Robust lower bounds on monopoly profit with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.svg" display="inline" id="d1e23"><mml:mi>α</mml:mi></mml:math>-concave demand

I extend Condorelli’s lower bound on monopoly profit from log-concave demand to a broader class of α -concave demand, with α = 0 corresponding to log-concavity and α = 1 to concavity. The monopoly profit is at least 1 ( 1 + α ) 1 / α of the area under the demand curve. I further derive upper bounds for consumer surplus and deadweight loss relative to monopoly profit and show all three bounds are sharp. • Extends Condorelli’s lower bound to α -concave demand. • Monopoly profit is at least 1 ( 1 + α ) 1 / α of the area under the demand curve. • Derives upper bounds for consumer surplus and deadweight loss. • All bounds are shown to be sharp with specific examples.