Question

The demand curve for original Iguanawoman comics is given by:

q = (481-p)^2/100 (0 ≤ p ≤ 481)
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 $36 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

Elasticity = dq/dp * p/q
p =36
q = 445
dq/dp = -2(481-p)/100 = -8.9

--> Elasticity = -8.9*(36/445) = -0.16

Revenue = p*q = p(481-p)^2/100
max revenue by setting dR/dp = 0
dR/dp = (481-p)^2/100 - 2p(481-p)/100 = 0

--> (p^2 -962p+481^2) = -2p^2 + 962p
--> 3p^2 - 1924p + 481^2 = 0
--> p = 160.33 or 481, however p can't be 481 or else revenue would be 0
--> p = 160.33

to get max revenue, plug in 160.33 for p
--> max revenue = 164,866