Tutorial Exercise Worldwide annual sales of smartphones in over a 5 year period were projected to be approximately q = −10p + 4,540 million phones at a selling price of $p per phone. (a) Obtain a formula for the price elasticity of demand E. (b) In one particular year the actual selling price was $277 per phone. What was the corresponding price elasticity of demand? Interpret your answer. (c) Use your formula for E to determine the selling price that would have resulted in the largest annual revenue. What, to the nearest $10 million, would have been the resulting annual revenue? Step 1 (a)Obtain a formula for the price elasticity of demand E. Recall that the price elasticity of demand E is the percentage rate of decrease of demand divided by the percentage increase of price, given by the formula. E = − dq dp · p q We are already given the formula q = −10p + 4,540 for the demand of smartphones (in millions). First, we find the derivative dq dp . dq dp = Next, substitute the values for dq dp and q into the formula for the price elasticity demand. E = − dq dp · p q = − · p −10p + 4,540 = p −10p + 4,540 Therefore, the price elasticity demand for smartphones is E =

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter3: Demand Analysis

Section: Chapter Questions

Problem 10E

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(a)Obtain a formula for the price elasticity of demand E.

Recall that the price elasticity of demand E is the percentage rate of decrease of demand divided by the percentage increase of price, given by the formula.

E = −

We are already given the formula

q = −10p + 4,540

for the demand of smartphones (in millions).

First, we find the derivative

Next, substitute the values for

and q into the formula for the price elasticity demand.

−

−10p + 4,540

Therefore, the price elasticity demand for smartphones is

E =

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