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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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 = 36 0.35 x

p = 0.05 x

To determine

To calculate: The consumer and producer surpluses if the demand function is p=360.35x

and supply function is p=0.05x.

Explanation

Given information:

The demand function is p=360.35x and supply function is p=0.05x.

Formula used:

Basic integration rule:

xndx=xn+1n+1+c

Consumer surplus:

0x(demand function price)dx

where x is the number of unit.

Producer surplus:

0x(pricesupply function)dx

where x is the number of unit.

Calculation:

Consider the demand function p=360.35x and supply function p=0.05x.

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

360.35x=0.05x0.35x0.05x=360.4x=36x=90

Substitute the value of x for 90 in p=0.05x.

p=0.05xp=0.05(90)p=4.50

Therefore, the price is $4.50.

To find the Consumer surplus,

Use the formula: 0x(demand function price)dx

0x(demand function price)dx=090[(360

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