2 marks, −0.667MicroeconomicsProduction and returns to scaleProduction functions and the elasticity of substitutionHardabout 2 min

IIT JAM 2022 Question 23: Production and returns to scale

Let a production function be $\log Q = \dfrac{\beta}{\alpha}\log(L^{\alpha} + K^{\alpha})$ , where $\alpha \in (-\infty, 1] - \{0\}$ and $\beta > 0$ . Identify the statement that is NOT correct.

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Answer and worked solution

Answer: MTA

In the exam this question was dropped and every candidate received the marks.

For context: $Q = (L^{\alpha} + K^{\alpha})^{\beta/\alpha}$ is homogeneous of degree $\beta$ , so returns to scale are governed by $\beta$ (statement (B) is correct), and the elasticity of substitution is $\dfrac{1}{1-\alpha}$ (statement (C) is correct). Statement (D) with $\dfrac{1}{1-\beta}$ is wrong, but statement (A) is also defensibly wrong because the degree of homogeneity is $\beta$ itself, not $\beta/\alpha$ . With two options arguably not correct, a single-answer MCQ is ill-posed, which is why every attempt was credited.

Plain-text version

Let a production function be log Q = β/αlog (L^α + K^α), where α ∈ (-∞, 1] - {0} and β > 0. Identify the statement that is NOT correct. (A) The ratio β/α helps in identification of returns to scale factors. (B) For β > 1 the function exhibits increasing returns to scale, and for β < 1 decreasing returns to scale. (C) The elasticity of substitution is 1/(1-α). (D) The elasticity of substitution is 1/(1-β).

Also written as: Let a production function be log Q = beta/alphalog (L^(alpha) + K^(alpha)), where alpha in (- inf, 1] - {0} and beta > 0. Identify the statement that is NOT correct.

Production and returns to scale has come up 92 times in 6 exams since 2007.

What this question tests

This question is on Production functions and the elasticity of substitution, part of Production and returns to scale in Microeconomics.

Cobb-Douglas, CES and fixed-proportions technologies, and how easily inputs substitute.

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