   Chapter 5, Problem 96RE ### 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 = 200 − 0.2 x                         p = 50 + 1.3 x

To determine

To calculate: The consumer and producer surpluses if the demand function is p=2000.2x and supply function is p=50+1.3x.

Explanation

Given information:

The demand function is p=2000.2x and supply function is p=50+1.3x.

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=2000.2x and supply function p=50+1.3x

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

2000.2x=50+1.3x150=1.5xx=100

Substitute the x for 100 in p=50+1.3x

p=50+1.3x=50+1.3(100)=180

The price of hundred units is \$180.

To find the Consumer surplus by the use the formula,

0x(demand function price)dx=0100[(2000.2x)180]dx=0100(200.2x)dx=[20x0

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