Explanation Given information: The given demand function for a certain ink-jet cartridge is, p = − 0.01 x 2 − 0.1 x + 6 (1) Where, p is the unit price in dollars, x is the quantity demanded each week and measured in thousand. The value of x is 10. Formula used: The formula to calculate elasticity of demand at price p is, E ( p ) = − p f ′ ( p ) f ( p ) (2) Calculation: Rewrite the given function to express x as a function of p . 0.01 x 2 + 0.1 x = 6 − p x 2 100 + x 10 = 6 − p x 2 + 10 x = 600 − 100 p Add 25 on both the sides to convert the left hand side in the form of ( a + b ) 2 , ( x + 5 ) 2 = 625 − 100 p [ ∵ ( x + 5 ) 2 = x 2 + 10 x + 25 ] x + 5 = 625 − 100 p x = − 5 + 625 − 100 p [ x = f ( p ) ] f ( p ) = − 5 + 625 − 100 p Differentiate the above expression f ( p ) , f ′ ( p ) = − 100 2 625 − 100 p [ ∵ d d u

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Differential Equations

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Chapter 3.6, Problem 46E

To determine

To compute: The elasticity of demand and determine whether the demand is inelastic, unitary or elastic when x=10 .

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Chapter 3.6, Problem 45E

Chapter 3.6, Problem 47E

Chapter 3 Solutions

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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 determine whether the demand is inelastic, unitary or elastic when x = 10 .

Solution Summary: The author calculates the elasticity of demand and determines whether the demand is inelastic, unitary or elastic when x=10.

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To compute: The elasticity of demand and determine whether the demand is inelastic, unitary or elastic when x=10 .

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