How to calculate point price elasticity of demand with examples

Point elasticity is the price elasticity of demand at a specific point on the demand curve instead of over a range of it. It uses the same formula as the general price elasticity of demand measure, but we can take information from the demand equation to solve for the “change in” values instead of actually calculating a change given two points.  Here is the process to find the point elasticity of demand formula:

Point Price Elasticity of Demand = (% change in Quantity)/(% change in Price)
Point Price Elasticity of Demand = (∆Q/Q)/(∆P/P)
Point Price Elasticity of Demand = (P/Q)(∆Q/∆P)

Where (∆Q/∆P) is the derivative of the demand function with respect to P.  You don’t really need to take the derivative of the demand function, just find the coefficient (the number) next to Price (P) in the demand function and that will give you the value for ∆Q/∆P because it is showing you how much Q is going to change given a 1 unit change in P.

Example 1:
Here is an example demand curve: Q = 15,000 - 50P

Given this demand curve we have to figure out what the point price elasticity of demand is at P = 100 and P = 10.

First we need to obtain the derivative of the demand function when it's expressed with Q as a function of P.  Since quantity goes down by 50 each time price goes up by 1,

This gives us (∆Q/∆P)= -50

Next we need to find the quantity demanded at each associated price and pair it together with the price: (100, 10,000), (10, 14,500)

e = -50(100/10,000) = -.5
e = -50(10/14,500) = -.034

And these results make sense, first, because they are negative (downward sloping demand) and second, because the higher level results in a relatively more price elasticity of demand measure.

Example 2:

How to find the point price elasticity of demand with the following demand function:
Q = 4,000 – 400P
We know that ∆Q/∆P in this problem is -400, and we need to find the point price elasticity of demand at a price of 10 and 8.

At a price of ten, we demand 0 of the good, so the measure is undefined.  At a price of 8 we will demand 400 of the good, so the associated measure is:

e = -400(8/400) = -8

What about a demand function of:

Q = 8,800 – 1,000P

Here our ∆Q/∆P will be -1,000 and we will need to find the associated measure at prices of 0, 2, 4, and 6.
This means we will end up with:

e = -1,000(0/8,800) = 0
e = -1,000(2/6,800) = -0.294
e = -1,000(4/4,800) = -0.8333
e = -1,000(6/2,800) = -2.14

Spread the knowledge!
Technorati Digg This Stumble Stumble Facebook Twitter


Anonymous said...

shouldn't quantity demanded what price equals 8 be 4000 - 3200 equals 800.

FreeEconHelp on September 3, 2014 at 5:34 PM said...

Yes, you are right! the equations should be adjusted to include 800 instead of 400 (but the methods/calculations are all correct except this).

Linkon Khan on December 26, 2014 at 8:09 PM said...

You shared your post here how to calculate price.Thanks for your post.
point to point

Jhon David on September 25, 2015 at 3:27 AM said...

Cloud is one of the tremendous technology that any company in this world would rely on(cloud computing training centers in chennai). Using this technology many tough tasks can be accomplished easily in no time. Your content are also explaining the same(Cloud computing course in Chennai). Thanks for sharing this in here. You are running a great blog, keep up this good work.

Kevin Nguyen on December 21, 2015 at 7:00 AM said...

That is really impressive post that can help us to get more knowledge. Thank for that, my friend ! review vacuum for car

Thanu Abi on March 27, 2016 at 11:27 PM said...

This post is amazing.It is very useful for me.Important topic to explained very nice.thanks a lot for this information.

cloud computing training in chennai

kovalan Jayamurugan on April 27, 2016 at 4:39 AM said...

Excellent post!!! The future of cloud computing is on positive side. With most of the companies integrate Salesforce CRM to power their business; there is massive demand for Salesforce developers and administrators across the world. Salesforce Training Institutes in Chennai

Post a Comment


I invite you to join dropbox!

I invite you to join dropbox!
Use the above link for an extra 250MB Free!
All content on this site is the copyright of webmaster. No re-posting is permitted. Powered by Blogger.
VigLink badge

Post Archive

| FreeEconHelp.com, Learning Economics... Solved! © 2009. All Rights Reserved | Template Style by My Blogger Tricks .com | Design by Brian Gardner Back To Top