Chapter 5.5, Problem 47E

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10th Edition

Ron Larson

ISBN: 9781305860919

Textbook Problem

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**Consumer and Producer Surpluses** In Exercises 43-48, 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). *See Example 5.*

*Demand Function Supply Function*

To determine

**To calculate:** The consumer and producer surpluses for a product whose demand and supply functions are modeled by

Explanation

**Given Information:**

The demand and supply functions for a product are modeled by

Here, *p* is the price (in dollars) and *x* is the number of units (in millions).

**Formula used:**

The consumer surplus is the area of the region bounded by the graph of the demand function, the horizontal line

The producer surplus is the area of the region bounded by the graph of the supply function, the horizontal line

Here

**Calculation:**

Consider the demand and supply functions,

Compute the points of intersection of two graphs by setting the functions equal to each other and solving for *x*,

Divide both sides by

Substitute

So, the equilibrium point occurs at

Use the formula for the consumer surplus and calculated it for the provided product as follows:

Sect-5.1 P-1CPSect-5.1 P-2CPSect-5.1 P-3CPSect-5.1 P-4CPSect-5.1 P-5CPSect-5.1 P-6CPSect-5.1 P-7CPSect-5.1 P-8CPSect-5.1 P-1SWUSect-5.1 P-2SWU

Sect-5.1 P-3SWUSect-5.1 P-4SWUSect-5.1 P-5SWUSect-5.1 P-6SWUSect-5.1 P-7SWUSect-5.1 P-8SWUSect-5.1 P-9SWUSect-5.1 P-10SWUSect-5.1 P-1ESect-5.1 P-2ESect-5.1 P-3ESect-5.1 P-4ESect-5.1 P-5ESect-5.1 P-6ESect-5.1 P-7ESect-5.1 P-8ESect-5.1 P-9ESect-5.1 P-10ESect-5.1 P-11ESect-5.1 P-12ESect-5.1 P-13ESect-5.1 P-14ESect-5.1 P-15ESect-5.1 P-16ESect-5.1 P-17ESect-5.1 P-18ESect-5.1 P-19ESect-5.1 P-20ESect-5.1 P-21ESect-5.1 P-22ESect-5.1 P-23ESect-5.1 P-24ESect-5.1 P-25ESect-5.1 P-26ESect-5.1 P-27ESect-5.1 P-28ESect-5.1 P-29ESect-5.1 P-30ESect-5.1 P-31ESect-5.1 P-32ESect-5.1 P-33ESect-5.1 P-34ESect-5.1 P-35ESect-5.1 P-36ESect-5.1 P-37ESect-5.1 P-38ESect-5.1 P-39ESect-5.1 P-40ESect-5.1 P-41ESect-5.1 P-42ESect-5.1 P-43ESect-5.1 P-44ESect-5.1 P-45ESect-5.1 P-46ESect-5.1 P-47ESect-5.1 P-48ESect-5.1 P-49ESect-5.1 P-50ESect-5.1 P-51ESect-5.1 P-52ESect-5.1 P-53ESect-5.1 P-54ESect-5.1 P-55ESect-5.1 P-56ESect-5.1 P-57ESect-5.1 P-58ESect-5.1 