9. A monopolist produces a good at a constant marginal cost of Suppose the monopolist is able to practice first-degree price discrimination (FDPD). The (in- verse) market demand function for the good is given by P=10-bQ where P is price, Q is quantity and b> 0 is a constant. Let DL(Q) denote the deadweight loss at quantity Q, and let CS(Q) denote the consumer surplus at Q. (a) Under FDPD, the marginal revenue function of the monopolist is the same as the market demand function. Is this true or false? Explain carefully. (b) Let Q be the monopolist's optimal quantity under FDPD. Calculate the value of CS(Q')-DL(Q). (c) Suppose a regulator imposes a per-unit tax of t on the monopolist and re- distributes tax revenue to consumers, so that tax revenue becomes part of consumer surplus. Let Q; be the monopolist's optimal quantity under FDPD given a per-unit tax of t. Calculate the value of t that maximises CS(Q)-DL(07).
9. A monopolist produces a good at a constant marginal cost of Suppose the monopolist is able to practice first-degree price discrimination (FDPD). The (in- verse) market demand function for the good is given by P=10-bQ where P is price, Q is quantity and b> 0 is a constant. Let DL(Q) denote the deadweight loss at quantity Q, and let CS(Q) denote the consumer surplus at Q. (a) Under FDPD, the marginal revenue function of the monopolist is the same as the market demand function. Is this true or false? Explain carefully. (b) Let Q be the monopolist's optimal quantity under FDPD. Calculate the value of CS(Q')-DL(Q). (c) Suppose a regulator imposes a per-unit tax of t on the monopolist and re- distributes tax revenue to consumers, so that tax revenue becomes part of consumer surplus. Let Q; be the monopolist's optimal quantity under FDPD given a per-unit tax of t. Calculate the value of t that maximises CS(Q)-DL(07).
Chapter14: Monopoly
Section: Chapter Questions
Problem 14.9P
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Transcribed Image Text:9. A monopolist produces a good at a constant marginal cost of 4. Suppose the
monopolist is able to practice first-degree price discrimination (FDPD). The (in-
verse) market demand function for the good is given by
P=10-bQ
where P is price, Q is quantity and b> 0 is a constant. Let DL(Q) denote the
deadweight loss at quantity Q, and let CS(Q) denote the consumer surplus at
Q.
(a) Under FDPD, the marginal revenue function of the monopolist is the same
as the market demand function. Is this true or false? Explain carefully.
(b) Let Q be the monopolist's optimal quantity under FDPD. Calculate the
value of CS(Q')-DL(Q").
(c) Suppose a regulator imposes a per-unit tax of t on the monopolist and re-
distributes tax revenue to consumers, so that tax revenue becomes part
of consumer surplus. Let Q; be the monopolist's optimal quantity under
FDPD given a per-unit tax of t. Calculate the value of t that maximises
CS(Q)-DL(Q7).
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