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)/2b (a-c)/b Solve the two reaction functions q1* = (a-c)/3b = q2* Market Price = a/3 + 2c/3 < Monopoly Price Firm 1 output Cournot model says total output is greater than monopoly, Price and total profits lower
Models of Oligopoly Augustin (Augie) Cournot model Cournot Example 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 Augustin (Augie) Cournot model Cournot Example 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 $5. The firm faces a market demand curve given by P = 53 - Q. Find profit-maximizing price, output, profit and resulting DWL. Suppose a second firm, with same cost structure, enters the market. Assuming the firms are Cournot duopolists, find each firm’s reaction function. What are the Cournot equilibrium, market price, and profits of each firm?
Models of Oligopoly Augie Cournot Hank Stackelberg Joe Bertrand Dominant Firm (or Price Leadership) model Cooperative (cartel) model
Models of Oligopoly Heinrich von (Hank) Stackelberg model Continue our previous example Is it advantageous to go first? How much will each firm produce now? Assume firm 1 acts first (the “Stackelberg leader”) and firm 2 is a “naive Cournot follower” Yes, it is advantageous to move first ( 1 = 22 ). Why? Fait accompli. Your output is large regardless of what rival does.
Models of Oligopoly Augie Cournot Hank Stackelberg Joe Bertrand Dominant Firm (or Price Leadership) model Cooperative (cartel) model
Models of Oligopoly Joe Bertrand Model Each firm assumes its rival does not change price Two catalog firms announce their prices when they send out fall edition Customers buy from lower-priced seller Low-priced seller supplies whole market With P>MC, under-cutting is profitable Equilibrium is same as competitive market, P = MC Price Criticisms Key assumptions: firms take their rivals’ output (or price) as given These are clearly wrong as the market is adjusting toward equilibrium monopoly (a+c)/2 cournot c bertrand 1 2 3 4 5 # firms
Models of Oligopoly Augie Cournot Hank Stackelberg Joe Bertrand Dominant Firm (or Price Leadership) model Cooperative (cartel) model
Models of Oligopoly Dominant Firm model (aka, Price Leadership model) Here the leader assumes its rivals behave as competitors in choosing qi Price ($/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 drug falls 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 Q’dom Qdom Qfringe 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 Pcipec not much above Pcomp P1 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 Qcipec Qtotal Qfringe Output Qc+c
Price Leadership Model of Oligopoly Example 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
Models of Oligopoly Augie Cournot Hank Stackelberg Joe Bertrand Dominant Firm (or Price Leadership) model Cooperative (cartel) model
Cartel Model of Oligopoly Banned by antitrust laws in the US, but not in many other countries Firms attempt 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 Output Price Dmkt S P1 Q Market Firm d AC MC dcartel mrcartel q*cartel P2 MRmkt Nq*cartel d’ q*cheater