(a) Explanation Given: The demand equation is, x = 2 3 36 − p 2 ( 0 ≤ p ≤ 6 ) Where, x is the demand (in thousands). p is the renal price (in dollars). Currently the rental price is $ 2 / disc . 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 = 2 3 36 − p 2 x = f ( p ) Differentiate the function f ( p ) with respect to p . f ′ ( p ) = 2 3 [ d d p ( 36 − p 2 ) ] = 2 3 [ 1 2 36 − p 2 ⋅ d d p ( 36 − p 2 ) ] = 2 3 [ ( − 2 p ) 2 36 − p 2 ] (b) To determine The relationship between the rental price and the revenue.

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Differential Equations

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Chapter 3.4, Problem 37E

(a)

To determine

The elasticity of demand and find whether the demand is elastic, unitary or inelastic at the rental price.

(b)

To determine

The relationship between the rental price and the revenue.

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Chapter 3.4, Problem 36E

Chapter 3.4, Problem 38E

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Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

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The elasticity of demand and find whether the demand is elastic, unitary or inelastic at the rental price.

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The elasticity of demand and find whether the demand is elastic, unitary or inelastic at the rental price.

The relationship between the rental price and the revenue.

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Chapter 3 Solutions