Robust lower bounds on monopoly profit with α-concave demand
将Condorelli关于对数凹需求下垄断利润的下界推广到更广泛的α-凹需求类，给出利润下界为需求曲线下面积的1/(1+α)^(1/α)，并推导消费者剩余和无谓损失的上界，所有界都是紧的。
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.