<p>It is not true that at the equilibrium point the elasticity of demand is equal to the elasticity of supply.</p>
<p><strong>This is a coincidence in your particular example,</strong> depending on the fact that the slope of the demand function and the slope of the supply function are equal in absolute value: they are <span class="math-container">$-2$</span> and <span class="math-container">$2$</span>.</p>
<p>Consider the formula of the point elasticity you wrote:</p>
<p><span class="math-container">$\epsilon=|Slope|\times \frac {P}{Q}$</span>.</p>
<p>The value of the elasticity <strong>depends on both <span class="math-container">$|Slope|$</span>, the absolute value of the slope of the functions,  and on the ratio <span class="math-container">$\frac {P}{Q}$</span>.</strong></p>
<p><span class="math-container">$\frac {P}{Q}$</span> at the equilibrium point is of course equal for demand and supply, because the equilibrium point is a point that belongs to both functions.</p>
<p>But <strong>nothing ensures that the slope of demand and supply functions are equal</strong> (in absolute value).</p>
<p>Consider the example in the graph below, where it is clear that the slopes of demand and supply, <span class="math-container">$-b$</span> and <span class="math-container">$a$</span>, are different in absolute value, and <span class="math-container">$a&gt;b$</span>:</p>
<p><a href="https://i.sstatic.net/fGRvp.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/fGRvp.png" alt="enter image description here" /></a></p>
<p>Therefore, the point elasticity of supply <span class="math-container">$\epsilon_S$</span> is</p>
<p><span class="math-container">$\epsilon_S= a\times \frac {30}{40}$</span></p>
<p>and the point elasticity of demand is</p>
<p><span class="math-container">$\epsilon_D= b\times \frac {30}{40}$</span>.</p>
<p>They are evidently different and <span class="math-container">$\epsilon_S&gt;\epsilon_D$</span>.</p>

CC BY-SA 4.0
2023-10-06T20:48:09.717Z
2023-10-06T23:01:26.270Z
2023-10-06T23:01:26.270Z
BakerStreet
<p>supply &amp; demand elasticities are independent of each other and don't depend on the equilibrium.</p>

CC BY-SA 4.0
2023-11-26T01:23:51.063Z
2023-11-26T01:23:51.063Z
Rayla Xadia
<p>No, the supply and demand elasticity are not always equal at the equilibrium.</p>
<p>Here is an example of a market where the elasticity of demand and supply are not equal at the equilibrium. Suppose the demand curve for a good is given by the equation Qd = 20 - 2P and the supply curve for the good is given by the equation Qs = 2P. The equilibrium price for the good is P = 5 and the equilibrium quantity is Q = 10. The elasticity of demand at the equilibrium is -1 and the elasticity of supply at the equilibrium is 1. Therefore, the elasticity of demand is not equal to the elasticity of supply at the equilibrium.</p>

CC BY-SA 4.0
2023-11-26T12:56:50.057Z
2023-11-26T12:56:50.057Z
Shree Priya Singh
<p>I am working through homeowrk problems and we were asked to calculate the supply and demand at the equilibruim using either the point or arc method. I chose to use the point method and will provide a picture of the graph within  this post. THe demand equation is 100-2p=Q and supply is -20+2p=Q.
Here are my calculations [note the equilibrium occurs at (40,30)]</p>
<p>Demand elasticity: point method
= Slope* (P/Q)</p>
<ul>
<li>= -2(30/40)</li>
<li>= -2(3/4)
Elasticity = -1.5 = 1.5
Therefore the demand elasticity is 1.5.</li>
</ul>
<p>Supply elasticity: point method
= 2(30/40)
=2(3/4)
Elasticity = 1.5
Therefore the supply elasticity is 1.5</p>
<p><a href="https://i.sstatic.net/K8QJw.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/K8QJw.png" alt="Graph with equilibrium" /></a></p>

<supply-and-demand><elasticity><general-equilibrium>
Is the supply and demand elasticity equal at the equilibrium?
jl2005
# Is the supply and demand elasticity equal at the equilibrium?

(Asked by: username_0 on 2023-10-06)

I am working through homeowrk problems and we were asked to calculate the supply and demand at the equilibruim using either the point or arc method. I chose to use the point method and will provide a picture of the graph within this post. THe demand equation is 100-2p=Q and supply is -20+2p=Q.
Here are my calculations [note the equilibrium occurs at (40,30)]

Demand elasticity: point method
= Slope\* (P/Q)

* = -2(30/40)
* = -2(3/4)
  Elasticity = -1.5 = 1.5
  Therefore the demand elasticity is 1.5.

Supply elasticity: point method
= 2(30/40)
=2(3/4)
Elasticity = 1.5
Therefore the supply elasticity is 1.5

[![Graph with equilibrium](https://i.sstatic.net/K8QJw.png)](https://i.sstatic.net/K8QJw.png)

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

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## 3 answers

### Answer by username_1 on 2023-10-06. Score: 2

It is not true that at the equilibrium point the elasticity of demand is equal to the elasticity of supply.

**This is a coincidence in your particular example,** depending on the fact that the slope of the demand function and the slope of the supply function are equal in absolute value: they are $-2$ and $2$.

Consider the formula of the point elasticity you wrote:

$\epsilon=|Slope|\times \frac {P}{Q}$.

The value of the elasticity **depends on both $|Slope|$, the absolute value of the slope of the functions, and on the ratio $\frac {P}{Q}$.**

$\frac {P}{Q}$ at the equilibrium point is of course equal for demand and supply, because the equilibrium point is a point that belongs to both functions.

But **nothing ensures that the slope of demand and supply functions are equal** (in absolute value).

Consider the example in the graph below, where it is clear that the slopes of demand and supply, $-b$ and $a$, are different in absolute value, and $a>b$:

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

Therefore, the point elasticity of supply $\epsilon\_S$ is

$\epsilon\_S= a\times \frac {30}{40}$

and the point elasticity of demand is

$\epsilon\_D= b\times \frac {30}{40}$.

They are evidently different and $\epsilon\_S>\epsilon\_D$.


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### Answer by username_2 on 2023-11-26. Score: 1

supply & demand elasticities are independent of each other and don't depend on the equilibrium.


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### Answer by username_3 on 2023-11-26. Score: 0

No, the supply and demand elasticity are not always equal at the equilibrium.

Here is an example of a market where the elasticity of demand and supply are not equal at the equilibrium. Suppose the demand curve for a good is given by the equation Qd = 20 - 2P and the supply curve for the good is given by the equation Qs = 2P. The equilibrium price for the good is P = 5 and the equilibrium quantity is Q = 10. The elasticity of demand at the equilibrium is -1 and the elasticity of supply at the equilibrium is 1. Therefore, the elasticity of demand is not equal to the elasticity of supply at the equilibrium.


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