(a) To determine To find: The elasticity of demand E for the demand function q = 48 , 000 − 10 p 2 . Explanation Formula used: Elasticity of Demand: Let q = f ( p ) , q is demand at a price p then the elasticity of demand is E = − p q ⋅ d q d p . Demand is inelastic if E < 1 . Demand is elastic if E > 1 . Demand has unit elasticity if E = 1 . Calculation: Differentiate the demand function q = 48 , 000 − 10 p 2 with respect to p as follows. d q d p = d d p ( 48 , 000 − 10 p 2 ) = 0 − 10 ( 2 ) p 2 − 1 = − 20 p Substitute d q d p = (b) To determine To find: The value of q at which the total revenue is maximized.

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 6.3, Problem 22E

(a)

To determine

To find: The elasticity of demand E for the demand function q=48,000−10p2 .

(b)

To determine

To find: The value of q at which the total revenue is maximized.

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Chapter 6.3, Problem 21E

Chapter 6.3, Problem 23E

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Calculus with Applications (11th Edition)

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