Demand curve problem

Question

The demand curve for a product is given by q equals 1000 minus 2 p^ 2 where p is the price. Find the price that maximizes revenue for sales of this product.

Answer 1

Demand

q = 1000 - 2p²

 

Price

p = p

 

Revenue

r = pq = p (1000 - 2p²) = -2p³ + 1000p

 

Find the critical values by taking the derivative

dr/dp = -6p² + 1000

 

and then setting the derivative equal to zero

-6p² + 1000 = 0

6p² = 1000

p² = 1000/6 = 500/3

p = ± 10√(5/3)

 

We can dismiss negative prices as being outside the domain of our problem (and otherwise an unlikely choice to maximize revenue).

p = 10√(5/3) ≈ 16.99