Question

Match the following:

• A. A-I, B-II, C-III, D-IV
• B. A-III, B-I, C-IV, D-II
• C. A-I, B-II, C-IV, D-III
• D. A-III, B-IV, C-I, D-II

Hint:

Returns to scale shortcut: \[ = \text{ means constant},\quad > \text{ means increasing},\quad < \text{ means decreasing} \]

Answer 1

The Correct Option is D

Concept:
A production function shows the relationship between inputs and output. If both inputs are increased by the same proportion \(t\), then output may increase by the same, more than the same, or less than the same proportion.

Step 1: Match Production Function.
A production function with two inputs is written as: \[ f(x_1,x_2) \] So: \[ A \rightarrow III \]

Step 2: Match Constant Returns to Scale.
Constant returns to scale means when inputs are increased \(t\) times, output also increases exactly \(t\) times. So: \[ f(tx_1,tx_2)=t f(x_1,x_2) \] Thus: \[ B \rightarrow IV \]

Step 3: Match Increasing Returns to Scale.
Increasing returns to scale means output increases more than proportionately. So: \[ f(tx_1,tx_2)>t f(x_1,x_2) \] Thus: \[ C \rightarrow I \]

Step 4: Match Decreasing Returns to Scale.
Decreasing returns to scale means output increases less than proportionately. So: \[ f(tx_1,tx_2)<t f(x_1,x_2) \] Thus: \[ D \rightarrow II \]

Step 5: Final matching.
The correct matching is: \[ A-III,\quad B-IV,\quad C-I,\quad D-II \] Hence: \[ \boxed{\text{(D)}} \]