<p>Did you know you can write price elasticity $\varepsilon$ as $\varepsilon \equiv  \frac{d \log Q}{d \log P}$? </p>

<p>(Indeed, $\frac{d \log Q}{d \log P} =\frac{dQ}{dP} \frac{P}{Q}$. Check out wiki on elasticity of a function if you want more detail!) </p>

<p>Using this "log notation" for elasticity, it is easy to see without putting pen to paper that in this example, $\varepsilon = -0.7$.</p>

CC BY-SA 3.0
2015-08-20T19:01:50.540Z
2015-08-20T19:01:50.540Z
TheCheuk
<p>The price elacitiy of demand is $\frac{\partial Q}{\partial P}\cdot \frac{P}{Q(P)}$. To get Q(P) you have to write both sides of the equations as an exponent of the base e. </p>

<p>$$ e^{ln(Q)}=e^{10-0.7ln(P)} $$</p>

<p>$$ Q=e^{10}\cdot e^{-0.7ln(P)}\Rightarrow Q= e^{10}\cdot \left(e^{ln(P)}\right)^{-0.7}$$</p>

<p>$$Q(P)=e^{10}\cdot p^{-0.7} $$ </p>

<p>Therfore</p>

<p>$$ \frac{\partial Q}{\partial P}=e^{10}\cdot (-0.7)\cdot p^{-1.7}$$</p>

<p>I think you can take it from here. If not, feel free to ask.</p>

CC BY-SA 3.0
2015-08-20T17:34:25.173Z
2015-08-21T02:06:58.607Z
2015-08-21T02:06:58.607Z
callculus42
<p>ln(Q) = 10-0.7ln(P), where P is price and Q is demand.</p>

<p>What is the price elasticity of demand?</p>

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2015-08-21T07:43:00.813Z
This question has been put on hold by the community as it appears to be a homework question with no individual effort shown.
Ubiquitous
<microeconomics><econometrics>
Find Price elasticity of demand in this example
UnusualSkill
# Find Price elasticity of demand in this example

(Asked by: username_0 on 2015-08-20)

ln(Q) = 10-0.7ln(P), where P is price and Q is demand.

What is the price elasticity of demand?

**Tags:** microeconomics, econometrics
> **Comments:**
> **username_1**: This question has been put on hold by the community as it appears to be a homework question with no individual effort shown.  

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## 2 answers

### Answer by username_2 on 2015-08-20. Score: 3

Did you know you can write price elasticity $\varepsilon$ as $\varepsilon \equiv \frac{d \log Q}{d \log P}$?

(Indeed, $\frac{d \log Q}{d \log P} =\frac{dQ}{dP} \frac{P}{Q}$. Check out wiki on elasticity of a function if you want more detail!)

Using this "log notation" for elasticity, it is easy to see without putting pen to paper that in this example, $\varepsilon = -0.7$.


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### Answer by username_3 on 2015-08-20. Score: 2

The price elacitiy of demand is $\frac{\partial Q}{\partial P}\cdot \frac{P}{Q(P)}$. To get Q(P) you have to write both sides of the equations as an exponent of the base e.

$$ e^{ln(Q)}=e^{10-0.7ln(P)} $$

$$ Q=e^{10}\cdot e^{-0.7ln(P)}\Rightarrow Q= e^{10}\cdot \left(e^{ln(P)}\right)^{-0.7}$$

$$Q(P)=e^{10}\cdot p^{-0.7} $$

Therfore

$$ \frac{\partial Q}{\partial P}=e^{10}\cdot (-0.7)\cdot p^{-1.7}$$

I think you can take it from here. If not, feel free to ask.


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