Question

The demand function p = 85 – 5x and supply function p = 3x – 35. Calculate the equilibrium price and quantity demanded. Also, calculate consumer’s surplus

Answer 1

Demand function p = 85 – 5x

Supply function p = 3x – 35

W.K.T. at equilibrium prices p_d = p_s

85 – 5x = 3x – 35

85 + 35 = 3x + 5x

120 = 8x

⇒ x = `120/8`

∴ x = 15

When x = 15

p₀ = 85 – 5(15)

= 85 – 75

= 10

C.S = `int_0^x` f(x) dx – x₀p₀

= `int_0^x` (85 – 5x) dx – (15)(10)

= `[5x - 5(x^2/2)]_0^15 - 150`

= `{85(15) - 5((15)^2/2) - [0]} - 150`

= `[1275 - (5(225))/2] - 150`

= `1275 - 1125/2 - 150`

= 1275 – 562.50 – 150

= 1275 – 712.50

∴ C.S = 562.50 units