(a) Explanation Given information: An electronic store can sell q = 10 , 000 / ( p + 50 ) − 30 cellular phone at a price p dollars per phone. Explanation: The demand function is f ( p ) = q = 10 , 000 / ( p + 50 ) − 30 . Differentiate with respect to p , f ' ( p ) = − 10 , 000 ( p + 50 ) − 2 Therefore, f ' ( p ) = − 10 , 000 / ( p + 50 ) 2 . By using the formula of elasticity, E ( p ) = − p f ' ( p ) f ( p ) = − p ( − 10 , 000 / ( p + 50 ) 2 ) 10 , 000 / ( p + 50 ) − 30 = 10 , 000 p ( p + 50 ) [ 10 , 000 − 30 ( p + 50 ) ] = 10 , 000 p [ 10 , 000 ( p + 50 ) − 30</ (b) To determine Whether the revenue increases or decreases if the price is lowered slightly.

Calculus & Its Applications (14th Edition)

14th Edition

ISBN: 9780134437774

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar

Publisher: PEARSON

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Chapter 5.3, Problem 20E

(a)

To determine

Whether the demand function q=10,000/(p+50)−30 at p=150 is elastic or inelastic.

(b)

To determine

Whether the revenue increases or decreases if the price is lowered slightly.

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Chapter 5.3, Problem 19E

Chapter 5.3, Problem 21E

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Whether the demand function q = 10 , 000 / ( p + 50 ) − 30 at p = 150 is elastic or inelastic.

Solution Summary: The author explains that the demand function q=10,000/(p+50)-30 is elastic or inelastic.