Question

Currently, the demand equation for necklaces is Q = 30 – 4P. The current price is $10 per necklace. Is this the best price to charge in order to maximize revenues?

Answer 1

Answer:

The correct answer is NO. The best price to be charged is $3.75

Step-by-step explanation:

Demand equation is given by Q = 30 - 4P, where Q is the quantity of necklaces demanded and P is the price of the necklace.

⇒ 4P = 30 - Q

⇒ P = $\frac{30-Q}{4}$

The current price of the necklace $10.

Revenue function is given by R = P × Q = $\frac{1}{4}$ × ( 30Q - $Q^{2}$)

To maximize the revenue function we differentiate the function with respect to Q and equate it to zero.

$\frac{dR}{dQ}$ =  $\frac{1}{4}$ × ( 30 - 2Q) = 0

⇒ Q = 15.

The second order derivative is negative showing that the value of Q is maximum.

Therefore P at Q = 15 is $3.75.

Thus to maximize revenue the price should be $3.75.