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

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

To determine

To calculate: The consumer and producer surpluses if the demand function is p=200−0.2x and supply function is p=50+1.3x.

Explanation

Given information:

The demand function is p=200−0.2x 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(price−supply function)dx

Where x is the number of units.

Calculation:

Consider the demand function p=200−0.2x and supply function p=50+1.3x

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

200−0.2x=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[(200−0.2x)−180]dx=∫0100(20−0.2x)dx=[20x−0

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Fill in the blanks. The set of input numbers x in a function is called the _______ of the function.

College Algebra (MindTap Course List)

Russia has recently started a push for stronger smoking regulations much like those in Western countries concer...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Why is it necessary to have a stable pattern within a phase?

Research Methods for the Behavioral Sciences (MindTap Course List)

The Economic Policy Institute periodically issues reports on wages of entry level workers. The institute report...

Statistics for Business & Economics, Revised (MindTap Course List)

Which is greater (n)n+1 or (n+1)n where n8?

Calculus (MindTap Course List)

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