Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 6 - Applications of the Derivative - 6.3 Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand - 6.3 Exercises - Page 330: 26

Answer

a. $200$ the demand is elastic b. $0.5$ the demand is inelastic

Work Step by Step

a. $\frac{dp}{dq}=-2$ $E=\frac{-p}{q}.\frac{dp}{dq}=\frac{-p}{300-2p}(-2)=\frac{2p}{300-2p}$ Let p=100 to get $\frac{2(100)^{2}}{300-2(100)}=200$ Since $200\gt 1$ the demand is elastic, and a percentage change in price will result in a smaller percentage change in demand. b. a. $\frac{dp}{dq}=-2$ $E=\frac{-p}{q}.\frac{dp}{dq}=\frac{-p}{300-2p}(-2)=\frac{2p}{300-2p}$ Let p=50 to get $\frac{2(50)}{300-2(50)}=0.5$ Since $0.5\lt1$ the demand is inelastic
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