<p>They are both related concepts and they are both price elasticities.</p>
<p>Price elasticity can be derived at a single point, for that we would use the point price elasticity of demand formula:</p>
<p><span class="math-container">$$e= \frac{dQ/Q}{dP/P}= dQ/dP \cdot P/Q $$</span></p>
<p>An alternative to point elasticity is the arc elasticity which tells you what the elasticity is between the two points.</p>
<p>This is usually calculated using the midpoint formula.</p>
<p><span class="math-container">$$e  = \frac{(Q_2-Q_1)/((Q_2+Q_1)/2)}{(P_2-P_1)/((P_2+P_1)/2)}$$</span></p>
<p>If someone just states calculate price elasticity of demand it could be either the point or arc method, depending on context.</p>

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2023-01-14T16:17:36.867Z
2023-01-16T11:31:03.493Z
2023-01-16T11:31:03.493Z
1muflon1
<p>I am very confused between the definitions of price elasticity of demand.
The actual definition I was given is <span class="math-container">$$E=\frac{\Delta Q \backslash Q}{\Delta P\backslash P}$$</span>
I was once asked the following : find the price elasticity of demand supposing the price of a product increases from 12\$ to 20\$ (<span class="math-container">$\frac{200}3$</span>% rise) and the quantity demanded falls from 55 to 45 (<span class="math-container">$\frac{-200}{11}$</span>% fall). So it should have an elasticity of <span class="math-container">$E=-0.27$</span> approximately. Simple application of the formula I was given, nothing crazy.
This is exactly the same procedure for what is being done <a href="https://en.wikipedia.org/wiki/Price_elasticity_of_demand#Definition" rel="nofollow noreferrer">here</a>.</p>
<p>However, the right answer was <span class="math-container">$-0.4$</span>... After a quick look on internet, this seems to be the <strong>arc</strong> price elasticity of demand : <span class="math-container">$$E=\frac{(Q_1-Q_0)(Q_1+Q_2)}{(P_1-P_0)(P_1+P_0)}=\frac{(45-55)(45+55)}{(20-12)(20+12)}=-0.4 $$</span></p>
<p>So these two concepts are different things right ?</p>

<microeconomics><elasticity>
Difference between price elasticity of demand and arc price elasticity of demand
Kilkik
# Difference between price elasticity of demand and arc price elasticity of demand

(Asked by: username_0 on 2023-01-14)

I am very confused between the definitions of price elasticity of demand.
The actual definition I was given is $$E=\frac{\Delta Q \backslash Q}{\Delta P\backslash P}$$
I was once asked the following : find the price elasticity of demand supposing the price of a product increases from 12\$ to 20\$ ($\frac{200}3$% rise) and the quantity demanded falls from 55 to 45 ($\frac{-200}{11}$% fall). So it should have an elasticity of $E=-0.27$ approximately. Simple application of the formula I was given, nothing crazy.
This is exactly the same procedure for what is being done [here](https://en.wikipedia.org/wiki/Price_elasticity_of_demand#Definition).

However, the right answer was $-0.4$... After a quick look on internet, this seems to be the **arc** price elasticity of demand : $$E=\frac{(Q\_1-Q\_0)(Q\_1+Q\_2)}{(P\_1-P\_0)(P\_1+P\_0)}=\frac{(45-55)(45+55)}{(20-12)(20+12)}=-0.4 $$

So these two concepts are different things right ?

**Tags:** microeconomics, elasticity

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## 1 answers

### Answer by username_1 on 2023-01-14. Score: 1 | Accepted answer

They are both related concepts and they are both price elasticities.

Price elasticity can be derived at a single point, for that we would use the point price elasticity of demand formula:

$$e= \frac{dQ/Q}{dP/P}= dQ/dP \cdot P/Q $$

An alternative to point elasticity is the arc elasticity which tells you what the elasticity is between the two points.

This is usually calculated using the midpoint formula.

$$e = \frac{(Q\_2-Q\_1)/((Q\_2+Q\_1)/2)}{(P\_2-P\_1)/((P\_2+P\_1)/2)}$$

If someone just states calculate price elasticity of demand it could be either the point or arc method, depending on context.


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