Question

Currently, the demand equation for necklaces is Q = 30 – 4P. The current price is $10 per necklace.

a. Is this the best price to charge in order to maximize revenues?

b. If $10 per necklace is not the best price, what is?

Answer 1

a). Demand Q=30-4P, rewrite it in form of P

P=7.5 - 0.25Q; find revenue

$Revenue=Price(P)\times quantity (Q)$

$Revenue=(7.5 - 0.25Q)\times Q=7.5Q - 0.25Q^2$

Marginal revenue=Marginal cost=0

Marginal revenue=7.5 - 0.5 Q=0

$\cancel{0.5}Q=\frac{7.5}{0.5}=15$

Substitute;

$P=7.5-(0.25\times15)=3.75$

A price of $10 is more than $3.75 hence a good price to maximize revenue but not in the long term.

b). The best price to charge is $3.75 since it is at the optimal point.