Question

Match List-I with List-II
List-I (Terms/relationship/principles, etc.):
(A) Factor -factor relationship
(B) Optimum enterprise combination
(C) Product-product relationship
(D) Least cost combination
List-II (Algebraic forms, etc.):
(I) $\Delta X_1 \Delta / X_2 = P_{X_2} / P_{X_1}$}
(II) $Y_1 = f(Y_2, X^0)$ or $Y_2 = f(Y_1, X^0)$
(III) $\Delta Y_1 / \Delta Y_2 = P_{Y_2} / P_{Y_1}$}
(IV) $X_1 = f(X_2, Y^0)$ or $X_2 = f(X_1, Y^0)$
Choose the correct answer from the options given below:

• (A) - (II), (B) - (III), (C) - (IV), (D) - (I)
• (A) - (III), (B) - (I), (C) - (IV), (D) - (II)
• (A) - (IV), (B) - (III), (C) - (II), (D) - (I)
• (A) - (IV), (B) - (II), (C) - (I), (D) - (III)

Hint:

"Factor-factor" refers to input substitution (only $X$ variables vary, with constant $Y^0$), while "Product-product" refers to output allocation (only $Y$ variables vary, with constant $X^0$).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
These optimization rules help firms determine the most cost-effective input combinations and the most profitable output combinations.
- Inputs are represented by $X$, and outputs are represented by $Y$.
- Constant factors are indicated by a superscript zero ($0$).
Detailed Explanation:
Let us match the economic concepts with their algebraic equations:
- (A) Factor-factor relationship: This describes input substitution ($X_1$ and $X_2$) to produce a fixed output ($Y^0$), represented by $X_1 = f(X_2, Y^0)$ or $X_2 = f(X_1, Y^0)$. This matches with (IV).
- (B) Optimum enterprise combination: This determines the profit-maximizing output levels where the marginal rate of product substitution equals the ratio of product prices: $\frac{\Delta Y_1}{\Delta Y_2} = \frac{P_{Y_2}}{P_{Y_1}}$. This matches with (III).
- (C) Product-product relationship: This describes producing multiple outputs ($Y_1$ and $Y_2$) with a fixed input ($X^0$), represented by $Y_1 = f(Y_2, X^0)$ or $Y_2 = f(Y_1, X^0)$. This matches with (II).
- (D) Least cost combination: This determines the cost-minimizing input mix where the marginal rate of technical substitution equals the ratio of input prices: $\frac{\Delta X_1}{\Delta X_2} = \frac{P_{X_2}}{P_{X_1}}$. This matches with (I).
This gives the sequence:
\[ \text{(A) - (IV), (B) - (III), (C) - (II), (D) - (I)} \]

Step 2: Final Answer:
The matched sequence corresponds to Option (C).