<p>In your second option, you computed the elasticity at the original point, and in your third option, at the end point. In your first point, you did the same as in the second one, but with a mistake: you wrote $133%$ instead of $33%$. </p>

CC BY-SA 3.0
2016-05-27T13:09:00.960Z
2016-05-27T13:09:00.960Z
rsm
<p>First year Econ. Question:</p>

<p>Demand function: $P=50-4Q$ (Price in cents/kilo)</p>

<p>Supply function: $P=25+Q$</p>

<p>Equilibrium Price and Quantity: 30 cents, 5 kilos. </p>

<p>Price change: 40 cents, 2.5 kilos. </p>

<p>I've tried 3 different methods of calculating point elasticity: </p>

<ul>
<li>$\frac{\% \Delta Q}{\% \Delta P}$ =  $\frac{-50\%}{133\%}= -.375$;</li>
<li>$\frac{\frac{Q_{1}-Q_0}{Q_0}}{\frac{P_1-P_0}{P_0}} = \frac{\frac{2.5-5}{5}}{\frac{40-30}{30}}=-1.5 $</li>
<li>$\frac{1}{slope}\frac{P}{Q}=\frac{-1}{4}\frac{40}{2.5} = -4$</li>
</ul>

<p>The right answer is -4, but why the variability?</p>

CC BY-SA 3.0
2016-05-29T01:51:27.490Z
See this post on arc elasticity, http://economics.stackexchange.com/a/10694/61
Alecos Papadopoulos
<elasticity>
Why am I getting 3 different answers for Point Elasticity of Demand?
Romaion
# Why am I getting 3 different answers for Point Elasticity of Demand?

(Asked by: username_0 on 2016-05-25)

First year Econ. Question:

Demand function: $P=50-4Q$ (Price in cents/kilo)

Supply function: $P=25+Q$

Equilibrium Price and Quantity: 30 cents, 5 kilos.

Price change: 40 cents, 2.5 kilos.

I've tried 3 different methods of calculating point elasticity:

* $\frac{\% \Delta Q}{\% \Delta P}$ = $\frac{-50\%}{133\%}= -.375$;
* $\frac{\frac{Q\_{1}-Q\_0}{Q\_0}}{\frac{P\_1-P\_0}{P\_0}} = \frac{\frac{2.5-5}{5}}{\frac{40-30}{30}}=-1.5 $
* $\frac{1}{slope}\frac{P}{Q}=\frac{-1}{4}\frac{40}{2.5} = -4$

The right answer is -4, but why the variability?

**Tags:** elasticity

> **Comments:**
> **username_1**: See this post on arc elasticity, http://economics.stackexchange.com/a/10694/61  

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## 1 answers

### Answer by username_2 on 2016-05-27. Score: 0 | Accepted answer

In your second option, you computed the elasticity at the original point, and in your third option, at the end point. In your first point, you did the same as in the second one, but with a mistake: you wrote $133%$ instead of $33%$.


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