   Chapter 13.4, Problem 22E ### 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 =   49   − x 2 , and the supply function is p =   4 x   +   4 . Find the equilibrium point and the consumers surplus there.

To determine

To calculate: The Equilibrium Point and Consumer’s Surplus for a product whose demand function is approximated by p=49x2 and supply function is p=4x+4.

Explanation

Given Information:

Demand function is approximated by p=49x2 dollars and

Supply function is p=4x+4 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 is,

CS=0x1f(x)dxp1x1.

Calculation:

Consider the demand function,

p=49x2

Since, to know the equilibrium point,

Demand Function =Supply Function

Now equate both the equations,

49x2=4x+4x2+4x45=0(x+9)(x5)=0

Now simplify for the value of x,

x=5

And

x=9 (Not possible, since x can’t be negative)

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

p=49(5)2=4925=24

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

x1=

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