<p>Price elasticity of demand is related (but not equal) to the <strong><em>inverse</em></strong> of the slope of the demand curve.</p>

<p><a href="https://en.wikipedia.org/wiki/Price_elasticity_of_demand" rel="nofollow noreferrer">This Wikipedia article defines PED as</a>:</p>

<blockquote>
  <p>Price elasticity of demand (PED or Ed) is a measure used in economics to show the responsiveness, or elasticity, of the quantity demanded of a good or service to a change in its price, ceteris paribus. More precisely, it gives the <strong>percentage change in quantity demanded in response to a one percent change in price</strong>. [emphasis added]</p>
</blockquote>

<p>Look at the following (canonical) supply-demand graph.</p>

<p><a href="https://i.sstatic.net/z7pZy.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/z7pZy.png" alt="enter image description here"></a></p>

<p>Let's define $P^*$ the price of market equilibrium, $Q_D$ as the quantity demanded and $E_D$ as price elasticity of demand. Then:</p>

<p>$$ {slope} = \frac{rise}{run} = \frac{\Delta P}{\Delta Q_D} $$</p>

<p>And in mathematical terms, the verbal description of the PED reduces to:</p>

<p>$$ E_D = \frac{\frac{\Delta Q_D}{Q_D} \cdot 100}{\frac{\Delta P}{P^*} \cdot 100} $$</p>

<p>$$ E_D = \frac{P^*}{Q_D} \cdot \frac{\Delta Q_D} {\Delta P} $$</p>

<p>$$ E_D = \frac{P^*}{Q_D} \cdot \frac{1}{slope} $$</p>

<h2>Edit</h2>

<p>Constructive comments have been incorporated into this answer.</p>

<p>In particular, @Kontorus pointed out:</p>

<blockquote>
  <p>The PED is a percentage change, the slope of the demand curve is an absolute change.</p>
</blockquote>

<p>And @denesp pointed out that:</p>

<blockquote>
  <p>... linear demand curves have constant slopes but changing elasticity. <em>Cobb-Douglas</em> derived demand (hyperbole) has changing slope but constant elasticity.</p>
</blockquote>

CC BY-SA 3.0
2016-07-15T17:20:34.670Z
Not precisely. The PED is a percentage change, the slope of the demand curve is an absolute change.
Kontorus
CC BY-SA 3.0
2016-07-15T17:31:15.083Z
The information in this answer is false. For example linear demand curves have constant slopes but changing elasticity. Cobb-Douglas derived demand (hyperbole) has changing slope but constant elasticity.
Giskard
CC BY-SA 3.0
2016-07-15T18:33:12.860Z
I edited this answer to reflect the two above constructive comments.
FreeMarketUnicorn
CC BY-SA 3.0
2016-07-15T18:35:18.190Z
If you give the PED formula so that relation is clear you'll get my + vote as well.
Giskard
CC BY-SA 3.0
2016-07-15T19:09:55.200Z
@denesp: How'd I do?
FreeMarketUnicorn
CC BY-SA 3.0
2016-08-01T23:00:42.210Z
Does the slope have any applications in economics?
etc
CC BY-SA 3.0
2016-07-15T15:43:27.620Z
2016-07-15T20:37:29.940Z
2016-07-15T20:37:29.940Z
FreeMarketUnicorn
<p>I see the elasticity value(s) of demand being used frequently to determine the relation between demand and variables such as price and income. I have however been unable to find any uses for the slope of the demand curve. Are there any?</p>

<p>Also, is there any relationship between the slope and the elasticity?</p>

<supply-and-demand><elasticity>
Usefulness of the value for the slope of the demand curve
etc
# Usefulness of the value for the slope of the demand curve

(Asked by: username_0 on 2016-07-14)

I see the elasticity value(s) of demand being used frequently to determine the relation between demand and variables such as price and income. I have however been unable to find any uses for the slope of the demand curve. Are there any?

Also, is there any relationship between the slope and the elasticity?

**Tags:** supply-and-demand, elasticity

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## 1 answers

### Answer by username_1 on 2016-07-15. Score: 4 | Accepted answer

Price elasticity of demand is related (but not equal) to the ***inverse*** of the slope of the demand curve.

[This Wikipedia article defines PED as](https://en.wikipedia.org/wiki/Price_elasticity_of_demand):

> Price elasticity of demand (PED or Ed) is a measure used in economics to show the responsiveness, or elasticity, of the quantity demanded of a good or service to a change in its price, ceteris paribus. More precisely, it gives the **percentage change in quantity demanded in response to a one percent change in price**. [emphasis added]

Look at the following (canonical) supply-demand graph.

[![enter image description here](https://i.sstatic.net/z7pZy.png)](https://i.sstatic.net/z7pZy.png)

Let's define $P^\*$ the price of market equilibrium, $Q\_D$ as the quantity demanded and $E\_D$ as price elasticity of demand. Then:

$$ {slope} = \frac{rise}{run} = \frac{\Delta P}{\Delta Q\_D} $$

And in mathematical terms, the verbal description of the PED reduces to:

$$ E\_D = \frac{\frac{\Delta Q\_D}{Q\_D} \cdot 100}{\frac{\Delta P}{P^\*} \cdot 100} $$

$$ E\_D = \frac{P^\*}{Q\_D} \cdot \frac{\Delta Q\_D} {\Delta P} $$

$$ E\_D = \frac{P^\*}{Q\_D} \cdot \frac{1}{slope} $$

## Edit

Constructive comments have been incorporated into this answer.

In particular, @Kontorus pointed out:

> The PED is a percentage change, the slope of the demand curve is an absolute change.

And @denesp pointed out that:

> ... linear demand curves have constant slopes but changing elasticity. *Cobb-Douglas* derived demand (hyperbole) has changing slope but constant elasticity.

> **Comments:**
> **username_2**: Not precisely. The PED is a percentage change, the slope of the demand curve is an absolute change.  
> **username_3**: The information in this answer is false. For example linear demand curves have constant slopes but changing elasticity. Cobb-Douglas derived demand (hyperbole) has changing slope but constant elasticity.  
> **username_1**: I edited this answer to reflect the two above constructive comments.  
> **username_3**: If you give the PED formula so that relation is clear you'll get my + vote as well.  
> **username_1**: @denesp: How'd I do?  
> **username_0**: Does the slope have any applications in economics?  

---

