<p>If you mean: <span class="math-container">$Q=a-b \ln(p)$</span> then</p>
<p>Elasticity <span class="math-container">$E = \frac{dQ}{dp} \frac{p}{Q}=-\frac{b}{p}\frac{p}{Q}$</span>.</p>
<p>Or, equivalently, <span class="math-container">$E = \frac{d \ln(Q)}{d \ln(p)} = -b/Q$</span></p>

CC BY-SA 4.0
2020-08-27T12:28:50.307Z
2020-08-27T12:28:50.307Z
LutzHendricks
<p>How do you show that the price elasticity of demand is a constant if the demand function is log-linear? To show this, how do you differentiate the log-linear demand curve to determine dQ/dp, and substitute that expression into the definition of the elasticity of demand?</p>
<p>There is an explanation in the textbook but I don't get it at all for the log-linear demand curve, although I get it for the exponential demand curve. How do you differentiate the log-linear demand curve? Can you please explain each step in detail? Because the steps are already in textbook but I don't understand it even as I reread it multiple times.</p>
<p>Thank you!!</p>

CC BY-SA 4.0
2020-08-27T16:15:18.983Z
What are the steps that your textbook takes? You should include the steps in your questions and say exactly which step(s) you don't understand.
Herr K.
CC BY-SA 4.0
2020-08-27T18:48:34.500Z
Log-linear?  Do you mean what is sometimes termed double-log, ie $ln(Q)=a-b  (ln(P))$?
Adam Bailey
<microeconomics><supply-and-demand><elasticity>
Microeconomics undergraduate ELASTICITY help (differentiating log-linear demand curve)
user30200
# Microeconomics undergraduate ELASTICITY help (differentiating log-linear demand curve)

(Asked by: username_0 on 2020-08-27)

How do you show that the price elasticity of demand is a constant if the demand function is log-linear? To show this, how do you differentiate the log-linear demand curve to determine dQ/dp, and substitute that expression into the definition of the elasticity of demand?

There is an explanation in the textbook but I don't get it at all for the log-linear demand curve, although I get it for the exponential demand curve. How do you differentiate the log-linear demand curve? Can you please explain each step in detail? Because the steps are already in textbook but I don't understand it even as I reread it multiple times.

Thank you!!

**Tags:** microeconomics, supply-and-demand, elasticity
> **Comments:**
> **username_1**: What are the steps that your textbook takes? You should include the steps in your questions and say exactly which step(s) you don't understand.  
> **username_2**: Log-linear?  Do you mean what is sometimes termed double-log, ie $ln(Q)=a-b  (ln(P))$?  

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## 1 answers

### Answer by username_3 on 2020-08-27. Score: 1

If you mean: $Q=a-b \ln(p)$ then

Elasticity $E = \frac{dQ}{dp} \frac{p}{Q}=-\frac{b}{p}\frac{p}{Q}$.

Or, equivalently, $E = \frac{d \ln(Q)}{d \ln(p)} = -b/Q$


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