(a) Explanation Given: The demand equation is, x = 400 − 5 p ( 0 ≤ p ≤ 80 ) Where, x is the demand (in thousands). p is the renal price (in dollars). The values of p are 40 and 60 . 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 = 400 − 5 p x = f ( p ) Differentiate the function f ( p ) with respect to p . f ′ ( p ) = [ d d p ( 400 − 5 p ) ] = [ 1 2 400 − 5 p ⋅ d d p ( 400 − 5 p ) ] = [ ( − 5 ) 2 400 − 5 p ] ( ∵ d d x ( x ) n = n x n − 1 ) = [ − 5 2 400 − 5 p (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 $ 60 then revenue is decreased or increased. (d) To determine If the value of the unit price is increases slightly from $ 40 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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Chapter 3.4, Problem 38E

(a)

To determine

The elasticity of demand and whether the demand is elastic or inelastic when p=40 and p=60 .

(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 $60 then revenue is decreased or increased.

(d)

To determine

If the value of the unit price is increases slightly from $40 then revenue is decreased or increased.

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Chapter 3.4, Problem 37E

Chapter 3.4, Problem 39E

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 whether the demand is elastic or inelastic when p = 40 and p = 60 .

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The elasticity of demand and whether the demand is elastic or inelastic when p=40 and p=60 .

The value of p at which the unitary demand.

If the value of the unit price is decreases slightly from $60 then revenue is decreased or increased.

If the value of the unit price is increases slightly from $40 then revenue is decreased or increased.

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Chapter 3 Solutions