   Chapter 13.4, Problem 23E ### 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

# In Problems 17-26, p and C are in dollars and x is the number of units.If the demand function for a product is p   =  1 2 / ( x +   1 ) and the supply function is p =   1   +   0.2 x , find the consumer’s surplus under pure competition.

To determine

To calculate: The Consumer’s Surplus under pure competition for a product whose demand function is approximated by p=12(x+1) and supply function is p=1+0.2x.

Explanation

Given Information:

Demand function is approximated by p=12(x+1) and

Supply function is p=1+0.2x.

Formula used:

According to the Consumer’s Surplus:

If the demand curve has equation p=f(x), the consumer surplus is given by the area between f(x) and the x-axis from 0 to x1, less the area of TR is,

CS=0x1f(x)dxp1x1.

Calculation:

Consider the demand function:

p=12(x+1)

Since, to know the equilibrium point:

Demand Function =Supply Function

Now equate both the equations,

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

Simplify further for the value of x,

x=5

And

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

Substitute x=5 in the demand function to get p1,

p=12(5+1)=126

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