(a) Explanation Given: The demand equation is, x = 1 5 ( 225 − p 2 ) ( 0 ≤ p ≤ 15 ) Where, x s the demand (in units of hundreds). p is the unit price (in dollars). The values of p are 8 and 10 . 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 , x = 1 5 ( 225 − p 2 ) x = 45 − p 2 5 f ( p ) = 45 − p 2 5 Differentiate the function f ( p ) with respect to p . f ' ( p ) = [ d d p ( 45 − p 2 5 ) ] = [ d d p ( 45 ) − d d p ( p 2 5 ) ] ( ∵ d d x ( x ) n = n x n − 1 ) = [ − 2 p 5 ] Substitute 45 − p 2 (b) To determine The value of p at which the unitary demand. (c) To determine If the value of the unit price is decreases slightly from $ 10 then revenue is decreased or increased. (d) To determine If the value of the unit price is increases slightly from $ 8 then revenue is decreased or increased.

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Differential Equations

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Chapter 3.4, Problem 35E

(a)

To determine

The elasticity of demand and find whether the demand is elastic or inelastic when p=8 and p=10 .

(b)

To determine

The value of p at which the unitary demand.

(c)

To determine

If the value of the unit price is decreases slightly from $10 then revenue is decreased or increased.

(d)

To determine

If the value of the unit price is increases slightly from $8 then revenue is decreased or increased.

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Chapter 3.4, Problem 34E

Chapter 3.4, Problem 36E

Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

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The elasticity of demand and find whether the demand is elastic or inelastic when p = 8 and p = 10 .

Solution Summary: The author analyzes the elasticity of demand and determines whether it is elastic or inelastic.

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The elasticity of demand and find whether the demand is elastic or inelastic when p=8 and p=10 .

The value of p at which the unitary demand.

If the value of the unit price is decreases slightly from $10 then revenue is decreased or increased.

If the value of the unit price is increases slightly from $8 then revenue is decreased or increased.

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Chapter 3 Solutions