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marshall27
29 days ago
9

Suppose that the demand equation for Bobby Dolls is given by q = 216 – p2, where p is the price per doll in dollars and q is the

number of dolls sold per week. a. Compute the price elasticity of demand when p = $5, and interpret your results. b. Find the price at which the weekly revenue is maximized. c. What is the maximum weekly revenue.
Business
1 answer:
marusya05 [3K]29 days ago
7 0

Answer:

P.Ed at p = 5: -0.26

Price that maximizes revenue = 8.5; Maximum total revenue = 1222

Explanation:

The price elasticity of demand indicates how demand varies in response to price changes. P.Ed = (dq / dp) x (p / q)

q = 216 - p²

dq / dp = -2p

P.Ed = dq / dp x (p / q)

Thus, PEd = (-2p) x (p / q)

[(-2p)(p)] / [216 - p²]

(-2p²) / (216 - p²)

Substituting P = 5 into P.Ed:

-2(25)

216 - 25

= -50 / 191

P.Ed = 0.26

Total revenue is the overall income generated from the sale of goods and services. TR = p x q

q = 216 - p²

TR = 216p - p³

To locate the price which maximizes total revenue, we take the derivative of the TR function relative to 'p':

dTR / dp = 216 - 3p²

dTR / dp = 216 - 3p² = 0

3p² = 216

p² = 216 / 3

p² = 72

p = √72

p = 8.5

To determine the maximum revenue, we substitute the price of 8.5 into the TR function:

TR = 216p - p³

216(8.5) - (8.5)³

1836 - 614

1222

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