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Question
Calculate consumer’s surplus if the demand function p = 122 – 5x – 2x2, and x = 6
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Solution
Demand function p = 122 – 5x – 2x2 and x = 6
When x = 6
p = 122 – 5(6) – 2(6)2
= 122 – 30 – 2(36)
= 122 – 102
= 20
∴ p0 = 20
.S = `int_^x` (demand function) dx – (Price × quantity demanded)
- `int_0^6` (122 – 5x – 2x2) dx – (20 × 6)
= `[122x - 5(x^2/2) - 2(x^3/3)]_0^6 - 120`
= `[122(6) - ((6)^2/2) - 2((6)^3/3) - [0]] - 120`
= `[732 - ((5(36))/2) - ((2(216))/3)] - 120`
= [732 – 5(18) – 2(72)] – 120
= 732 – 90 – 144 – 120
= 732 – 354
= 378
∴ CS = 378 units
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