Question

Given below are two statements:
Statement (I): The expression $\Delta X_1 / \Delta X_2$ is termed as the marginal rate of substitution (MRS) of $X_1$ for $X_2$.
Statement (II): If $\Delta Y_1 / \Delta Y_2 < P_{Y2}/P_{Y1}$, more of $Y_2$ should be produced at the expense of $Y_1$.}
In light of the above statements, choose the most appropriate answer from the options given below:

• A. Both Statement (I) and Statement (II) are true.
• B. Both Statement (I) and Statement (II) are false.
• C. Statement (I) is true but Statement (II) is false.
• D. Statement (I) is false but Statement (II) is true.

Hint:

To remember the optimal product combination rule: if the substitution rate of $Y_1$ for $Y_2$ is less than their price ratio ($\Delta Y_1/\Delta Y_2 < P_{Y2}/P_{Y1}$), always shift production towards $Y_2$ to increase total revenue.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This question evaluates the definitions of technical substitution in input relationships (factor-factor) and enterprise choice optimization in product-product relationships.

Step 3: Detailed Explanation:
Let us evaluate each statement:
- Statement (I): The marginal rate of technical substitution (MRTS or MRS) of $X_1$ for $X_2$ represents the quantity of input $X_2$ that can be replaced by one unit of input $X_1$ without changing the total output level. Mathematically, it is defined as: \[ MRS_{X1,X2} = -\frac{\Delta X_2}{\Delta X_1} \] The expression given in the statement, $\Delta X_1 / \Delta X_2$, represents the MRS of $X_2$ for $X_1$. Thus, Statement (I) is incorrect.
- Statement (II): In product-product relationships (enterprise choice), the optimum combination of products $Y_1$ and $Y_2$ is achieved where the marginal rate of product substitution (MRPS) of $Y_1$ for $Y_2$ equals their inverse price ratio: \[ \frac{\Delta Y_1}{\Delta Y_2} = \frac{P_{Y2}}{P_{Y1}} \] If $\Delta Y_1 / \Delta Y_2 < P_{Y2}/P_{Y1}$, it indicates that the rate at which $Y_1$ must be sacrificed to produce an additional unit of $Y_2$ is lower than the relative market price of $Y_2$ to $Y_1$.
This means the revenue gained from producing more $Y_2$ exceeds the revenue lost from reducing $Y_1$. Therefore, to maximize profits, the producer should shift resources to produce more $Y_2$ at the expense of $Y_1$. Thus, Statement (II) is correct.

Step 4: Final Answer:
Statement (I) is false but Statement (II) is true, corresponding to option (D).