Find the consumer surplus when x=40

Question

The demand function, in dollars per unit, for a commodity is given by D(x)=3000-0.6x^2 where x is the number of units demanded.

Answer 1

D = 3000 - 0.6x^2 x= 40

3000 -(3/5)40^2 =3000 - (3/5)1600= 3000-960 = 2040

$20.40 is the price when 40 are sold

consumer surplus is the area below the demand curve and above P=20.40

It's a right triangle from 3000-2040 = 960 as the height, base = 40

area =bh/2 = 40(960)/2 = 20(960) = 19200 = $192 consumer surplus