Calculus: Find E for q=Cp^(-k) & Maximize Revenue

  • Thread starter rain
  • Start date
  • Tags
    Calculus
In summary, the conversation discusses a demand function with variables C and k, and how to find E in relation to maximizing revenue. The answer for part a is E=k, and for parts b, c, and d, the value of k determines how prices should be set to maximize revenue. If k<1, prices should be set lower, if k>1, prices should be set higher, and if k=1, prices can be set at any value. The demand function is also questioned for its realism. The definition of "elasticity" is not provided, but it is connected to how demand varies.
  • #1
rain
11
0
I have some question on elasticity.
If the demand function is q=Cp^(-k), where C and k are positive constants.

a)Find E.
b)if 0<k<1, what does your answer from part a say about how prices should be set to maximize the revenue?
c)if k>1, what does your answer from part a say about how prices should be set to maximize the revenue?
d)if k=1, what does your answer from part a tell you about setting prices to maximize revenue?
e)is this demand function realistic?

part a) my answer is E=k
How do you use part a in answering parts b,c,d,e?
 
Physics news on Phys.org
  • #2
What is the definition of "elasticity"?

How is that connected to how demand varies?
 

FAQ: Calculus: Find E for q=Cp^(-k) & Maximize Revenue

What is the basic concept behind calculus?

Calculus is a branch of mathematics that deals with the study of continuous change. It involves the use of derivatives and integrals to study the rates of change of various quantities.

How is calculus used to find the value of E for the given equation?

In this equation, E represents the maximum revenue, and it can be found by taking the derivative of the equation with respect to Cp and setting it equal to zero. This will give the value of Cp that maximizes the revenue, which can then be substituted back into the original equation to find the value of E.

What is the significance of maximizing revenue in calculus?

In calculus, maximizing revenue is important as it helps businesses and individuals make informed decisions about their products and services. By finding the maximum revenue, they can determine the optimal price to charge for their goods or services.

What role does the constant k play in the given equation?

The constant k represents the rate at which the revenue decreases as the price (Cp) increases. It is a crucial factor in determining the optimal price, as a higher k value would mean a steeper decrease in revenue with increasing price.

Can calculus be applied to other real-world problems besides maximizing revenue?

Yes, calculus is a fundamental tool in many fields such as physics, engineering, economics, and more. It can be used to solve a wide range of problems involving rates of change, optimization, and approximation.

Similar threads

Proving piecewise function is k-differentiable
Replies
5
Views
1K
Prove ##|\{ q\in\mathbb{Q}: q>0 \} |=|\mathbb{N}|##.
Replies
3
Views
1K
Finding the derivative of a revenue function
Replies
7
Views
3K
Computing conditional extinction probabilities for pollen cells
Replies
1
Views
732
Demand and revenue question: help?
Replies
2
Views
1K
Multivariable Limit Problem: Find Values of k That Make Limit Exist
Replies
9
Views
1K
Find Values of Osculating Circle Tangent to a Parabola
Replies
4
Views
838
Show N is a normal subgroup and G/N has finite element
Replies
2
Views
1K
How should I show that the transformation makes the system Hamiltonian?
Replies
4
Views
699
Economics Homework -- Maximizing Profits....
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top