Question

Find the consumer’s surplus and producer’s surplus for the demand function p_d = 25 – 3x and supply function p_s = 5 + 2x

Answer 1

Given p_d = 25 – 3x and p_s = 5 + 2x

At market equilibrium, p_d = ps_s

⇒ 25 – 3x = 5 + 2x

⇒ 5x = 20

⇒ x = 4

When x₀ = 4

p₀ = 25 – 12 = 13

C.S = `int_0^4 (25 - 3x)  "d"x - 13(4)`

= `(25x - (3x^2)/2)_0^4 - 52`

= `100 - 3/2 (16) - 52`

= 24

So the consumer’s surplus is 24 units.

P.S = `13(4) - int_0^4 (2x + 5)  "d"x`

= `52 - (x^2 + 5x)_0^4`

= `52 - 16 - 20`

= 16

So the producer’s surplus is 16 units.