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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 = 250 x                             p = 150 + x

To determine

To calculate: The consumer and producer surpluses if the demand function is p=250x and supply function is p=150+x.

Explanation

Given information:

The demand function is p=250x and supply function is p=150+x.

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=250x and supply function p=150+x

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

250x=150+x100=2xx=50

Substitute the x for 50 in p=150+x

p=150+x=150+(50)=200

The price of 50 units is $200

To find the consumer surplus use the formula,

0x(demand functionprice)dx=050[(250x)200]dx=050

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