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In: Economics

Microeconomics

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?

Solutions

Expert Solution

The demand equation is;

Q = 30 - 4P

Where Q is the quantity of necklaces demanded and P is the price of the necklace.

4P = 30 - Q

P = (30 - Q)/4

The current price of the necklace $10.

Revenue function

R = P × Q

R = (30 - Q)/4 × Q

R = 1/4 × ( 30Q - Q2)

Differentiate the function with respect to Q to maximize the revenue.

dR/dQ =  1/4 × ( 30 - 2Q) = 0

Q = 15.

Finding the second order derivative

negative showing that the value of Q is maximum.

Therefore,

P = (30 - Q)/4, but Q = 15

 P = $3.75.

To maximize revenue the price should be $3.75.

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

Joes answered 3 years ago
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