1 © 2006 by Nelson, a division of Thomson Canada Limited Christopher Michael Trent University Managerial Economics – Econ 340 Lecture 8 Price and Output Determination: Oligopoly

2 © 2006 by Nelson, a division of Thomson Canada Limited Topics Cournot Oligopoly Collusion versus Competition Price Leadership Kinked Demand Curve Oligopolistic Rivalry and Game Theory

3 © 2006 by Nelson, a division of Thomson Canada Limited Overview Oligopolistic Market Structures »Few Firms Consequently, each firm must consider the reaction of rivals to price, production, or product decisions These reactions are interrelated »Heterogeneous or Homogeneous Products Example -- athletic shoe market »Nike has 47% of market »Reebok has 16% »Adidas has 7%

4 © 2006 by Nelson, a division of Thomson Canada Limited Nokia’s Challenge in Cell Phones The market shares of oligopolists change. In 1998, the market leader in cell phones was Motorola with 25% market share and Nokia second with 20% In 2002, leadership reversed: Nokia held 37% of the market and Motorola 17% However, technology in phones is changing, bringing wireless web, photos, and other high-speed G3 technologies Entry of other firms and new products, such as Dell, Palm, NEC and Panasonic pose threats to Nokia’s profit margins Nokia must decide whether or not to invest heavily in the 3G technology for the future. Being a leader in a oligopoly does not mean that you remain the leader for long.

5 © 2006 by Nelson, a division of Thomson Canada Limited The Cournot Oligopoly Models vary depending on assumptions of actions of rivals to pricing and output decisions. Augustin Cournot (1838) created a model that is the basis of Competition Policy. »Relatively simple assumption: ignore the interdependency with rivals »This makes the math easy Cournot

6 © 2006 by Nelson, a division of Thomson Canada Limited A Numerical Example: Competition, Monopoly, and Cournot Oligopoly IN COMPETITION »P = MC, so Q = 50 »P C = $50 and Q M = 900 IN MONOPOLY »MR = MC, so Q = 50 »Q M = 450 so »P M = = $500 IN DUOPOLY »Let Q = q 1 + q 2 D P M P cournot P C Q M Q Cournot Q C $500 $350 $50 Let: P = Q and MC =50

7 © 2006 by Nelson, a division of Thomson Canada Limited Cournot Solution: Case of 2 Firms (Duopoly) Assume each firm maximizes profit Assume each firm believes the other will NOT change output as they change output. »The so-called: Cournot Assumption Find where each firm sets MR = MC

8 © 2006 by Nelson, a division of Thomson Canada Limited Q Let Q = q 1 + q 2 l P = Q = q 1 - q 2 and MC = 50 l TR 1 = P q 1 = ( q 1 -q 2 )q 1 =950q 1 - q q 1 q 2 and l TR 2 = P q 2 = ( q 1 -q 2 )q 2 =950q 2 - q 2 q 1 - q 2 2 l Set MR 1 = MC & MR 2 = MC q 1 - q 2 = q 1 - 2q 2 = 50 2 equations & 2 unknowns

9 © 2006 by Nelson, a division of Thomson Canada Limited With 2 Equations & 2 Unknowns: Solve for Output q 1 - q 2 = q 1 - 2q 2 So, q 2 = q 1 Then plug this into the demand equation we find: q 1 - q 1 = q 1 = 50. Therefore q 1 = 300 and Q = 600 The price is: P = = $ 350 P Q Competition Cournot Monopoly Cournot’s answer is between the other two.

10 © 2006 by Nelson, a division of Thomson Canada Limited N-Firm Cournot Model For 3 firms with linear demand and cost functions: »Q = q 1 + q 2 + q 3 »In linear demand and cost models, the solution is higher output and lower price Q Cournot = { N / (N+1) }Q Competition QCQC N N PCPC THEREFORE, Increasing the Number of Firms increases competition. This is the historical basis for Competition Policy

11 © 2006 by Nelson, a division of Thomson Canada Limited Example: Cournot as N Increases If N = 3 Triopoly P = Q & MC=50 Then, Q = (3/4)(900) Q = 675 P =$275 If N = 5 P = Q and MC = 50 Then Q = (5/6)(900) Q = 750 P = $200 N = 3 N = 5

