If a Production Function is given as Q(x,y) = Axay, where (a + b) = 2, the function is said to display:

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:

Answer 1

A production function exhibits increasing returns to scale when the sum of its input exponents exceeds 1. This means a proportional increase in all inputs yields a greater proportional increase in output. For Q(x, y) = Ax^ay^b, with a + b = 2 (which is>1), this condition is met.

In simpler terms, doubling the inputs results in more than double the output. Consequently, the correct answer is (c) Increasing returns to scale.

If a Production Function is given as Q(x,y) = Axay, where (a + b) = 2, the function is said to display:

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The Correct Option is C

Solution and Explanation

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