Rabin Model of Monopoly Pricing

Preliminaries Monopolist has cost c per unit Consumer values the good  Monopolist picks price p  [c,  ] Consumer picks a reservation price r  [c,  ] If p  r the good sells Payoff for firm is p-c Payoff for consumer is  -p If p>r the good does not sell, payoff for all is 0 Nash equilibrium allows any solution If players care only about material payoff, equilibrium is p=r=  and the monopolist gets all surplus value

Highest price in fairness equilibrium Since monopolist sets price, question is if it gets p-c or 0 If r  p  consumer is maximizing own and monopolists payoff If r<p  minimizing fairness Using Rabin’s fairness functions we can find that f c (r,p)=0 if r  p f c (r,p)=-1 if r<p which together imply the equilibrium trade happens only when p=r. Call a value when trade takes place z, so p=r=z. Then because we consider only z if c<z<  So if the monopolist sets p>c the consumer thinks the monopolist is unfair, hence any monopoly price is unfair

Consumer Utility To see if p=r=z is a fairness equilibrium for a given z we have to see if the consumer will set r<z, thus giving the monopolist a profit of 0 Consumers total utility from setting r<z is Consumer total utility from sticking with r=z is Requiring U c  0 shows the highest equilibrium z is given by

Conclusion The highest fairness equilibrium price is less than the conventional monopoly price This is where Kahneman, et al, get that a monopolist interested in profit should consider consumer’s views of fairness and set the price lower than the maximum monopoly price. Question – in general, what does fairness do to total welfare and efficiency in a monopoly?