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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
Solution
Demand function p = 85 – 5x
Supply function p = 3x – 35
W.K.T. at equilibrium prices pd = ps
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
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