In microeconomics, which option correctly calculates the opportunity cost of producing 1 more unit of good X in terms of good Y (i.e., the amount of Y forgone)?

• A. The marginal rate of transformation (MRT), computed as the absolute value of the slope of the PPF: $\left|\frac{dY}{dX}\right|$
• B. The opportunity cost equals the sum of outputs of X and Y: $X+Y$
• C. The opportunity cost equals the total output of X divided by total output of Y: $\frac{X}{Y}$
• D. The opportunity cost equals the marginal product of X: $MP{X}_{\mathrm{}}$

Answer: (A)

Verified step by step guidance

1. Understand that the opportunity cost of producing one more unit of good X in terms of good Y is the amount of good Y that must be given up to produce that additional unit of X.
2. Recognize that the Production Possibility Frontier (PPF) shows the maximum possible combinations of goods X and Y that can be produced given resources and technology.
3. Identify that the slope of the PPF at any point represents the rate at which one good must be sacrificed to produce more of the other good. This slope is called the Marginal Rate of Transformation (MRT).
4. Express the MRT mathematically as the absolute value of the derivative of Y with respect to X, which is \(\left| \frac{dY}{dX} \right|\). This gives the opportunity cost of producing one more unit of X in terms of units of Y forgone.
5. Conclude that the opportunity cost is not simply the sum or ratio of total outputs or the marginal product of X, but specifically the MRT derived from the PPF's slope.