Question

Currently, the demand equation for toasters is Q = 80 – 2P. The current price is $30 per toaster. Is this the best price to charge in order to maximize revenues? If not, what is?

Answer 1

The demand equation is given as:

Q = 80 - 2P

Or, 2P = 80 - Q

Or, P = 40 - (Q/2) = 40 - 0.5Q

Multiplying both sides by Q, we get,

PQ = Total revenue (TR) = 40Q - 0.5Q²

Total revenue is maximized, when d(TR)/dQ = 0

Or, 40 - (0.5*2)Q = 0

Or, 40 - Q = 0

Or, Q = 40

Therefore, total revenue is maximized when Q = 40 units. Now from the demand equation we get, P = 40 - (0.5 * 40) = $(40 - 20) = $20.

It means the price that maximizes total revenue is $20 per toaster. So, the current price $30 per toaster is not the best price.