   Chapter 13.4, Problem 20E ### 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.The demand function for a certain product is p   = 100 / ( 1   + 2 x ) . If the equilibrium quantity is 12 units, what is the consumer’s surplus?

To determine

To calculate: The Consumer’s Surplus for a product whose demand function is approximated by p=100(1+2x) dollars. Where, the equilibrium quantity is 12 unit.

Explanation

Given Information:

Demand function is approximated by p=100(1+2x) dollars.

The equilibrium quantity is 12 unit.

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=100(1+2x)

Since, to know the equilibrium price at which the given quantity can be purchased,

Let, x=12

Substitute the value x=12 in the demand function to get p1,

p=100(1+212)=10025=4

Thus, the equilibrium point (x1,p1) will be,

x1=12p1=4

Consider the formula:

CS=0x1f(x)dx

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