A manufacturer of DVD players has been selling 800 each week at 150$each. From a market survey it is discovered that for each $5 reduction in price, they will sell an extra 40DVD players each week.

Question

A manufacturer of DVD players has been selling 800 each week at 150$each. From a market survey it is discovered that for each $5 reduction in price, they will sell an extra 40DVD players each week.

a)What is the demand function?

b)How large a reduction in price (rebate) should the manufacturer give a buyer so that revenue will be maximised?

Answer 1

a) Actually, the inverse demand function, for evaluating the price from the description is:

p(x) = 150-5x

b) Need to find the demand, x to maximize the revenue.

Revenue = Quantity × Price

R(x) = (800+40x)(150-5x)

R(x) = 120000-4000x+6000x-200x² = -200x²+2000x+120000

To maximize the revenue, find the derivative of R(x), set that to zero and solve for x

R'(x) = -400x+2000 = 0

x = 5

Reduction = 5x = $25

The maximum revenue for reducing the price by $25 is $125000