Find the consumer and producer surpluses where p=-0.00625x^3+100 is the demand function and p=0.025x^2+40 is the supply function

Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Functions
Section9.CR: Review Problem Set
Problem 37CR: A garden has 60 yards of fencing and wants to enclose a rectangular garden that requires fencing...
icon
Related questions
icon
Concept explainers
Topic Video
Question

Find the consumer and producer surpluses where p=-0.00625x^3+100 is the demand function and p=0.025x^2+40 is the supply function
 
Expert Solution
Step 1

Given:

Calculus homework question answer, step 1, image 1

Step 2

Consumer and Producer Surplus:

Given a demand function p=d(q)p = D(x) and a supply function p=s(q)p = S(x), and the equilibrium point (x*,p*). Then,

The consumer surplus is

Calculus homework question answer, step 2, image 1

The producer surplus is

Calculus homework question answer, step 2, image 2

(q,p)

Step 3

First, find an equilibrium point. The equilibrium point is a point at which demand and supply functions are equal.

Calculus homework question answer, step 3, image 1

Using calculator we get,

Calculus homework question answer, step 3, image 2

Now find p, using one of the demand or supply function at x=20.

Calculus homework question answer, step 3, image 3

Therefore, the equilibrium point is (x*,p*)=(20, 50).

steps

Step by step

Solved in 5 steps with 8 images

Blurred answer
Knowledge Booster
Application of Algebra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Intermediate Algebra
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning