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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

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

Explanation

Given information:

The demand function is p=500−x 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(price−supply function)dx

Where x is the number of units.

Calculation:

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

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

500−x=0.008x2+1700.008x2+x−330=08x2+1000x−330000=08x2+2200x−1200x−330000=0

Simplify the above equation,

8x(x+275)−1200(x+275)=0(8x−1200)(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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Define and compute the three measures of central tendency.

Research Methods for the Behavioral Sciences (MindTap Course List)

The accompanying relative frequency table is based on data from the 2016 College Bound Seniors Report (collegeb...

Introduction To Statistics And Data Analysis

Verify that the functions are inverses by showing that fg and gf are the identity function. fx=x5-2 and gx=x+25

College Algebra (MindTap Course List)

Area In Exercises 75 and 76, find the area of the given region using any method. y=125x2

Calculus (MindTap Course List)

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