A monopolist sells in 2 markets and produces in 1 factory. Although the monopolist can charge difference prices in the two markets, it must sell all units within a market at the same price. a) Suppose this monopolist does not have a marginal cost (MC = 0). If demand in market 1 is X1(p1) = a1 − b1p1 and demand in market 2 is X2(p2) = a2 − b2p2, set up the monopolist’s profit maximization problems and solve for the market prices that result in each market. b) Under what conditions on a1, b1, a2, b2 from above will the monopolist not price discriminate? c) If demand in market i, where i = 1 , 2, is instead Xi(pi) = ai p−bi i and the monopolist has some constant marginal cost of c, where c > 0, set up the monopolist’s profit maximization problem and solve for the market prices. d) Under what conditions on a1, b1, a2, b2 from above will the monopolist not price discriminate?
A monopolist sells in 2 markets and produces in 1 factory. Although the monopolist
can charge difference prices in the two markets, it must sell all units within a market at the same
price.
a) Suppose this monopolist does not have a marginal cost (MC = 0). If demand in market 1 is
X1(p1) = a1 − b1p1 and demand in market 2 is X2(p2) = a2 − b2p2, set up the monopolist’s
profit maximization problems and solve for the market prices that result in each market.
b) Under what conditions on a1, b1, a2, b2 from above will the monopolist not
c) If demand in market i, where i = 1 , 2, is instead Xi(pi) = ai p−bi
i and the monopolist has some constant marginal cost of c, where c > 0, set up the monopolist’s profit maximization
problem and solve for the market prices.
d) Under what conditions on a1, b1, a2, b2 from above will the monopolist not price discriminate?
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