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