Question

Supply and Demand Suppose that the supply function for walnuts is $p=S(q)=0.25 q+3.6,$ where $p$ is the price in dollars per pound and $q$ is the quantity in bushels. Suppose also that the equilibrium price is $\$ 5.85,$ and the demand is 4 bushels when the price is $\$ 7.60 .$ Find an equation for the demand function, assuming it is linear.

          Supply and Demand Suppose that the supply function for walnuts is $p=S(q)=0.25 q+3.6,$ where $p$ is the price in dollars per pound and $q$ is the quantity in bushels. Suppose also that the equilibrium price is $\$ 5.85,$ and the demand is 4 bushels when the price is $\$ 7.60 .$ Find an equation for the demand function, assuming it is linear.
        
Show more…

Added by Daniel L.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
Supply and Demand Suppose that the supply function for walnuts is $p=S(q)=0.25 q+3.6,$ where $p$ is the price in dollars per pound and $q$ is the quantity in bushels. Suppose also that the equilibrium price is $\$ 5.85,$ and the demand is 4 bushels when the price is $\$ 7.60 .$ Find an equation for the demand function, assuming it is linear.
Close icon
Play audio
Feedback
Powered by NumerAI
Danielle Fairburn Kathleen Carty
Ivan Kochetkov verified

Vincenzo Zaccaro and 81 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.

*

Recommended Videos

-
supply-and-demand-suppose-that-the-supply-function-for-honey-is-psq05-q25-where-p-is-the-price-in-do

Supply and Demand Suppose that the supply function for honey is $p=S(q)=0.5 q+2.5,$ where $p$ is the price in dollars for an $8-$ oz container and $q$ is the quantity in barrels. Suppose also that the equilibrium price is $\$ 5$ and the demand is 4 barrels when the price is $\$ 6.5 .$ Find an equation for the demand function, assuming it is linear.

Calculus with Applications

Linear Functions

Linear Functions and Applications

supply-and-demand-suppose-that-the-supply-function-for-honey-is-psq03-q27-where-p-is-the-price-in-do

Supply and Demand Suppose that the supply function for honey is $p=S(q)=0.3 q+2.7,$ where $p$ is the price in dollars for an 8 -oz container and $q$ is the quantity in barrels. Suppose also that the equilibrium price is $\$ 4.50$ and the demand is 2 barrels when the price is $\$ 6.10$ . Find an equation for the demand function, assuming it is linear.

Finite Mathematics and Calculus with Applications

Linear Functions

Linear Functions and Applications

supply-and-demand-suppose-that-the-supply-function-for-honey-is-psq03-q27-where-p-is-the-price-in-do

Supply and Demand Suppose that the supply function for honey is $p=S(q)=0.3 q+2.7,$ where $p$ is the price in dollars for an 8 -oz container and $q$ is the quantity in barrels. Suppose also that the equilibrium price is $\$ 4.50$ and the demand is 2 barrels when the price is $\$ 6.10$ . Find an equation for the demand function, assuming it is linear.

Finite Mathematics and Calculus with Applications

Linear Functions

Linear Functions and Applications


*

Recommended Textbooks

-
Calculus: Early Transcendentals

Calculus: Early Transcendentals

James Stewart 8th Edition
achievement 1,733 solutions
Calculus: Early Transcendentals

Calculus: Early Transcendentals

William Briggs, Lyle Cochran, Bernard Gillet 3rd Edition
achievement 1,120 solutions
Thomas Calculus

Thomas Calculus

George B. Thomas Jr. 14th Edition
achievement 1,879 solutions

*

Transcript

-
00:01 Okay, so first of all, we know that our demand function is a function of the form q equals ap, oh, this one is p, ap plus b, because we know that our demand function is linear.
00:19 Okay, perfect.
00:21 Now here we are going to use two things.
00:24 The first thing is this.
00:26 We know that the equilibrium price is 5 .85.
00:32 So, p star, the equilibrium price, is 5 .85.
00:38 And well, this pink implies what? this pink implies that 5 .85 is equal to s of q star, the equilibrium quantity, which is going to and be 0 .25 q star plus 3 .6 perfect and we know that this q star here is exactly the evaluation of our demand function at p star so q star is a multiplied by p star a a multiplied by p star which is 5 .85 plus b okay perfect now we are going to plug this value of q star into this equation here so what are we going to get well we are going to get 5 .85 which is the equilibrium price equals this guy here which is 0 .25 multiplied by a 5 .85 plus b plus 3 .6 so we are gonna have a multiplied by 0 .25 multiplied by 5 .85 let's compute this guy so 5 .85 divided by 4 which is 1 .4625 plus okay, let me do plus 3 .6 first.
02:36 Oh, my bad.
02:39 Here we have this guy multiplied by a, so we can add 3 .6 to this guy.
02:47 Okay, so that being said, we are going to have a multiplied by 1 .4625 plus 0 .25b plus 3 .6b plus 3 .6 .6.
03:03 Okay perfect now what are we gonna have we are gonna have that the demand is four bushels when the price is 7 .60 and we are gonna use this thing here we are gonna use this equation here together with this one to find a and b okay so we have okay for equals.
03:35 Okay, 4 is going to be equal to a multiplied by 7 .60 plus b...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever