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? If not, what is?

Solve for the best price to charge in order to maximize revenues. Show any steps or processes used to reach the answer above. Explain your process as though you are teaching the concept to a student who is a beginner in economics.

Answer 1

Revenue maximization is a theoretical idea that any firms follow to earn maximum revenue by selling the product at a certain cost. Here our objective is to find out that per unit cost of the product for which the firm will earn maximum revenue. Revenue will be maximized at that price when marginal revenue will be zero which means there will be no extra money by selling one unit of extra product. If marginal revenue is positive then the firm will continue earning revenue by selling extra unit of the product thus when MR is zero the revenue is maximized . Here the demand function is Q=30-4P and price is P thus

Total Revenue= (30-4P)*P = 30P-4P²

Marginal Revenue = 30-8P Taking P=10 we have MR= -50

here at price $10 per necklace the marginal revenue is negative means firm is running in loss right now there is negative profit and negative revenue

Thus revenue maximizing price will be; 30-8P=0 ; P=3.75

Here at Q₀ MR=0 thus revenue is maximum and at the AR curve P₀ is the price at which revenue is maximum.