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Chapter 12 - Monopoly Goals: 1. The sources of monopoly power 2. The monopolist’s problem 3. Seeking more surplus Part 1: Price Discrimination Part 2: Bundling Goods. Sources of Monopoly Power. Exclusive control over crucial inputs. Economies of scale with a downward sloping LAC natural monopolies Network economies Patents temporary monopoly rights Licensing by governments or other institutions The Monopolist’s Problem. The monopolist’s problem ◦ Objective of the monopolist : maximize profits. ◦ Temporary assumption: the monopolist charges a single price. ◦ In general: Max (Q) = TR(Q) – TC(Q)=P(Q)*Q - TC(Q) MR(Q) = MC(Q). Note that MR(Q) = ( P/ Q)*Q + P(Q) ≠ P optimum Q* and P* Monopolist’s Problem The Monopolist’s Problem Example: ◦ A monopolist faces a demand for its product given by: P=15 – 1/2Q. Its total cost takes the following form: TC 5 Q 2 ◦ Find the monopolist’s profit maximizing price and quantity. How much economic profit the monopolist earn? Seeking more surplus: Price Discrimination. So far, monopolist charges a single price to the entire market. What if the monopolist can charge multiple prices? ◦ First-degree price discrimination ◦ Second-degree price discrimination. ◦ Third-degree price discrimination. Degree = ability to identify consumers. Price Discrimination. Third Degree Price Discrimination: ◦ Low ability to distinguish consumers. ◦ Consumers are divided in groups/markets. ◦ Charge different prices across groups/markets. ◦ For each group, it is still a single price. Price Discrimination Third Degree Price MR Discrimination. MC 0 Q 1 ◦ Exercise: A monopolist two market segments MR MC faces 0 Q each with a well defined demand function. 5 Q ◦ Demand in market 1 is P = 10 – Q1 ◦ Demand in market 2 is P = 20 – Q2 Total Cost = 5 Q 2 1 2 2 2 If the monopolist exercises his monopoly power to price discriminate in the two market, what are the prices and quantity he charges in each market? What is his profit? If the monopolist cannot price discriminate, what is the market price and quantity? What is his profit in this case? Price Discrimination Third Degree Price Discrimination – Steps to solve the monopolist’s problem. Max = TR – TC where TR = TR1 + TR2 and Q= Q1 + Q2 ◦ First order conditions: Q1 Q2 MR1 MC 0 MR2 MC 0 ◦ Solve for Q1 and Q2. ◦ Substitute into the demand function to get P1 and P2. Price Discrimination. Third Degree Price Discrimination. Price Discrimination. Second Degree Price Discrimination. ◦ Charge small number of different prices in one group/market (quantity discount) Price Discrimination Second Degree Price Discrimination. ◦ Exercise (Hurdle Model of Price Disc.) 2 A monopolist has the total cost curve as: TC= 5 Q He sets two price PH and PL . To be eligible to buy at PL, buyer needs to present a coupon cut from a local newspaper (hurdle). Suppose the demand curve is: P = 20 – Q. What are the profit maximizing values of PH and PL . What is the resulting economic profit? A new law prevent the monopolist to price discriminate. What is his profit under this law? Are buyers better or worse off under this new law? Price Discrimination Second Degree Price Discrimination - Hurdle Model of Price Disc. ◦ The monopolist charges two prices PL and PH associated with quantity purchased QL and QH : Max = TR – TC where TR = PHQH + PLQL , Q= QL + QH and PH = a + bQH ; PL = a + b(QL + QH) ◦ First order conditions: QL QH MRL MRH MC MC 0 0 ◦ Solve for QL and QH. ◦ Substitute into the demand function to get PL and PH. Price Discrimination. First-degree price discrimination: ◦ Charge different price for each different unit purchased. Price Discrimination. Practical application – Two part Tariff. ◦ Necessary conditions: Individual demand curves are all known No arbitrage opportunity. ◦ Method: Total amount (= tariff) the consumer pays for q units is T(q) = F + p*q F: fixed fee, p: per-unit charge Result: Charge consumer p=MC and F equal to the would-be consumer surplus when p=MC. Hence F is different for each consumer. Special case: if consumers are identical F is equal across consumers. Price Discrimination First Degree Price Discrimination – 2 part tariff. ◦ Exercise: Consider the monopolist presented in the previous exercise with demand curve given by P=120 – Q and the MC =2Q. ◦ If the monopolist is allowed and is able to first price discriminate, using the two part tariff method to identify his fixed fee and the per unit price and quantity associated with that price. ◦ What happen to the DWL? Other pricing method: Sell in Bundle. Example: Sell Word and Excel separately or sell the bundle called Microsoft office. Two types of consumers, A and B. A’s valuations are 120 for Word and 80 for Excel. B’s valuations are opposite: 80 for Word and 120 for Excel. MC=0. Microsoft can sell all programs separately for 2*80+2*80=$320 Microsoft can also sell two times MS Office Suite for 2*200=$400