Economics 202: Intermediate Microeconomic Theory

Economics 202: Intermediate Microeconomic Theory • Finish Chapter 15

Oligopoly with Fixed Number of Firms • Reaction Functions • P = a - bQ, MC = c, Q = q1 + q2 • Profits for firm 1? (q1) = Pq1 - cq1 = (a-bq1-bq2) q1 - cq1 Max   MR = MC  a -2bq1-bq2= c Solving for q1  q1= (a-c-bq2)/2b This is firm 1’s “Reaction Function” Cournot Duopoly Firm 2 output (a-c)/b • (a-c)/2b q2* • Firm 2 has same solution • Which pair of quantities is Nash equilibrium? q1* (a-c)/b (a-c)/2b Firm 1 output • Solve the two reaction functions • q1* = (a-c)/3b = q2* • Market Price = a/3 + 2c/3 < Monopoly Price • Cournot model says total output is greater than monopoly, Price and total profits lower

Models of Oligopoly • Augustin (Augie) Cournot model • Each firm assumes its rival does not change output • Qmonopoly < Qcournot < Qcompetitive, thus Pmono > Pcournot > Pcomp • Cournot Example • A local carrot monopolist can produce at constant marginal cost of $5. The firm faces a market demand curve given by P = 53 - Q. • Find profit-maximizing price, output, profit and resulting DWL. • Suppose a second firm, with same cost structure, enters the market. Assuming the firms are Cournot duopolists, find each firm’s reaction function. • What are the Cournot equilibrium, market price, and profits of each firm?

Models of Oligopoly • Augie Cournot • Hank Stackelberg • Joe Bertrand • Dominant Firm (or Price Leadership) model • Cooperative (cartel) model

Models of Oligopoly • Heinrich von (Hank) Stackelberg model • Continue our previous example • Is it advantageous to go first? • How much will each firm produce now? • Assume firm 1 acts first (the “Stackelberg leader”) and firm 2 is a “naive Cournot follower” • Yes, it is advantageous to move first ( 1 = 22 ). Why? • Fait accompli. Your output is large regardless of what rival does.

Models of Oligopoly • Joe Bertrand Model • Each firm assumes its rival does not change price • Two catalog firms announce their prices when they send out fall edition • Customers buy from lower-priced seller • Low-priced seller supplies whole market • With P>MC, under-cutting is profitable • Equilibrium is same as competitive market, P = MC Price • Criticisms • Key assumptions: firms take their rivals’ output (or price) as given • These are clearly wrong as the market is adjusting toward equilibrium monopoly (a+c)/2 cournot c bertrand 1 2 3 4 5 # firms

Models of Oligopoly • Dominant Firm model (aka, Price Leadership model) • Here the leader assumes its rivals behave as competitors in choosing qi Price ($/unit) • How much can dominant firm sell? Sfringe • Now dominant firm sets MR = MC P1 • At Pdom, competitive rivals produce Qfringe MCdomin Pdom • Qdom + comp < Q comp + comp MCdom P2 • Pdom > MCdom & Pdom = MCfringe Dmkt MRdomin Qdom Qfringe Qd+c Qc+c Output

Price Leadership Model of Oligopoly • Application: pharmaceutical industry • Patent on drug X expires  copycats • Pbrand-name drug ? • Pbrand-name drugfalls • Brand-name manufacturers often then engage in 3rd-degree price discrimination • PHMO/Hosp < Plocal pharmacy • Why? • But there are drawbacks to this market segmentation strategy • Pharmacies have sued brand-name manufacturers to give them same low price Price ($/unit) Sfringe S’fringe MCdomin Pdom P’dom Dmkt MRdomin Qdom Qfringe Q’dom Qd+c Output

OPEC and CIPEC • OPEC is the Organization of Petroleum Exporting Countries • CIPEC is the French acronym for Int’l Council of Copper Exporting Countries • Why has OPEC been successful in raising its price, but CIPEC has not? • OPEC cartel as a dominant firm Price Oil Market Snon-opec • How much can dominant firm sell? P1 • Now dominant firm sets MR = MC • At Popec, rivals produce Qfringe • Qopec + comp < Q comp + comp Popec • Popec >> Pcomp • Inelastic Snon-opec & inelastic Dmkt inelastic Dopec Popec >> Pcomp • Price controls on gas in 1970s actually reinforced OPEC’s strategy!! • Encouraged domestic consumption • Discouraged domestic production Pcomp MCopec P2 Dmkt MRopec Qopec Qtotal Qfringe Output Qc+c

OPEC and CIPEC • CIPEC (Chile, Peru, Zambia, Zaire) • MCCIPEC is not much less than MCnon-cipec • Why has OPEC been successful in raising its price, but CIPEC has not? • CIPEC cartel as a dominant firm Price Copper Market • How much can dominant firm sell? • Now dominant firm sets MR = MC Snon-cipec • At Pcipec, rivals produce Qfringe P1 • Pcipec not much above Pcomp MCcipec • Why can’t CIPEC increase copper prices much? • D for copper is more elastic (aluminum is a good substitute) • Comp’ve supply more elastic than for oil (if P rises, simply go to scrap heap) • Successful cartel needs relatively inelastic D & inelastic Snon-cartel. Not easy Pcipec Pcomp P2 Dmkt MRcipec Qtotal Qcipec Qfringe Output Qc+c

Price Leadership Model of OligopolyExample • Assume an industry has two firms and market demand is given by P = 100 – 2Q where Q = qA + qB • The firms have the following cost functions • TCA = qA2 TCB = 3qB2 • Let A be the price leader (dominant firm), and firm B the competitive fringe firm, the follower • Calculate A and B

CartelModel of Oligopoly Firm Market Price MC S Price AC P2 P2 d’ P1 d dcartel Dmkt MRmkt mrcartel q*cartel q*cheater Nq*cartel Q Output Output • Cartel model of oligopoly • Banned by antitrust laws in the US, but not in many other countries • Firmsattempt to coordinate price and output decisions to earn monopoly  • MC1 = MC2 = … = MCN = MR • Why do cartels fail? caviar cartel story (1) incentive to cheat (2) heterogeneous cost structures/size/output (3) econ >0  entry

Economics 202: Intermediate Microeconomic Theory