Question

Match List-I with List-II \[\begin{array}{|c|c|} \hline \textbf{Types of Production Functions} & \textbf{Their Functional Forms} \\ \hline \text{(A) Translog Production Function} & \text{(I) \( q = \prod_{i=1}^{n} x_i^{a_i} \)} \\ \hline \text{(B) Generalised Leontief Production Function} & \text{(II) \( q = \sum_{i=1}^{n} a_i x_i^{\rho}, \ \rho \leq 1 \)} \\ \hline \text{(C) Cobb Douglas Production Function} & \text{(III) \( q = \sum_{i=1}^{n} a_{ij} x_i x_j \), where \( a_{ij} = a_{ji} \)} \\ \hline \text{(D) Constant Elasticity of Substitution Production Function} & \text{(IV) \( q = a_0 + \sum_{i=1}^{n} a_i \ln x_i + 0.5 \sum_{i=1}^n \ln x_i \)} \\ \hline \end{array}\] Choose the correct answer from the options given below:

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

Hint:

The Cobb-Douglas production function is a popular form where output is a product of powers of inputs, while the Leontief function assumes fixed input coefficients.

Answer 1

The Correct Option is B

Step 1: Understanding the production functions and their forms.
- **Translog Production Function (A):** This function allows for flexibility in functional forms. Its functional form is **\( q = \prod_{i=1}^{n} x_i^{a_i} \)**. This corresponds to **(I)** in List-II.
- **Generalised Leontief Production Function (B):** This production function is characterized by a linear combination of input quantities raised to a power. Its form is **\( q = \sum_{i=1}^{n} a_i x_i^{\rho} \), where \( \rho \leq 1 \)**. This corresponds to **(II)** in List-II.
- **Cobb Douglas Production Function (C):** This is a widely used production function in economics. Its functional form is **\( q = \sum_{i=1}^{n} a_{ij} x_i x_j \), where \( a_{ij} = a_{ji} \)**. This corresponds to **(III)** in List-II.
- **Constant Elasticity of Substitution Production Function (D):** This function expresses the relationship between inputs and outputs in terms of elasticity. Its form is **\( q = a_0 + \sum_{i=1}^{n} a_i \ln x_i + 0.5 \sum_{i=1}^n \ln x_i \)**. This corresponds to **(IV)** in List-II.

Step 2: Conclusion.
The correct answer is **(A) - (I), (B) - (II), (C) - (III), (D) - (IV)**.