# Find Price Elasticity of Demand

• MHB
• mathkid3
In summary, the price elasticity of demand for the given demand function at the indicated x-value is elastic. Using a graphing utility, the revenue function can be graphed and the intervals of elasticity and inelasticity can be identified. The price elasticity of demand is given by the formula 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. The demand function is p = (500)/(x^2) + 5, with an x-value
mathkid3
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)

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:
$E_d=\frac{p}{x \frac{dp}{dx}}$
$E_d=\frac{x}{p}\frac{dp}{dx}$
(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

I am happy to assist you with this problem. To find the price elasticity of demand, we will use the formula N = (p/x)/(dp/dx) as given in the definition.
First, we need to find the derivative of the demand function with respect to x.
dp/dx = -1000/x^3
Now, we can plug in the given x-value of 5 into both the demand function and the derivative to find the corresponding values.
p = (500)/(5^2) + 5 = 105
dp/dx = -1000/(5^3) = -8
Now, we can plug these values into the price elasticity of demand formula to find the value of N at x=5.
N = (105/5)/(-8) = -21/8
Since the absolute value of N is greater than 1, we can conclude that the demand is elastic at x=5.
To graph the revenue function, we can use a graphing utility and plot the function R(x) = x*p(x) where p(x) is the demand function given.
We can see that the graph has two intervals of elasticity, one on the left side of x=5 and one on the right side. The interval of inelasticity is between these two intervals of elasticity.
I hope this helps you understand the problem better. Let me know if you need any further clarification.

## 1. What is price elasticity of demand?

Price elasticity of demand is a measure of how responsive consumers are to changes in the price of a product. It specifically measures the percentage change in quantity demanded of a product in response to a percentage change in its price. A high price elasticity of demand indicates that consumers are very sensitive to price changes, while a low price elasticity of demand indicates that consumers are less sensitive to price changes.

## 2. How is price elasticity of demand calculated?

Price elasticity of demand is calculated by dividing the percentage change in quantity demanded by the percentage change in price. The formula is: Price Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price).

## 3. What factors affect price elasticity of demand?

There are several factors that can affect price elasticity of demand, including the availability of substitutes, the necessity of the product, and the proportion of a person's income spent on the product. Products with readily available substitutes tend to have a higher price elasticity of demand, while products that are considered necessities or make up a small portion of a person's income tend to have a lower price elasticity of demand.

## 4. How does price elasticity of demand impact pricing decisions?

Price elasticity of demand is an important factor to consider when making pricing decisions. A higher price elasticity of demand means that small changes in price can have a large impact on quantity demanded, so companies may need to be more cautious when raising prices. On the other hand, a lower price elasticity of demand means that changes in price will have less of an effect on quantity demanded, so companies may have more flexibility in setting prices.

## 5. How can a company use price elasticity of demand to increase sales?

Companies can use price elasticity of demand to increase sales by understanding the demand for their product and adjusting their pricing accordingly. If a company's product has a high price elasticity of demand, they may want to consider lowering their prices to attract more customers. Additionally, companies can use pricing strategies such as discounts and promotions to make their product more appealing to consumers with a lower price elasticity of demand.

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