   Chapter 13.4, Problem 17E ### 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 product is p   = 34   −   x 2 . If the equilibrium price is \$9 per unit, what is the consumer's surplus?

To determine

To calculate: The Consumer’s Surplus for a product whose demand function is approximated by p=34x2 dollars. If, the equilibrium price is 9 dollars per unit.

Explanation

Given Information:

The Equilibrium Surplus for a product whose demand function is approximated by p=34x2 dollars. Where, the equilibrium price is 9 dollars per 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=34x2

Since, to know the quantity to be purchased at equilibrium price,

Let, p=9

Substitute the value p=9 in the demand function to get x1,

9=34x2x2=349x2=25x=5

Thus, the equilibrium point (x1,p1) can determine as,

x1=5p1=9

Consider the formula,

CS=x

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