Lecture 6 Oligopoly II PDF

Lecture 6 Oligopoly II 5ECON010C-n Intermediate Microeconomics LECTURE OUTLINE 1. Oligopoly 2. Price Competition 3. Competition versus Collusion: The Prisoners’ Dilemma 4. Implications of the Prisoners’ Dilemma for Oligopolistic Pricing  Cournot Model: Example of Competitive...

Lecture 6 Oligopoly II 5ECON010C-n Intermediate Microeconomics LECTURE OUTLINE 1. Oligopoly 2. Price Competition 3. Competition versus Collusion: The Prisoners’ Dilemma 4. Implications of the Prisoners’ Dilemma for Oligopolistic Pricing  Cournot Model: Example of Competitive Equilibrium Two firms demand curve: 𝑃 = 30 – 𝑄 (where Q= 𝑄1 +𝑄2 ) Marginal costs for both firms is zero: 𝑀𝐶1 = 𝑀𝐶2 = 0 Total revenue for Firm 1: 𝑅1 = 𝑃𝑄1 = (30 – 𝑄)𝑄1 ∆𝑅1 Then: 𝑀𝑅1 = = 30 – 2𝑄1 – 𝑄2 ∆𝑄1 Setting 𝑀𝑅1 = 0 (MC) and solving for 𝑄1 , we find Firm 1’s reaction curve: 𝑸𝟐 𝑸𝟏 = 𝟏𝟓 − 𝟐 By the same calculation, Firm 2’s reaction curve: 𝑸𝟏 𝑸𝟐 = 𝟏𝟓 − 𝟐 Cournot equilibrium: 𝑄1 = 𝑄2 = 10 Total quantity produced: 𝑄1 + 𝑄2 = 20  Stackelberg model Last week we saw how oligopolistic firms set their quantities at the same time Now let’s see what happens if one of the firms can set its output first Then two questions arise: 1. Is it advantageous to go first? 2. How much will each firm produce? This market situation is explained by Stackelberg model  First Mover Advantage—The Stackelberg Model Stackelberg model: Oligopoly model in which one firm sets its output before other firms do. Suppose Firm 1 sets its output first and then Firm 2, after observing Firm 1’s output, makes its output decision. In setting output, Firm 1 must therefore consider how Firm 2 will react. P = 30 – Q (where Q= 𝑄1 +𝑄2 ) Also, MC1 = MC2 = 0 Firm 2’s reaction curve: Q 2 = 15 − 1 Q1 2 Firm 1’s revenue: R1 = PQ 1 = 30Q 1 − Q12 − Q 2Q 1 2 1 R1 = 30Q1 − Q1 − Q1 15 − Q1 2 1 R1= 15Q1 − Q21 ; MR1 = ΔR1 ΔQ1 = 15 − Q1 2 Setting MR1 = 0 gives Q1 = 15, and Q2 = 7.5 We conclude that Firm 1 produces twice as much as Firm 2 and makes twice as much profit. Going first gives Firm 1 an advantage.  Price competition: Bertrand model So far, we learned how oligopolies compete or collude on output levels But they also can compete on prices If they produce very similar or the same product, their price competition is explained by Bertrand model In Bertrand model two players set their prices at the same time and treat each other’s prices as constant Price Competition Price Competition with Homogeneous Products Bertrand model: Oligopoly model in which firms produce a homogeneous good, each firm treats the price of its competitors as fixed, and all firms decide simultaneously what price to charge. Let’s return to the duopoly example of the last section and see the price set in Cournot Model first. P = 30 – Q MC1 = MC 2 = $3 Q1 = Q2 = 9, and in Cournot equilibrium, the market price is $12, so that each firm makes a profit of $81. Price Competition Price Competition with Homogeneous Products—The Bertrand Model Now suppose that these two duopolists compete by simultaneously choosing a price instead of a quantity. P = 30 – Q MC1 = MC 2 = $3 Nash equilibrium in the Bertrand model results in both firms setting price equal to marginal cost: P1 = P2 = $3. Then industry output is 27 units, of which each firm produces 13.5 units, and both firms earn zero profit. In the Cournot model, because each firm produces only 9 units, the market price is $12. Now the market price is $3. In the Cournot model, each firm made a profit; in the Bertrand model, the firms price at marginal cost and make no profit. Price competition: Bertrand model In simultaneous price competition, both players keep lowering their prices to gain bigger market share This inevitably leads to prices reaching average cost (or constant marginal cost) When prices reach this level, competition stops, because here firms make zero profit So, equilibrium in Bertrand model is zero-profit price level Price Competition Price Competition with Differentiated Products Suppose each of two duopolists has fixed costs of $20 but zero variable costs, and that they face the same demand curves: FC=20,VC=0; Firm 1’s demand: Q 1 = 12 − 2P 1 + P 2 𝜋1 =? Firm 2’s demand: Q 2 = 12 − 2P 2 + P 1 Firm 1’s profit is: 𝜋1 = 𝑃1 𝑄1 − 20 𝜋1 = 𝑃1 12 − 2𝑃1 + 𝑃2 − 20 