Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

In a purely competitive market, the price of a go…

04:37

Question

Answered step-by-step

Problem 7 Medium Difficulty

If a supply curve is modeled by the equation $ p = 125 + 0.002x^2 $, find the producer surplus when the
selling price is $625.


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Brett Boyer
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Brett Boyer

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 8

Further Applications of Integration

Section 4

Applications to Economics and Biology

Related Topics

Applications of Integration

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Calculus 2 / BC Courses

Lectures

Join Course
Recommended Videos

01:10

If a supply curve is model…

02:45

The supply curve for produ…

02:11

Find the producers' s…

07:54

Calculate the producers &#…

04:55

Find the consumers' s…

07:04

Calculate the producers &#…

11:53

Calculate the producers &#…

06:03

Calculate the producers &#…

03:17

Given the demand curve $p=…

05:27

Calculate the producers &#…

Watch More Solved Questions in Chapter 8

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23

Video Transcript

Okay, So the question asks what producer surplus will be when we're given a good that is priced at $625 and I will dash that line and then a supply curve that'll draw in here of P is equal to 1 25 plus 0.2 x squared. So as a quick refresher producer surplus is going to be this area shaded in green to get it, we're going to first find this point of intersection. Then we're going to solve four this blue area, then this red area and subtract the two, which will leave us with the green area. So first to find the point of intersection. So to do that, we just set 625 equal to 1 25 plus 0.2 x squared. And then we subtract. Getting that 500 is equal to 0.2 x weird. And then once we divide out by 0.2 we get that X squared is equal to 250,000 so x could be plus or minus 500. And if you look at this price versus quantity graph. You can see that we're considering the positive branch of this parabola. So the value of X that we're concerned about is positive. 500. So now that we've found the point of intersection, first we get the blue area, which is just the area of a rectangle. So we solved for that by simply taking 625 multiplying by 500 and getting 312,000 500. Then for the red, I'm going to take the integral from zero 2 500 of 1 25 close 0.2 x squared DX. So we're going to get 1 25 x evaluated at zero and 500 plus 0.2 over three x cubed taken from bureau 2 500 which is 62,000 500 plus a 3333. And then there is a 0.3 repeating so altogether we're going to get 3 12 500 minus stuff in red again, 62,500 for the first part and 83,333 only three for the second part. And when all is said is said and done. We're going to get 166,000 666 point 66 dot, dot dot and because we're talking about dollars, we're going to get 166,000 600 and 67 dollars, and this right here is the answer.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
162
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
70
Hosted by: Alonso M
See More

Related Topics

Applications of Integration

Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Recommended Videos

01:10

If a supply curve is modeled by the equation $p=200+0.2 x^{3 / 2}$ . find the …

02:45

The supply curve for product X is given by QXS = -520 + 20PX . How much surplus…

02:11

Find the producers' surplus at a price level of $\bar{p}=\$ 55$ for the price-s…

07:54

Calculate the producers 'surplus for each of the supply equations at the indica…

04:55

Find the consumers' surplus and the producers' surplus at the equilibrium price…

07:04

Calculate the producers 'surplus for each of the supply equations at the indica…

11:53

Calculate the producers 'surplus for each of the supply equations at the indica…

06:03

Calculate the producers 'surplus for each of the supply equations at the indica…

03:17

Given the demand curve $p=35-q^{2}$ and the supply curve $p=3+q^{2},$ find the …

05:27

Calculate the producers 'surplus for each of the supply equations at the indica…
Additional Mathematics Questions

01:48

Construct a table of values of the following functions using the interval of…

02:12

ASSESSMENT Credit Checkpoint Complete the following problems Show all your w…

03:00

Are the graphs of each pair of equations parallel perpendicular; or neither?…

03:27

Learning Task 2. Find the equation of the line Write in slope intercept form…

01:17

Length: x = 3x+2 Width: y=x+5
Question 2
Question
Write an expressi…

01:21

Graph the line by plotting any two ordered pairs with integer value coordina…

02:04

Astraw is placed inside a rectangular box that is 7 inches by 10 inches by 1…

01:20

Given that XY is a line segment with the angle @ = 61= work out the value of…

01:43

Greg's driveway is 20.5 meters long:
Distance Equivalent 1m = 3.28 f…

02:21

Let ab5c be all four-digit multiples of number 36 with distinct digits How m…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started