12 © 2006 by Nelson, a division of Thomson Canada Limited Collusion versus Competition? Sometimes collusion succeeds Sometimes forces of competition win out over collective action When will collusion tend to succeed? »There are six factors that influence successful collusion as follows:

13 © 2006 by Nelson, a division of Thomson Canada Limited 1.Number and Size Distribution of Sellers. Collusion is more successful with few firms or if there exists a dominant firm. 2.Product Heterogeneity. Collusion is more successful with products that are standardized or homogeneous 3.Cost Structures. Collusion is more successful when the costs are similar for all of the firms in the oligopoly. 4.Size and Frequency of Orders. Collusion is more successful with small, frequent orders. 5.Secrecy and Retaliation. Collusion is more successful when it is difficult to give secret price concessions. 6.Percentage of External Orders. Collusion is more successful when percentage of orders outside of the cartel is small. Factors Affecting Likelihood of Successful Collusion

14 © 2006 by Nelson, a division of Thomson Canada Limited Oligopolies & Incentives to Collude When there are just a few firms, profits are enhanced if all reduce output But each firm has incentives to “cheat” by selling more MC  MC P q D QMQM incentive to cut price MR Representative firm Industry

15 © 2006 by Nelson, a division of Thomson Canada Limited Examples of Cartels Ocean Shipping De Beers -- diamonds OPEC - oil cartel, with Saudi Arabia making up 33% of the group’s exports Siemens and Thompson-CSF -- airport radar systems Major League Baseball

16 © 2006 by Nelson, a division of Thomson Canada Limited PRICE LEADERSHIP Barometric : One (or a few firms) sets the price One firm is unusually aware of changes in cost or demand conditions The barometer firm senses changes first, or is the first to ANNOUNCE changes in its price list Find barometric price leader when the conditions unsuitable to collusion & firm has good forecasting abilities or good management

17 © 2006 by Nelson, a division of Thomson Canada Limited Dominant Firm Price Leadership Dominant Firm: large market share. No price or quantity collusion Dominant Firm (L) expects the other firms (F) to follow its price and produce where  MC F = P L DTDT  MC F DLDL Net Demand Curve: D L = D T -  MC F leader’s demand

18 © 2006 by Nelson, a division of Thomson Canada Limited Find leader’s demand curve, D L = (D T -  MC F ) Find where MR L = MC L DTDT   MC F DLDL MR L Graphical Approach to Dominant Firm Price Leadership

19 © 2006 by Nelson, a division of Thomson Canada Limited At Q L, find the leader’s price, P L Followers will supply the remainder of Demand: (Q T - Q L ) = Q F D   MC F DLDL MR L MC L PLPL QLQL Graphical Approach to Dominant Firm Price Leadership

20 © 2006 by Nelson, a division of Thomson Canada Limited Followers will supply the remainder of Demand: (Q T - Q L ) = Q F D   MC F DLDL MR L MC L PLPL QLQL QTQT Graphical Approach to Dominant Firm Price Leadership

21 © 2006 by Nelson, a division of Thomson Canada Limited Implications of Dominant Firm Price Leadership Market Share of the Dominant Firm Declines Over Time »Entry expands  MC F, and Shrinks D L and MR L Profitability of the Dominant Firm Declines Over Time Market Share of the Dominant Firm is PROCYCLICAL » rises in booms, declines in recessions TIME profits

22 © 2006 by Nelson, a division of Thomson Canada Limited Numerical Example of Dominant Firm Price Leadership Aerotek is the leader, with 6 other firms, given the following: 1.P = 10,000 – 10 Q T is the market demand 2.Q T = Q L + Q F is the sum of leader & followers 3.MC L = Q L and SMC F = Q F

23 © 2006 by Nelson, a division of Thomson Canada Limited From 2, Q L = Q T – Q F and From 1, Q T = 1, P Since followers sell at P=MC, From 3, P = Q F, which rearranged to be Q F = 0.5P - 25 So, Q L = (1, P) – (0.5P - 25) = 1, P, which can be rearranged to be P = 1,708.3 – 1.67 Q L MR L = 1,708.3 – 3.34 Q L And MR L = MC L where: 1,708.3 – 3.34 Q L = Q L The optimal quantity for Aerotek, the leader is Q L  254 P = 1,708.3 – 1.67 Q L = 1,708.3 – 1.67(254)  $1,284. What is Aerotek’s Price and Quantity?