Profit-maximizing price is: ∆𝜋1 = 12 − 4𝑃1 + 𝑃2 = 0 𝜋1 = 12𝑃1 − 2𝑃12 + 𝑃1 𝑃2 − 20 ∆𝑃 1 1 Firm 1’s reaction curve: 𝑃1 = 3 + 𝑃2 4 1 Similarly, Firm 2’s curve: 𝑃2 = 3 + 𝑃1 4 Solve these equations and you get 𝑷𝟏 = 𝑷𝟐 = 𝟒  Price Competition NASH EQUILIBRIUM IN PRICES 1 Firm 1’s reaction curve: 𝑃1 = 3 + 𝑃2 4 1 Similarly, Firm 2’s curve: 𝑃2 = 3 + 𝑃1 4 Solve these two as system of equations and you get: 𝑷𝟏 = 𝑷𝟐 = 𝟒 This is Nash equilibrium price  Competition vs. collusion Both players know that if they compete, they can charge no more than 4 dollars If they collude – they can charge 6 dollars and make greater profit But if one of the players cheats, he might get even higher profit at the expense of the competitor Assume, both players agreed to charge 6 dollars. Let’s see what happens if both players hold to their promises Competition v collusion: example Q 1 = 12 − 2P 1 + P 2 Q 2 = 12 − 2P 2 + P 1 Recall their profit functions: 𝜋1 = 12𝑃1 − 2𝑃12 + 𝑃1 𝑃2 − 20 𝜋2 = 12𝑃2 − 2𝑃22 + 𝑃1 𝑃2 − 20 If both of them honor the agreement, their profits are: 𝜋1 = 12 6 − 2(6)2 + 6 6 − 20 = 16 𝜋2 = 12 6 − 2(6)2 + 6 6 − 20 = 16 If Firm 1 cheats and charges 4 dollars to gain market share, the profits are: 𝜋1 = 12 4 − 2(4)2 + 4 6 − 20 = 20 𝜋2 = 12 6 − 2(6)2 + 6 4 − 20 = 4 Competition v collusion Similarly, if Firm 2 cheats and charges 4 dollars to gain market share, the profits are: 𝜋1 = 12 6 − 2(6)2 + 6 4 − 20 = 4 𝜋2 = 12 4 − 2(4)2 + 4 6 − 20 = 20 If they both cheat and charge 4 dollars, they go back to competitive equilibrium and make profits of: 𝜋1 = 12 4 − 2(4)2 + 4 4 − 20 = 12 𝜋2 = 12 4 − 2(4)2 + 4 4 − 20 = 12 So, when colluding, each player is going after higher profit, but also taking a risk of being cheated by the competitor Competition versus Collusion: The Prisoners’ Dilemma PAYOFF MATRIX payoff matrix: Table showing profit (or payoff) to each firm given its decision and the decision of its competitor. TABLE 12.3 PAYOFF MATRIX FOR PRICING GAME FIRM 2 FIRM 2 Charge $4 Charge $6 Firm 1 Charge $4 $12, $12 $20, $4 Firm 1 Charge $6 $4, $20 $16, $16 Noncooperative game: Game in which negotiation and enforcement of binding contracts are not possible. Implications of the Prisoners’ Dilemma for Oligopolistic Pricing Price Signaling and Price Leadership Price signaling: Form of implicit collusion in which a firm announces a price increase in the hope that other firms will follow suit. Price leadership: Pattern of pricing in which one firm regularly announces price changes that other firms then match. In some industries, a large firm might naturally emerge as a leader, with the other firms deciding that they are best off just matching the leader’s prices, rather than trying to undercut the leader or each other. Price leadership can also serve as a way for oligopolistic firms to deal with the reluctance to change prices, a reluctance that arises out of the fear of being undercut or “rocking the boat.”  Dominant player The Dominant Firm Model Dominant firm: Firm with a large share of total sales that sets price to maximize profits, taking into account the supply response of smaller firms. What if there is one big player competing with many small firms? Then the dominant firm’s demand (𝐷𝐷 ) would be the difference between total market demand (𝐷) and combined supply of all small fringe firms (𝑆𝐹 ) At 𝑃1 supply by fringe firms is equal to market demand i.e. small firms fully satisfy the market. So, demand for the products of the dominant player is 0 Dominant player At 𝑃2 fringe firms supply zero output. So, demand for the products of the dominant player is equal to market demand. Between 𝑃1 and 𝑃2 the dominant player faces 𝐷𝐷 demand curve. At prices below 𝑃2 the dominant player faces market demand curve. Dominant player Dominant player chooses the output level where 𝑀𝑅 = 𝑀𝐶 and supply 𝑄𝐷 Fringe firms altogether supply 𝑄𝐹 Total output is, hence: 𝑸𝑻 = 𝑸𝑫 + 𝑸𝑭  Reading Mandatory reading Pindyck & Rubinfeld (2015). “Microeconomics”, 8th edition. Chapter 12 Optional reading https://www.jstor.org/stable/193221?seq=11#metadata_info_tab_contents Workshop reading Boeing and Airbus, the new ‘super duopoly’ (2,000 words), https://www.washingtonpost.com/news/wonk/wp/2018/04/25/boeing-and- airbus-the-new-super-duopoly/ 5ECON010C-n Intermediate Microeconomics