Constant Elasticity Demand

Constant elasticity demand has the multiplicative form

where the price elasticity of demand $|E|$ is the same at every point on the curve. The unit-elastic special case $|E| = 1$ (e.g. $P = k/Q$) gives constant total revenue $PQ = k$ and $MR = 0$ everywhere — there is no interior $MR = MC$ solution.

When to use

Constant elasticity demand is the cleanest setting for applying the Lerner Index pricing rule $P^* = MC / (1 - 1/|E|)$ — because $|E|$ is constant, you can solve $P^*$ in one step without iterating. It is also useful when an exam asks for a market where the monopolist's markup ratio is constant across cost shifts, and it is the standard demand specification in empirical industrial-organisation work.