24 © 2006 by Nelson, a division of Thomson Canada Limited Kinked Oligopoly Demand Curve Belief in price rigidity founded on experience of the great depression Price cuts lead to everyone following »highly inelastic Price increases, no one follows »highly elastic everyone follows price cuts no one follows a price increase a kink at the price P

25 © 2006 by Nelson, a division of Thomson Canada Limited A Kink Leads to Breaks in the MR Curve Although MC rises, the optimal price remains constant Expect to find price rigidity in markets with kinked demand QUESTION: »Where would we more likely find KINKS and where NOT? P D D MR MC 2 MC 1

26 © 2006 by Nelson, a division of Thomson Canada Limited Oligopolistic Rivalry & Game Theory John von Neuman & Oskar Morgenstern— »Game Theory used to describe situations where individuals or organizations have conflicting objectives »Examples: pricing of a few firms, strategic arms race, advertising plans for a few firms, output decisions of an oligopoly Strategy—is a course of action »The PAYOFF is the outcome of the strategy. » Listing of PAYOFFS appear in a payoff matrix. A Strategy Game – involves decisions with consciously interdependent behaviour of two or more participants.

27 © 2006 by Nelson, a division of Thomson Canada Limited Two Person Game Each player knows the alternatives of all players Preferences of all players are known Single period game Each player can invade the territory of the other (Maraude) or Guard own territory Kahn’s payoff is given first, Randle’s payoff is second. Randle ranks Guard above Maraude. Randle has a Dominant Strategy: a decision that maximizes welfare independent of the other player’s strategy choice Knowing what Randle will do, Kahn decides to Guard as well. An Equilibrium—none of the participants can improve their payoff ASSUMPTIONS

28 © 2006 by Nelson, a division of Thomson Canada Limited Randle Kahn Guard Maraude Guard Maraude Better, 1 st Worst, 4 th Worse, 2 nd Best, 3 rd We will get to {Guard, Guard} which is an Equilibrium Two Person Game

29 © 2006 by Nelson, a division of Thomson Canada Limited Six or Seven Territories? Sharp and Xerox compete in copiers. Payoffs for Xerox are in the lower triangle The payoffs depend on the number of territories in which they compete Sharp has a dominant strategy of 6 territories. What should Xerox do? We see we get to {6, 6} as the iterated dominant strategy. Sharp Xerox 6 territories 7 territories $40 $70 $35 $55 $30 $60 $45 $45

30 © 2006 by Nelson, a division of Thomson Canada Limited Other Strategic Games These are viewed as single period, but businesses tend to be on-going, or multiple-period games These are two-person games, but oligopolies often represent N-person games, where N is greater than 2 Some games are zero-sum games in that what one player wins, the other player loses, like poker Other games are non-zero sum games where the whole payoffs depend on strategy choices by all players.

31 © 2006 by Nelson, a division of Thomson Canada Limited The Prisoner’s Dilemma Often the payoffs vary depending on the strategy choices The Prisoner’s Dilemma »Two suspects are caught and held separately Their strategies are either to Confess (C) or Not Confess (NC) »a one-period game »Suspect 1 in lower triangle (Bold Red) Noncooperative Solution »both confess: {C, C} Cooperative Solution »both do not confess {NC,NC} Off-diagonal represents a Double Cross suspect 2 suspect 1 NC C NC C 1 yr 0 yrs 15 yrs 6 yrs 1 yr 15 yrs 0 yrs 6 yrs

32 © 2006 by Nelson, a division of Thomson Canada Limited Paradox? The Prisoner’s Dilemma highlights the situation where both parties would be best off if they cooperated But the logic of their situation ends up with a non-cooperative solution The solution to cooperation appears to be transforming a one-period game into a multiple-period game. The actions you take now will then have consequences in future periods.