P-59ESect-5.1 P-60ESect-5.1 P-61ESect-5.1 P-62ESect-5.1 P-63ESect-5.1 P-64ESect-5.1 P-65ESect-5.1 P-66ESect-5.1 P-67ESect-5.1 P-68ESect-5.1 P-69ESect-5.1 P-70ESect-5.1 P-71ESect-5.1 P-72ESect-5.1 P-73ESect-5.1 P-74ESect-5.1 P-75ESect-5.2 P-1CPSect-5.2 P-2CPSect-5.2 P-3CPSect-5.2 P-4CPSect-5.2 P-5CPSect-5.2 P-6CPSect-5.2 P-7CPSect-5.2 P-8CPSect-5.2 P-1SWUSect-5.2 P-2SWUSect-5.2 P-3SWUSect-5.2 P-4SWUSect-5.2 P-5SWUSect-5.2 P-6SWUSect-5.2 P-7SWUSect-5.2 P-8SWUSect-5.2 P-9SWUSect-5.2 P-1ESect-5.2 P-2ESect-5.2 P-3ESect-5.2 P-4ESect-5.2 P-5ESect-5.2 P-6ESect-5.2 P-7ESect-5.2 P-8ESect-5.2 P-9ESect-5.2 P-10ESect-5.2 P-11ESect-5.2 P-12ESect-5.2 P-13ESect-5.2 P-14ESect-5.2 P-15ESect-5.2 P-16ESect-5.2 P-17ESect-5.2 P-18ESect-5.2 P-19ESect-5.2 P-20ESect-5.2 P-21ESect-5.2 P-22ESect-5.2 P-23ESect-5.2 P-24ESect-5.2 P-25ESect-5.2 P-26ESect-5.2 P-27ESect-5.2 P-28ESect-5.2 P-29ESect-5.2 P-30ESect-5.2 P-31ESect-5.2 P-32ESect-5.2 P-33ESect-5.2 P-34ESect-5.2 P-35ESect-5.2 P-36ESect-5.2 P-37ESect-5.2 P-38ESect-5.2 P-39ESect-5.2 P-40ESect-5.2 P-41ESect-5.2 P-42ESect-5.2 P-43ESect-5.2 P-44ESect-5.2 P-45ESect-5.2 P-46ESect-5.2 P-47ESect-5.2 P-48ESect-5.2 P-49ESect-5.2 P-50ESect-5.2 P-51ESect-5.2 P-52ESect-5.2 P-53ESect-5.2 P-54ESect-5.2 P-55ESect-5.2 P-56ESect-5.2 P-57ESect-5.2 P-58ESect-5.2 P-59ESect-5.2 P-60ESect-5.2 P-61ESect-5.2 P-62ESect-5.3 P-1CPSect-5.3 P-2CPSect-5.3 P-3CPSect-5.3 P-4CPSect-5.3 P-5CPSect-5.3 P-6CPSect-5.3 P-7CPSect-5.3 P-1SWUSect-5.3 P-2SWUSect-5.3 P-3SWUSect-5.3 P-4SWUSect-5.3 P-5SWUSect-5.3 P-6SWUSect-5.3 P-7SWUSect-5.3 P-8SWUSect-5.3 P-1ESect-5.3 P-2ESect-5.3 P-3ESect-5.3 P-4ESect-5.3 P-5ESect-5.3 P-6ESect-5.3 P-7ESect-5.3 P-8ESect-5.3 P-9ESect-5.3 P-10ESect-5.3 P-11ESect-5.3 P-12ESect-5.3 P-13ESect-5.3 P-14ESect-5.3 P-15ESect-5.3 P-16ESect-5.3 P-17ESect-5.3 P-18ESect-5.3 P-19ESect-5.3 P-20ESect-5.3 P-21ESect-5.3 P-22ESect-5.3 P-23ESect-5.3 P-24ESect-5.3 P-25ESect-5.3 P-26ESect-5.3 P-27ESect-5.3 P-28ESect-5.3 P-29ESect-5.3 P-30ESect-5.3 P-31ESect-5.3 P-32ESect-5.3 P-33ESect-5.3 P-34ESect-5.3 P-35ESect-5.3 P-36ESect-5.3 P-37ESect-5.3 P-38ESect-5.3 P-39ESect-5.3 P-40ESect-5.3 P-41ESect-5.3 P-42ESect-5.3 P-43ESect-5.3 P-44ESect-5.3 P-45ESect-5.3 P-46ESect-5.3 P-47ESect-5.3 P-48ESect-5.3 P-49ESect-5.3 P-50ESect-5.3 P-51ESect-5.3 P-52ESect-5.3 P-53ESect-5.3 P-54ESect-5.3 P-55ESect-5.3 P-56ESect-5.3 P-57ESect-5.3 P-58ESect-5.3 