   Chapter 5, Problem 98RE ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Consumer and Producer Surpluses In Exercises 95-98, find the consumer and producer surpluses by using the demand and supply functions, where p is the price (in dollars) and x is the number of units (in millions). Demand Function Supply Function p = 500 − x                            p = 0.008 x 2 + 170

To determine

To calculate: The consumer and producer surpluses if the demand function is p=500x and supply function is p=0.008x2+170.

Explanation

Given information:

The demand function is p=500x and supply function is p=0.008x2+170.

Formula used:

The integration formula,

xndx=xn+1n+1+c

Consumer surplus is defined as,

0x(demand function price)dx

Where x is the number of units.

Producer surplus is defined as,

0x(pricesupply function)dx

Where x is the number of units.

Calculation:

Consider the demand function p=500x and supply function p=0.008x2+170

Equate the demand and supply functions to determine the equilibrium point.

500x=0.008x2+1700.008x2+x330=08x2+1000x330000=08x2+2200x1200x330000=0

Simplify the above equation,

8x(x+275)1200(x+275)=0(8x1200)(x+275)=0x=12008,275x=275,150

Substitute the x for 150 in p=0.008x2+170

p=0.008x2+170=0

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