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Question
Calculate the producer’s surplus at x = 5 for the supply function p = 7 + x
Solution
The supply function p = 7 + x
When x = 5
⇒ p = 7 + 5 = 12
∴ x0 = 5 and p0 = 12
Producer’s surplus
P.S = `x_0"p"_0 - int_0^(x_0) "g"(x) "d"x`
= `(5)(12) - int_0^5 (7 + x) "d"x`
= `60 - [7x + x^2/2]_0^5`
= `60 - {7(5) + (5)^2/2 - (0)}`
= `60 - [35 + 25/2]`
= `60 - (35 + 12.5)`
= `60 - 47.5`
= 12.5
= `25/2`
∴ P.S = `25/2` units
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