   Chapter 5.5, Problem 48E ### 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
1 views

# 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 p = 62 − 0.3 x                        p = 0.002 x 2 + 12

To determine

To calculate: The consumer and producer surpluses for a product whose demand and supply functions are modeled by Demand:p=620.3x and Supply:p=0.002x2+12

Explanation

Given Information:

The demand and supply functions for a product are modeled by

Demand:p=620.3x and Supply:p=0.002x2+12

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 p=p0 and the vertical line x=0.

Consumer surplus=0x0[demand functionprice]dx

The producer surplus is the area of the region bounded by the graph of the supply function, the horizontal line p=p0 and the vertical line x=0.

Producer surplus=0x0[pricesupply function]dx

Here (x0,p0) is the equilibrium point at which the demand function and supply function intersect.

Calculation:

Consider the demand and supply functions,

Demand:p=620.3x and Supply:p=0.002x2+12

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

Demand=Supply620.3x=0.002x2+120.002x2+0.3x50=0x2+150x25,000=0

Simplify further,

x2+250x100x25,000=0x(x+250)100(x+250)=0(x+250)(x100)=0x=250, 100

The value of x cannot be negative, so

x=100

Substitute x=100 in the demand function p=620.3x and compute the price,

p0=620.3×100=6230=32

So, the equilibrium point occurs at x=100 million and the price is \$ 32 per unit.

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

Consumer surplus=0x0[demand functionprice]dx=0100[(620

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Place the following set of n = 20 scores in a frequency distribution table.

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### Find the minimum cost C (in dollars), given that 5(C 25) 1.75 + 2.5C

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In problems 31-36, simplify each expression. 34.

Mathematical Applications for the Management, Life, and Social Sciences

#### Estimate 14(x3x2) using the Left Endpoint Rule and n = 5. a) 203 b) 20 c) 24 d) 30

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### The scalar projection of on is:

Study Guide for Stewart's Multivariable Calculus, 8th 