Question

Calculate consumer’s surplus if the demand function p = 50 – 2x and x = 20

Answer 1

Demand function p = 50 – 2x and x = 20

When x = 2

p = 50 – 2(20)

p = 50 – 40 = 10

∴ p₀ = 10

CS = `int _0^x` (demand function) dx – (Price × quantity demanded)

= `int _0^20` (50 – 2x) dx – (10 × 20)

= `[50x - 2(x^2/x)]_0^20 - 200`

= `[50x - x^2]_0^20 - 200`

= {50(20) – (20)² – [0]} – 200

= (1000 – 400) – 200

= 600 – 200

∴ C.S = 400 units