What is the elasticity of substitution of f(K, L) = KL²?(a) 1/3(b) 1/2(c) 2/3(d) 1(e) 3/2(f) 2Which of the following represents increasing returns to scale?(a) f(K, L) = (K² + L²)¹/2(b) f(K, L) = (K¹/2 + [¹/2)²(c) f(K, L) = (K + L)(d) f(K, L) = (K + L)²Suppose the production function for good q is given by q = (k¹/2+1¹/2)2. Consider thefollowing three statements about this function:I. The function exhibits constant returns to scale.II. The function exhibits diminishing marginal productivities in both inputs.III. The function has a constant rate of technical substitution.Which of these statements is true?(a) All of them(b) None of them(c) I and II, but not III(d) II and III, but not I

Answered: What is the elasticity of substitution…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.7P

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What is the elasticity of substitution of f(K, L) = KL²?
(a) 1/3
(b) 1/2
(c) 2/3
(d) 1
(e) 3/2
(f) 2
Which of the following represents increasing returns to scale?
(a) f(K, L) = (K² + L²)¹/2
(b) f(K, L) = (K¹/2 + [¹/2)²
(c) f(K, L) = (K + L)
(d) f(K, L) = (K + L)²
Suppose the production function for good q is given by q = (k¹/2+1¹/2)2. Consider the
following three statements about this function:
I. The function exhibits constant returns to scale.
II. The function exhibits diminishing marginal productivities in both inputs.
III. The function has a constant rate of technical substitution.
Which of these statements is true?
(a) All of them
(b) None of them
(c) I and II, but not III
(d) II and III, but not I

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The elasticity of substitution measures the percentage change in the capital-labor ratio due to a one percent change in the marginal rate of substitution. In other words, it depicts how easy it is for the firm to substitute one input with the other keeping the output constant.

Elasticity of substitution = percentage change in (K/L) / percentage change in MRTS

Elasticity of substitution = dln(K/L) / dlnMRTS

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