Question

The demand curve for original Iguanawoman comics is given by
q=(343-p)^2/100

(0

where q is the number of copies the publisher can sell per week if it sets the price at $p.

(a) Find the price elasticity of demand when the price is set at $33 per copy. (Round your answer to two decimal places.)


(b) Find the price at which the publisher should sell the books in order to maximize weekly revenue. (Round your answer to the nearest cent.)

(c) What, to the nearest $1, is the maximum weekly revenue the publisher can realize from sales of Iguanawoman comics?

Answer 1

a.) When p = $33, q = (343 - 33)^2/100 = 961 units.
q'(p) = -(343 - p) / 50
q'(33) = -(343 - 33)/50 = -6.2
Price elasticity of demand = price / quantity * q'(p) = 33/961 * -6.2 = -0.2129

b.) Revenue = quantity * price = p(343 - p)^2/100
For maximum revenue, dR/dp = 0
-2p(343 - p)/100 + (343 - p)^2/100 = 0
-686p + 2p^2 + 117649 - 686p + p^2 = 0
3p^2 - 1372p + 117649 = 0
p = 343 or p = 114.33
For maximum revenue, he should sell for $114.33

c.) Maximum Revenue = 114.33(343 - 114.33)^2 / 100 = $59,783