The demand curve for original Iguanawoman comics is given by

The demand curve for original Iguanawoman comics is given by

q =

      (0 p 382)

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 $39 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?
$

Solution

a) Price Elasticity, E is given by:

E = - (p/q)[dq/dp]

here q = (1/50)(382 - p)²

=> dq/dp = ( - 2/50)(382 - p)

therefore E = - (p) x 50 x (382 - p)^-2 ( - 2/50)(382 - p)

at p = $ 39,

E = 0.23

which is less than 1.

b) Revenue collected will be: number of copies sold x price at which they were sold.

That is, R = qp

=> R = p(1/50)(382 - p)² = (1/50) [145924p - 764p² + p³]

dR/dp = (1/50)[145924 - 1528p + 3p²]

for maximizing revenue, dR/dp = 0

therefore, 145924 - 1528p + 3p² = 0

whose solutions are: p = $ 382 and p = $ 127.33

but p cannot be $ 382 since q will then be zero [see the function]. Therefore p = $ 127.33

for which q = (1/50)[382 - 127.33]² = 1297

so the Maximum Revenue generated per week will be: R = 1297 x 127.33 = $ 165160.