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**CONSUMERS’ SURPLUS**

A demand curve for a commodity shows the amount of the commodity that will be bought by people at any given price p.

Suppose that the prevailing market price is p_{0 }. At this price an amount x_{0} of the commodity determined by the demand curve will be sold. However there are buyers who would be willing to pay a price higher than p_{0} . All such buyers will gain from the fact that the prevailing market price is only p_{0} . This gain is called Consumers’ Surplus . It is represented by the area below the demand curve p = f(x) and above the line p = p_{0} . Thus Consumers’ Surplus, CS = [Total area under the demand function bounded by x = 0, x = x_{0} and x-axis - Area of the rectangle OAPB]

**Example 26 Fig. 5.9 Find the consumers’ surplus for the demand function p = 25 - x - x ^{2} when p = 19. **

Solution :

Given that, The demand function is p = 25 - x - x

**Example 27 The demand of a commodity is p = 28 - x 2 Find the consumers’ surplus when demand x _{0} = 5 **

Solution : Given that,

The demand function, p = 28 - x 2

when x

= 3

∴ p

**Example 28 The demand function for a commodity is . Find the consumers’ surplus when the prevailing market price is 2.**

Solution : Given that, Demand function,

**PRODUCERS’ SURPLUS**

A supply curve for a commodity shows the amount of the commodity that will be brought into the market at any given pricep. Suppose the prevailing market price is p0 . At this price an amount x0 of the commodity, determined by the supply curve, will be offered to buyers. However, there are producers who are willing to supply the commodity at a price lower than p0 . All such producers will gain from the fact that the prevailing market price is only p0 . This gain is called ‘Producers’ Surplus’. It is represented by the area above the supply curve p = g(x ) and below the line p = p0 . Thus Producers’ Surplus, PS = [ Area of the whole rectangle OAPB Area under the supply curve bounded by x = 0, x = x0 and x - axis]

**Example 29 The supply function for a commodity is p = x ^{2} + 4x + 5 where x denotes supply. Find the producers’ surplus when the price is 10.**

Solution : Given that, Supply function, p = x ^{2} + 4x + 5

For p_{0} = 10,

10 = x ^{2} + 4x + 5 + x 2 + 4x + 5 = 0

⇒ (x + 5) (x + 1) = 0 + x = + 5 or x = 1

Since supply cannot be negative, x = + 5 is not possible.

∴ x = 1

∴ p = 10 and x_{0} = 1

⇒ p_{0}xP_{0} = 10

Producers’ Surplus,

**Example 30 Find the producers’ surplus for the supply function p = x ^{2 }+ x + 3 when x = 4.**

Solution :

Given that,

supply function p = x 2 + x + 3

when x_{0} = 4, p_{0} = 4 + 4 +3 = 23

∴ p x = 92.

Producers’ Surplus

**Example 31 Find the producers’ surplus for the supply function p = 3 + x ^{2 }when the price is 12. **

Solution :

Given that,

supply function, p = 3 + x^{2} . When p_{0} = 12,

12 = 3 + x^{2} or x^{2 }= 9 or x = + 3

Since supply cannot be negative,

12 = 3 + x^{2} or x 2 = 9 or x = + 3

Since supply cannot be negative

x = 3. i.e. x_{0 }= 3,

∴ p x = 36.

Producers’ Surplus,

**Example 32**

**The demand and supply functions under pure competition are p _{d }= 16 - x and p_{s} = 2x + 4. Find the consumers’ surplus and producers’ surplus at the market equilibrium price. **

Solution : For market equilibrium, Quantity demanded = Quantity supplied

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