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

Answer : Total Revenue (TR) = P*Q = P * (30 - 4P) [Q is given]

=> TR = 30P - 4P^2

Now to get the price level which maximize the revenue we have to take derivative for TR with respect to P. So,

dTR / dP = 30 - 8P = 0

=> 30 = 8P

=> P = 30 / 8

=> P = 3.75

At P = $3.75 the total revenue = (30 * 3.75) - 4 * (3.75)^2 = 112.5 - 56.25 = $56.25 .

At P = $10 the total revenue = (30 * 10) - 4 * (10)^2 = 300 - 400 = - $100 .

Now we can see that if the price level is $10 then the revenue is - $100 but if the price is $3.75 then the revenue is $56.25 . Therefore, the price $10 does not maximize the revenue. The price level which maximizes the revenue, is $3.75 .

answered by: anonymous