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.

P.Ed at p = 5 :- 0.26

Revenue maximising price = 8.5 ; Maximum Total Revenue = 1222

Explanation:

Price Elasticity of Demand shows responsive change in demand, due to change in price.  P.Ed = ( dq / dp ) x ( p / q )

q = 216 - p^2

dq / dp = - 2p  

P.Ed = dq / dp x ( p / q )  

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

[ (- 2p) (p) ] / [ 216 - p^2 ]

(- 2p^2 ) / ( 216 - p^2 )

Putting value of P = 5 in P.Ed

- 2(25)

216 - 25

= - 50 / 191

P.Ed = 0.26

Revenue is the total value of receipts from sale of goods & services. TR = p x q

q = 216 - p^2

TR = 216p - p^3

To find price maximising TR , we will derivate TR function with respect to 'p'  

d TR / d p = 216 - 3p^2  

d TR / d p = 216 - 3p^2   = 0

3p^2 = 216

p^2 = 216 / 3

p^2 = 72

p = √ 72

p = 8.5

Finding maximum revenue ; Putting price = 8.5 in TR function

TR = 216p - p^3

216 (8.5) - (8.5)^3

1836 - 614

1222