Elasticity when the demand function is given Given the demand function, $ q = kp^{-\epsilon} $, how do I calculate the elasticity? As a result, I do know that the elasticity when the demand function is in this form is $ - \epsilon $. But I'd like to know how. I also found a derivation online that proceeded like this:

(1) Take logarithm on both sides
(2) Differentiate on boths ides
(3) You'll get: $$ \frac {\text{d} \ln(q)}{\text{d} \ln (p)} = - \epsilon $$
(4) The LHS of the above equation is simply elasticity. 

How does $$  \frac {\text{d} \ln(q)}{\text{d} \ln (p)} $$ represent elasticity?
The definition of elasticity of demand with respect to price is: $\varepsilon_{q,p} = \frac{dq}{dp} \cdot \frac{p}{q}$. So in your demand function we have:

$$q = kp^{-\epsilon}$$
$$\frac{dq}{dp} = -\epsilon kp^{-\epsilon - 1}$$
$$\varepsilon_{q,p} = \frac{dq}{dp}\cdot \frac{p}{q}  = -\epsilon kp^{-\epsilon - 1} \cdot \frac{p}{kp^{-\epsilon}} = -\epsilon$$ 

And we have the answer you're looking for.