A supply function g(x) represents the quantity that can be supplied at a price p.

**Producer surplus**

A supply function g(x) represents the quantity that can be
supplied at a price p. Let p_{0} be the market price for the
corresponding supply x_{o} . But there can be some producers who are
willing to supply the commodity below the market price gain from the fact that
the price is p_{0}. This gain is called the producerâ€™s surplus. It is
represented in the following diagram.

Mathematically, producerâ€™s surplus (PS) can be defined as,

PS = (Area of the rectangle OAPB) âˆ’ (Area below the supply function from *x* = 0 to *x *=* x _{0} *)

**Example 3.28**

Find the producerâ€™s surplus defined by the supply curve *g*(*x*)
= 4*x*+8 when *x*_{o}= 5.

*Solution:*

=
140 â€“ (50 + 40)

= 50 units

Hence the producerâ€™s surplus= 50 units.

**Example 3.29**

The demand and supply function of a commodity are p_{d} =
18 âˆ’ 2x âˆ’ x^{2} and p_{s} = 2x âˆ’ 3 . Find the consumerâ€™s
surplus and producerâ€™s surplus at equilibrium price.

*Solution:*

Hence at equilibrium price,

(i) the consumerâ€™s surplus is 27 units

(ii) the producerâ€™s surplus is 9 units.

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12th Business Maths and Statistics : Chapter 3 : Integral Calculus - II : Integration: Producer surplus | Example Solved Problems with Answer, Solution, Formula

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