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

Chapter: 12th Business Maths and Statistics : Chapter 3 : Integral Calculus - II

Integration: Producer surplus

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 p0 be the market price for the corresponding supply xo . 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 p0. This gain is called the producer’s surplus. It is represented in the following diagram. 


Mathematically, producer’s surplus (PS) can be defined as,

PS = (Area of the rectangle OAPB) (Area below the supply function from x = 0 to x = x0 )



Example 3.28

Find the producer’s surplus defined by the supply curve g(x) = 4x+8 when xo= 5.

Solution:


= 140 – (50 + 40)

 = 50 units

 Hence the producer’s surplus= 50 units.

 

Example 3.29

The demand and supply function of a commodity are pd = 18 − 2x − x2 and ps = 2x − 3 . Find the consumer’s surplus and producer’s surplus at equilibrium price.

Solution:


Hence at equilibrium price,

(i) the consumer’s surplus is 27 units

(ii) the producer’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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12th Business Maths and Statistics : Chapter 3 : Integral Calculus - II


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