# Microeconomics undergraduate ELASTICITY help (differentiating log-linear demand curve) [closed]

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!!

• 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. Aug 27, 2020 at 16:15
• Log-linear? Do you mean what is sometimes termed double-log, ie $ln(Q)=a-b (ln(P))$? Aug 27, 2020 at 18:48

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