Question

Match List-I with List-II

Choose the correct answer from the options given below:

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

Hint:

Scale multiplier rules:
Output multiplier \(= t \implies\) Constant Returns to Scale.
Output multiplier \(> t \implies\) Increasing Returns to Scale.
Output multiplier \(< t \implies\) Decreasing Returns to Scale.

Answer 1

The Correct Option is D

Concept:
In production theory, returns to scale examine how output responds when all factor inputs are increased proportionally by a positive scalar factor \(t > 1\).

Step 1: Matching Each Mathematical Expression:
- (A) \(q = f(y_1, y_2)\): This mathematical notation defines a general production function showing output \(q\) as a function of factor inputs \(y_1\) and \(y_2\). Thus, (A) matches (III).
- (B) \(f(t y_1, t y_2) = t \cdot f(y_1, y_2)\): When scaling all inputs by \(t\) increases output by exactly the factor \(t\), the technology exhibits Constant Returns to Scale (CRS). Thus, (B) matches (IV).
- (C) \(f(t y_1, t y_2) > t \cdot f(y_1, y_2)\): When output increases by a proportion greater than \(t\), the technology exhibits Increasing Returns to Scale (IRS). Thus, (C) matches (I).
- (D) \(f(t y_1, t y_2) < t \cdot f(y_1, y_2)\): When output increases by a proportion less than \(t\), the technology exhibits Decreasing Returns to Scale (DRS). Thus, (D) matches (II).

Step 2: Verifying the Matching Set:
The resulting sequence of pairings is: \[ \text{(A)-(III), (B)-(IV), (C)-(I), (D)-(II)} \] Final Answer:
This correspondence uniquely matches option (D).