Question

The price P for demand D is given as P = 183 + 120 D – 3D2 . Find D for which the price is increasing.

Answer 1

The given function is p = 183 + 120 D – 3D2

:. dP/dD = 120 – 6D

Now dP/dD = 0 ⇒ 120 – 6 D = 0 ⇒ D = 20

For increasing the price

dP/dD > 0

120 – 6D > 0

– 6D > – 120

D < 120/6

D < 20.

Demand and price cannot be negative ∴ Price is increasing in the internal (0, 20).