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Question
Find the consumer’s surplus and producer’s surplus for the demand function pd = 25 – 3x and supply function ps = 5 + 2x
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Solution
Given pd = 25 – 3x and ps = 5 + 2x
At market equilibrium, pd = pss
⇒ 25 – 3x = 5 + 2x
⇒ 5x = 20
⇒ x = 4
When x0 = 4
p0 = 25 – 12 = 13
C.S = `int_0^4 (25 - 3x) "d"x - 13(4)`
= `(25x - (3x^2)/2)_0^4 - 52`
= `100 - 3/2 (16) - 52`
= 24
So the consumer’s surplus is 24 units.
P.S = `13(4) - int_0^4 (2x + 5) "d"x`
= `52 - (x^2 + 5x)_0^4`
= `52 - 16 - 20`
= 16
So the producer’s surplus is 16 units.
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