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Mathematical Applications for the Management, Life, and Social Sciences11th Edition

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Chapter 13.4, Problem 24E
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Mathematical Applications for the ...

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

Solutions

Chapter
Section
Problem 1CP
Problem 2CP
Problem 3CP
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
BuyFindarrow_forward

Mathematical Applications for the ...

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

CONSUMER'S SURPLUS

In 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=110−x2 and supply function is p=2−65x+15x2.

Explanation

Given Information:

Demand function is approximated by p=110−x2 dollars and

Supply function is p=2−65x+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)dx−p1x1.

Calculation:

Consider the demand function,

p=110−x2

The supply function can be re-written as,

p=2−1210x+210x2=2−65x+15x2

Since, to know the equilibrium point,

Demand Function= Supply Function

Now, equate both the equations,

110−x2=2−65x+15x2550−5x2=10−6x+x2

Simplify further,

6x2−6x−540=0x2−x−90=0(x−10)(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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Chapter 13.4,
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