MHB Find Price Elasticity of Demand

  • Thread starter Thread starter mathkid3
  • Start date Start date
  • Tags Tags
    Elasticity
mathkid3
Messages
23
Reaction score
0
Find price elasticity of demand for the demand function at the indicated x-value.

Is the demand elastic, inelastic or of unit elasticity at the indicated x-value?

Use a graphing utility to graph the revenue function, and identify the intervals of elasticity and inelasticity. ... I will list all information I can to help someone to help me to solve and understand the problem.

Demand Function = p = (500)/(x^2) + 5

x-value = 5

The following may be of help as well...

Definition of Price Elasticity of Demand - If p = f(x) is a differentiable function, then the price elasticity of demand is given by

N = (p/x)/(dp/dx)

where N is the lowercase Greek letter eta. For a given price, the demand is elastic when abs(absolute) value N > 1, the demand is inelastic when abs N < 1, and the demand has unit elasticity when abs N = 1Thanks in advance for any and all assistance on this Calculus problem

-mathkid3 (Happy)
 
Mathematics news on Phys.org
Well, I would begin by computing $\displaystyle \frac{dp}{dx}|_{x=5}$

Next, I would compute $\displaystyle \frac{p(5)}{5}$.

Once you have these two numbers, then compute their quotient to get the price elasticity of demand $\displaystyle \eta$.

Now, let's see what you get...

By the way, this site also supports the rendering of $\displaystyle \LaTeX$. The difference is (at least the way I do it) is to enclose your code with the tags:

Code:
$\displaystyle insert code here$
 
Last edited:
Mark,

so glad you are on this site and you have already helped me so much with understanding some of these Calculus problems.

ok ..let's see...

You said first to find the derV of p so I get

(x-1000)/(x^3)

next you say find p(5)/(5)

Areyou saying to plug 5 into the original function and then divided the outcome by 5?

if so I get x = 5

am I correct thus far and if so tell me again what to do next?

If I am not correct, would you explain to me again what to do ?

Thank You
 
Last edited by a moderator:
mathkid3 said:
The following may be of help as well...

Definition of Price Elasticity of Demand - If p = f(x) is a differentiable function, then the price elasticity of demand is given by

N = (p/x)/(dp/dx)

where N is the lowercase Greek letter eta. For a given price, the demand is elastic when abs(absolute) value N > 1, the demand is inelastic when abs N < 1, and the demand has unit elasticity when abs N = 1

Your definition of elasticity:
\[E_d=\frac{p}{x \frac{dp}{dx}}\]
is the reciprical of that given on the Wikipedia page linked to in your other thread:
\[E_d=\frac{x}{p}\frac{dp}{dx}\]
(Note that the Wikipedia page uses \(Q\) for demand (quantity) and \(P\) for price).

Now the table the Wikipedia page gives for interpreting \(E_p\) is exactly the same as that given above by you, so there is a mistake somewhere.

CB
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
Back
Top