(a) Explanation Given information: The demand equation is, x = 144 − p ( 0 ≤ p ≤ 144 ) . Where, x is the demand (in units of thousands) and p is the unit price (in dollars). 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 , f ( p ) = 144 − p Differentiate the function, f ( p ) , f ′ ( p ) = [ d d p ( 144 − p ) ] = [ 1 2 144 − p ⋅ d d p ( 144 − p ) ] ( ∵ d d x ( x ) n = n x n − 1 ) = [ − 1 2 144 − p ] Substitute 144 − p for f ( p ) and − 1 2 144 − p for f ' ( p ) </ (b) To determine Interpret the results of part (a). (c) To determine Whether the demand is elastic unitary or inelastic at p = 63 , p = 96 and p = 108

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Question

Chapter 3.4, Problem 36E

(a)

To determine

The elasticity of demand at p=63 , p=96 and p=108 .

(b)

To determine

Interpret the results of part (a).

(c)

To determine

Whether the demand is elastic unitary or inelastic at p=63 , p=96 and p=108

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Chapter 3.4, Problem 35E

Chapter 3.4, Problem 37E

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Applied Calculus for the Managerial, Life, and Social Sciences

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The elasticity of demand at p = 63 , p = 96 and p = 108 .

Solution Summary: The author explains the elasticity of demand at p=63, and the value of E(p)=1.

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The elasticity of demand at p=63 , p=96 and p=108 .

Interpret the results of part (a).

Whether the demand is elastic unitary or inelastic at p=63 , p=96 and p=108

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Chapter 3 Solutions