   Chapter 13.4, Problem 33E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Find the producers surplus at market equilibrium for a product with demand function p =   12 / ( x +   1 ) and supply function p =   1   + 0.2 x .

To determine

To calculate: The producer’s surplus at market equilibrium for a product whose demand function is approximated by p=12(x+1) dollars and supply function is p=1+0.2x.

Explanation

Given Information:

The Producer’s Surplus at market equilibrium for a product whose demand function is approximated by p=12(x+1) dollars and supply function is p=1+0.2x dollars.

Formula used:

The producer’s surplus for a supply function g(x) at equilibrium is,

PS=p1x10x1g(x)dx.

Where p1 is the equilibrium price ad x1 is the unit sold at equilibrium.

Calculation:

Consider the supply function, p=1+0.2x and demand function, p=12(x+1).

The supply function is equal to the demand function at equilibrium point.

12(x+1)=1+0.2x12=1+1.2x+0.2x22x2+12x110=02(x+11)(x5)=0

Further solve the above, to get

x=5

And

x=11 (Not possible, Since x can’t be negative)

Substituting 5 for x in the supply function p=1+0

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