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Question
The demand function for a commodity is p =`36/(x + 4)`. Find the consumer’s surplus when the prevailing market price is ₹ 6
Solution
The demand function for a commodity
p = `36/(x + 4)`
When p = 6
⇒ 6 = `36/(x + 4)`
x + 4 = `36/6`
⇒ x + 4 = 6
x = 2
∴ p0 = 6 and x0 = 2
The consumer’s surplus
C.S = `int_0^x` f(x) dx – x0p0
= `int_0^2 (36/(x + 4)) "d"x - 2(6)`
= `36 [log (x + 4)]_0^2 - 12`
= 36 [log (2 + 4) – log (0 + 4)] – 12
= 36 [log6 – log4] – 12
= `36 [log(6/4)] - 12`
∴ C.S = `36 log(6/4) - 12` units
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