P-1QYSect-5.3 P-2QYSect-5.3 P-3QYSect-5.3 P-4QYSect-5.3 P-5QYSect-5.3 P-6QYSect-5.3 P-7QYSect-5.3 P-8QYSect-5.3 P-9QYSect-5.3 P-10QYSect-5.3 P-11QYSect-5.3 P-12QYSect-5.3 P-13QYSect-5.3 P-14QYSect-5.3 P-15QYSect-5.3 P-16QYSect-5.3 P-17QYSect-5.3 P-18QYSect-5.3 P-19QYSect-5.3 P-20QYSect-5.3 P-21QYSect-5.4 P-1CPSect-5.4 P-2CPSect-5.4 P-3CPSect-5.4 P-4CPSect-5.4 P-5CPSect-5.4 P-6CPSect-5.4 P-7CPSect-5.4 P-8CPSect-5.4 P-9CPSect-5.4 P-1SWUSect-5.4 P-2SWUSect-5.4 P-3SWUSect-5.4 P-4SWUSect-5.4 P-5SWUSect-5.4 P-6SWUSect-5.4 P-7SWUSect-5.4 P-1ESect-5.4 P-2ESect-5.4 P-3ESect-5.4 P-4ESect-5.4 P-5ESect-5.4 P-6ESect-5.4 P-7ESect-5.4 P-8ESect-5.4 P-9ESect-5.4 P-10ESect-5.4 P-11ESect-5.4 P-12ESect-5.4 P-13ESect-5.4 P-14ESect-5.4 P-15ESect-5.4 P-16ESect-5.4 P-17ESect-5.4 P-18ESect-5.4 P-19ESect-5.4 P-20ESect-5.4 P-21ESect-5.4 P-22ESect-5.4 P-23ESect-5.4 P-24ESect-5.4 P-25ESect-5.4 P-26ESect-5.4 P-27ESect-5.4 P-28ESect-5.4 P-29ESect-5.4 P-30ESect-5.4 P-31ESect-5.4 P-32ESect-5.4 P-33ESect-5.4 P-34ESect-5.4 P-35ESect-5.4 P-36ESect-5.4 P-37ESect-5.4 P-38ESect-5.4 P-39ESect-5.4 P-40ESect-5.4 P-41ESect-5.4 P-42ESect-5.4 P-43ESect-5.4 P-44ESect-5.4 P-45ESect-5.4 P-46ESect-5.4 P-47ESect-5.4 P-48ESect-5.4 P-49ESect-5.4 P-50ESect-5.4 P-51ESect-5.4 P-52ESect-5.4 P-53ESect-5.4 P-54ESect-5.4 P-55ESect-5.4 P-56ESect-5.4 P-57ESect-5.4 P-58ESect-5.4 P-59ESect-5.4 P-60ESect-5.4 P-61ESect-5.4 P-62ESect-5.4 P-63ESect-5.4 P-64ESect-5.4 P-65ESect-5.4 P-66ESect-5.4 P-67ESect-5.4 P-68ESect-5.4 P-69ESect-5.4 P-70ESect-5.4 P-71ESect-5.4 P-72ESect-5.4 P-73ESect-5.4 P-74ESect-5.4 P-75ESect-5.4 P-76ESect-5.4 P-77ESect-5.4 P-78ESect-5.4 P-79ESect-5.5 P-1CPSect-5.5 P-2CPSect-5.5 P-3CPSect-5.5 P-4CPSect-5.5 P-5CPSect-5.5 P-6CPSect-5.5 P-1SWUSect-5.5 P-2SWUSect-5.5 P-3SWUSect-5.5 P-4SWUSect-5.5 P-5SWUSect-5.5 P-6SWUSect-5.5 P-7SWUSect-5.5 P-8SWUSect-5.5 P-1ESect-5.5 P-2ESect-5.5 P-3ESect-5.5 P-4ESect-5.5 P-5ESect-5.5 P-6ESect-5.5 P-7ESect-5.5 P-8ESect-5.5 P-9ESect-5.5 P-10ESect-5.5 P-11ESect-5.5 P-12ESect-5.5 P-13ESect-5.5 P-14ESect-5.5 P-15ESect-5.5 P-16ESect-5.5 P-17ESect-5.5 P-18ESect-5.5 P-19ESect-5.5 P-20ESect-5.5 P-21ESect-5.5 P-22ESect-5.5 P-23ESect-5.5 P-24ESect-5.5 P-25ESect-5.5 P-26ESect-5.5 P-27ESect-5.5 P-28ESect-5.5 P-29ESect-5.5 P-30ESect-5.5 P-31ESect-5.5 P-32ESect-5.5 P-33ESect-5.5 P-34ESect-5.5 P-35ESect-5.5 P-36ESect-5.5 P-37ESect-5.5 