   Chapter 13.4, Problem 24E ### 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

# CONSUMER'S SURPLUSIn Problems 17-26, p and C are in dollars and x is the number of units.If the demand function for a good is p = 110 − x 2 and the supply function for it is p = 2 − 6 5 x + 1 5 x 2 **, 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=110x2 and supply function is p=265x+15x2.

Explanation

Given Information:

Demand function is approximated by p=110x2 dollars and

Supply function is p=265x+15x2 dollars.

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,

CS=0x1f(x)dxp1x1.

Calculation:

Consider the demand function,

p=110x2

The supply function can be re-written as,

p=21210x+210x2=265x+15x2

Since, to know the equilibrium point,

Demand Function= Supply Function

Now, equate both the equations,

110x2=265x+15x25505x2=106x+x2

Simplify further,

6x26x540=0x2x90=0(x10)(x+9)=0

Evaluate the value of x,

x=10

And

x=9

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

Substitute x=10 in the demand function

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