Explanation Given information: The equation is x = − 5 4 p + 20 and the value of p is 10 . Definition used: (1) If the value of E ( p ) > 1 then the demand is said to be elastic. (2) If the value of E ( p ) = 1 then the demand is said to be unitary. (3) If the value of E ( p ) < 1 then the demand is said to inelastic. Formula used: The elasticity of demand is given by the relation, E ( p ) = − p f ′ ( p ) f ( p ) (1) Calculation: Rewrite the given equation as a function of p , x = f ( p ) = − 5 4 p + 20 Differentiate the function, f ( p ) , f ′ ( p ) = − 5 4 ( ∵ d d x ( x ) n = n x n − 1 ) Substitute − 5 4 p + 20 for f ( p ) and − 5 4 for f ′ ( p ) in equation (1) to find the demand of elasticity, E ( p )

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 3.4, Problem 26E

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Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

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The elasticity of demand and check whether the demand is elastic, unitary or inelastic.

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