X?

ScanSolve AI Tutor · Accepted Answer

The production possibility frontier (PPF) equation is given by:

Y = 100 - 20X

Understand opportunity cost.
The opportunity cost of producing one more unit of good X is the amount of good Y that must be sacrificed. This is represented by the absolute value of the slope of the PPF.
Find the slope of the PPF.
The equation is already in the form $Y = mX + c$ , where $m$ is the slope.
In this case, the slope is the coefficient of $X$ , which is $-20$ .
So, $\frac{dY}{dX} = -20$ .
Calculate the opportunity cost.
The opportunity cost of producing one more unit of X is the absolute value of the slope.
$\text{Opportunity Cost} = \left| \frac{dY}{dX} \right| = |-20| = 20$
This means that for every additional unit of X produced, 20 units of Y must be given up. Therefore, the opportunity cost is 20 units of Y.
Match with the given options.
Comparing this result with the given options:
A 20X
B 0.05X
C 20Y
D 0.05Y

The correct option is C.

The final answer is $\boxed{\text{C}}$

A country produces two goods X and Y. Its production possibility frontier is given by the equation. Y = 100 − 20X What is the opportunity cost of producing one more unit of X?

Answer

Step-by-step solution

Understand opportunity cost.

Find the slope of the PPF.

Calculate the opportunity cost.

Match with the given options.

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