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

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Chapter 5, Problem 20TYS
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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
1 views

The demand and supply functions for a product are modeled by

Demand: p =   − 0.625 x   +   10 and Supply: p =   0.25 x   +   3 where p is the price (in dollars) and x is the number of units (in millions). Find the consumer and producer surpluses for this product.

To determine

To calculate: The consumer and producer surpluses if the demand function is p=−0.625x+10 and supply function is p=0.25x+3.

Explanation

Given information:

The demand function is p=−0.625x+10 and supply function is p=0.25x+3.

Formula used:

Basic integration rule,

∫xndx=xn+1n+1+c

Consumer surplus is defined as,

∫0x(demand function− price)dx

Where x is the number of units.

Producer surplus,

∫0x(price−supply function)dx

Where x is the number of units.

Calculation:

Consider the demand function p=−0.625x+10 and supply function p=0.25x+3

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

−0.625x+10=0.25x+30.875x=7x=8

Substitute the x for 8 in p=0.25x+3

p=0.25x+3=0.25(8)+3=5

The price is $5

To find the consumer surplus by the use the formula,

∫0x(demand function− price)dx=∫08[(−0.625x+10)−5]dx=∫08(−0.625x+5)dx=[−0

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Research Methods for the Behavioral Sciences (MindTap Course List)

Data for a sample of 55 members of the Baseball Hall of Fame in Cooperstown, New York, are shown here. Each obs...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

The accompanying frequency distribution summarizes data on the number of times smokers who had successfully qui...

Introduction To Statistics And Data Analysis

For each of the following, identify which of the three basic principles of the Belmont Report is being violated...

Research Methods for the Behavioral Sciences (MindTap Course List)

The Bureau of Transportation Statistics Omnibus Household Survey is conducted annually and serves as an informa...

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

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