<p>The Answer can be found in the comments by user brunosalcedo:</p>

<p>"<em>Remember that elasticity measures percentual rates of change. How does q change per unit of percentual change of p? If <span class="math-container">$p=0$</span>, then any percentual change of p results in no change at all because 0 multiplied by any number is 0. The elasticity is not just 0 at p=0, it is also continuous at <span class="math-container">$p=0$</span>. If you compute the elasticity for small but positive prices, and then take the limit as p goes to 0, the limit is 0.</em>"</p>

CC BY-SA 4.0
2020-06-11T18:45:15.730Z
2020-06-11T18:45:15.730Z
Pycruncher
<p>Given a linear demand curve <span class="math-container">$q(p) = a - bp$</span>, how would one find the price elasticity of demand at <span class="math-container">$p = 0$</span>? The quantity that would be demanded is given: <span class="math-container">$Q_0 = a$</span></p>

<p>The formula for the price elasticity of demand then dictates: </p>

<p><span class="math-container">$\epsilon_{p=0} = \frac{dq}{dp} *\frac {p}{q} = -b * \frac{p}{a} = -b * \frac{0}{a}= 0$</span>, </p>

<p>this would mean perfectly inelastic. Thus, no matter the change in price there should be no change in quantity. This does not seem to make sense as at this point demand should be the most elastic. Where did I go wrong?</p>

<p>As an example one could think of a free good (e.g. straws), the demand for which can be observed. Then a levy is imposed and the new demand is being observed, allowing one to derive a linear demand function. How would one find the price elasticity for straws when they are free (<span class="math-container">$p=0$</span>)?</p>

CC BY-SA 4.0
2020-06-11T17:35:30.853Z
Remember that elasticity measures percentual rates of change. How does q change per unit of percentual change of p?  If p=0, then any percentual change of p results in no change at all because 0 multiplied by any number is 0. The elasticity is not just 0 at p=0, it is also continuous at p=0. If you compute the elasticity for small but positive prices, and then take the limit as p goes to 0, the limit is 0.
brunosalcedo
CC BY-SA 4.0
2020-06-11T18:42:07.540Z
Alright, yes that makes a lot of sense, I don't know why I got confused. I took the limits myself but I thought I must be doing something wrong. Thank you very much!!
Pycruncher
<microeconomics><elasticity><taxation><demand><nonexpert>
Find Price Elasticity of Demand for p = 0
Pycruncher
# Find Price Elasticity of Demand for p = 0

(Asked by: username_0 on 2020-06-11)

Given a linear demand curve $q(p) = a - bp$, how would one find the price elasticity of demand at $p = 0$? The quantity that would be demanded is given: $Q\_0 = a$

The formula for the price elasticity of demand then dictates:

$\epsilon\_{p=0} = \frac{dq}{dp} \*\frac {p}{q} = -b \* \frac{p}{a} = -b \* \frac{0}{a}= 0$,

this would mean perfectly inelastic. Thus, no matter the change in price there should be no change in quantity. This does not seem to make sense as at this point demand should be the most elastic. Where did I go wrong?

As an example one could think of a free good (e.g. straws), the demand for which can be observed. Then a levy is imposed and the new demand is being observed, allowing one to derive a linear demand function. How would one find the price elasticity for straws when they are free ($p=0$)?

**Tags:** microeconomics, elasticity, taxation, demand, nonexpert
> **Comments:**
> **username_1**: Remember that elasticity measures percentual rates of change. How does q change per unit of percentual change of p?  If p=0, then any percentual change of p results in no change at all because 0 multiplied by any number is 0. The elasticity is not just 0 at p=0, it is also continuous at p=0. If you compute the elasticity for small but positive prices, and then take the limit as p goes to 0, the limit is 0.  
> **username_0**: Alright, yes that makes a lot of sense, I don't know why I got confused. I took the limits myself but I thought I must be doing something wrong. Thank you very much!!  

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## 1 answers

### Answer by username_0 on 2020-06-11. Score: 1

The Answer can be found in the comments by user brunosalcedo:

"*Remember that elasticity measures percentual rates of change. How does q change per unit of percentual change of p? If $p=0$, then any percentual change of p results in no change at all because 0 multiplied by any number is 0. The elasticity is not just 0 at p=0, it is also continuous at $p=0$. If you compute the elasticity for small but positive prices, and then take the limit as p goes to 0, the limit is 0.*"


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