(a) Explanation Given: The equation is p = 0.604 q 2 − 20.16 q + 263.067 . 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: The elasticity of demand can be written as follows, E = − p q ⋅ d q d p = − p q ⋅ 1 d p d q Differentiate p = 0.604 q 2 − 20.16 q + 263.067 with respect to q as follows, d p d q = d d q ( 0.604 q 2 − 20.16 q + 263.067 ) d p d q = ( 2 ) 0.604 q 2 − 1 − 20.16 ( 1 ) + 0 d p d q = 1.208 q − 20.16 Substitute d p d q = 1.208 q − 20.16 and p = 0.604 q 2 − 20.16 q + 263.067 in E = − p q ⋅ 1 d p d q , E = − 0 (b) To determine Whether the demand for spruce is elastic or inelastic. (c) To determine To explain: The elasticity as q approaches to 16.6887 and discuss the limitation of this model for the price as a function of the demand.

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

11th Edition

ISBN: 9780133886832

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

Publisher: PEARSON

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Question

Chapter 6.3, Problem 32E

(a)

To determine

To find: The elasticity when the demand is 11 thousand cubic meters a day.

(b)

To determine

Whether the demand for spruce is elastic or inelastic.

(c)

To determine

To explain: The elasticity as q approaches to 16.6887 and discuss the limitation of this model for the price as a function of the demand.

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Chapter 6.3, Problem 31E

Chapter 6.3, Problem 33E

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Chapter 6 Solutions

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

Ch. 6.1 - YOUR TURN 1 Find the absolute extrema of the...Ch. 6.1 - Prob. 2YT Ch. 6.1 - Prob. 1WE Ch. 6.1 - Prob. 2WE Ch. 6.1 - Prob. 1E Ch. 6.1 - Find the locations of any absolute extrema for the...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

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