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?