P-38ESect-5.5 P-39ESect-5.5 P-40ESect-5.5 P-41ESect-5.5 P-42ESect-5.5 P-43ESect-5.5 P-44ESect-5.5 P-45ESect-5.5 P-46ESect-5.5 P-47ESect-5.5 P-48ESect-5.5 P-49ESect-5.5 P-50ESect-5.5 P-51ESect-5.5 P-52ESect-5.5 P-53ESect-5.5 P-54ESect-5.5 P-55ESect-5.5 P-56ESect-5.5 P-57ESect-5.5 P-58ESect-5.6 P-1CPSect-5.6 P-2CPSect-5.6 P-3CPSect-5.6 P-1SWUSect-5.6 P-2SWUSect-5.6 P-3SWUSect-5.6 P-4SWUSect-5.6 P-5SWUSect-5.6 P-6SWUSect-5.6 P-7SWUSect-5.6 P-8SWUSect-5.6 P-9SWUSect-5.6 P-10SWUSect-5.6 P-1ESect-5.6 P-2ESect-5.6 P-3ESect-5.6 P-4ESect-5.6 P-5ESect-5.6 P-6ESect-5.6 P-7ESect-5.6 P-8ESect-5.6 P-9ESect-5.6 P-10ESect-5.6 P-11ESect-5.6 P-12ESect-5.6 P-13ESect-5.6 P-14ESect-5.6 P-15ESect-5.6 P-16ESect-5.6 P-17ESect-5.6 P-18ESect-5.6 P-19ESect-5.6 P-20ESect-5.6 P-29ESect-5.6 P-30ESect-5.6 P-31ESect-5.6 P-33ECh-5 P-1RECh-5 P-2RECh-5 P-3RECh-5 P-4RECh-5 P-5RECh-5 P-6RECh-5 P-7RECh-5 P-8RECh-5 P-9RECh-5 P-10RECh-5 P-11RECh-5 P-12RECh-5 P-13RECh-5 P-14RECh-5 P-15RECh-5 P-16RECh-5 P-17RECh-5 P-18RECh-5 P-19RECh-5 P-20RECh-5 P-21RECh-5 P-22RECh-5 P-23RECh-5 P-24RECh-5 P-25RECh-5 P-26RECh-5 P-27RECh-5 P-28RECh-5 P-29RECh-5 P-30RECh-5 P-31RECh-5 P-32RECh-5 P-33RECh-5 P-34RECh-5 P-35RECh-5 P-36RECh-5 P-37RECh-5 P-38RECh-5 P-39RECh-5 P-40RECh-5 P-41RECh-5 P-42RECh-5 P-43RECh-5 P-44RECh-5 P-45RECh-5 P-46RECh-5 P-47RECh-5 P-48RECh-5 P-49RECh-5 P-50RECh-5 P-51RECh-5 P-52RECh-5 P-53RECh-5 P-54RECh-5 P-55RECh-5 P-56RECh-5 P-57RECh-5 P-58RECh-5 P-59RECh-5 P-60RECh-5 P-61RECh-5 P-62RECh-5 P-63RECh-5 P-64RECh-5 P-65RECh-5 P-66RECh-5 P-67RECh-5 P-68RECh-5 P-69RECh-5 P-70RECh-5 P-71RECh-5 P-72RECh-5 P-73RECh-5 P-74RECh-5 P-75RECh-5 P-76RECh-5 P-77RECh-5 P-78RECh-5 P-79RECh-5 P-80RECh-5 P-81RECh-5 P-82RECh-5 P-83RECh-5 P-84RECh-5 P-85RECh-5 P-86RECh-5 P-87RECh-5 P-88RECh-5 P-89RECh-5 P-90RECh-5 P-91RECh-5 P-92RECh-5 P-93RECh-5 P-94RECh-5 P-95RECh-5 P-96RECh-5 P-97RECh-5 P-98RECh-5 P-99RECh-5 P-100RECh-5 P-101RECh-5 P-102RECh-5 P-103RECh-5 P-104RECh-5 P-105RECh-5 P-106RECh-5 P-107RECh-5 P-108RECh-5 P-109RECh-5 P-110RECh-5 P-111RECh-5 P-112RECh-5 P-113RECh-5 P-114RECh-5 P-115RECh-5 P-1TYSCh-5 P-2TYSCh-5 P-3TYSCh-5 P-4TYSCh-5 P-5TYSCh-5 P-6TYSCh-5 P-7TYSCh-5 P-8TYSCh-5 P-9TYSCh-5 P-10TYSCh-5 P-11TYSCh-5 P-12TYSCh-5 P-13TYSCh-5 P-14TYSCh-5 P-15TYSCh-5 P-16TYSCh-5 P-17TYSCh-5 P-18TYSCh-5 P-19TYSCh-5 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