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ECON191 (Spring 2011) 4 & 6.5.2011 (Tutorial 10) Chapter 12 Monopolistic Competition and Oligopoly Monopolistic competition Market in which firms can enter freely, each producing its own brand or version of a differentiated product Key characteristics: (1) Firms compete by selling differentiated products that are highly substitutable. The cross elasticities of demand are large (2) Free entry and exit The amount of monopoly power depends on the degree of differentiation Equilibrium in the SR and the LR Short-run Demand is downward sloping (differentiated products) and is relatively elastic (close substitutes are available) Profits are maximized when MR = MC. P > MR = MC as the firm has monopoly power to a certain extent This firm is making economic profits Long-run Profits will attract new firms to the industry (no barriers to entry) The existing firm’s demand will decrease to DLR Firm’s output and price will fall Industry output will rise No economic profit (P = AC) P > MC (some monopoly power) 1 Monopolistic competition and economic efficiency The monopoly power yields a higher price than perfect competition and is not efficient which comes from the following two sources: (1) P > MC If price was lowered to the point where MC = D, consumer surplus would increase by the yellow triangle (Deadweight loss) (2) Excess capacity With no economic profits in the long run, the firm is still not producing at minimum AC and excess capacity exists. Firm faces downward sloping demand so zero profit point is to the left of minimum average cost Excess capacity is inefficient because average cost would be lower with fewer firms Inefficiencies would make consumers worse off, should monopolistic competition be regulated? NO (1) Market power relatively small and deadweight loss is small (2) Inefficiency is balanced by the benefit of increased product diversity which may easily outweigh deadweight loss 2 Oligopoly Oligopoly: market or industry with two or a few firms. The simplest case is Duopoly. Characteristics: Small number of firms Product differentiation may or may not exist Barriers to entry (Scale economies, Patents, Technology, Name recognition, Strategic action) The Cournot model Oligopoly model in which firms produce a homogeneous good, each firm treats the output of its competitors as fixed, and all firms decide simultaneously how much to produce Firm 1’s profit-maximizing output depends on how much it thinks that Firm 2 will produce. If it thinks Firm 2 output = 0, Firm 1’s demand curve is D1(0), which is the market demand curve. The corresponding MR curve is MR1(0) Firm 1 produces 50 units where MC1 = MR1 If Firm 1 thinks that Firm 2 will produce 50 units, its demand curve becomes D1(50) and profit maximizing output = 25 If Firm 1 thinks that Firm 2 will produce 75 units, Firm 1 will produce only 12.5 units. Cournot equilibrium: a pair of output levels, one for each firm, which are such that after they are choose, neither firm has incentive to change its output level. (Cournot equilibrium is determined by the intersection of the reaction curves) Reaction function: relationship between a firm’s profit maximizing output and the amount it think its competitor will produce In Cournot equilibrium, each firm correctly assumes the amount that its competitor will produce and thereby maximizes its own profits. Therefore, neither firm will move from this equilibrium. Nash equilibrium: set of strategies or actions in which each firm does the best it can given its competitors’ actions 3 Representing the Cournot duopoly game by algebra Market demand: p a (q1 q2 ) Cost functions: c(q1 ) cq1 , c(q2 ) cq2 Firm 1 and firm 2 each faces a maximizing problem at the same time and the two firms are symmetric. MC for both firm = c Firm 1’s Profit function: TR TC pq1 cq1 Firm 1’s maximizing problem: Max 1 aq1 q12 q1q 2 cq1 0 q1 FOC: a 2q1 q2 c 0 q1C (a, c are constant, a c q 2C (Firm 1’s reaction function) 2 ac is the y-intercept of firm 1’s reaction function and slope = –1/2) 2 Firm 2’s maximizing problem: Max 2 aq2 q 22 q1q 2 cq2 0 q2 FOC: a 2q2 q1 c 0 a c q1C q (Firm 2’s reaction function) 2 C 2 Solving the two reaction functions for the Cournot equilibrium, it yields, ac 2(a c) q1C q2C 、 q1C q2C 3 3 a 2c pC 3 2 a 2c a c (a c) C C C c Profit for firm 1: 1 ( p c)q1 9 3 3 2 a 2c a c (a c) c Profit for firm 2: 2C ( p C c)q 2C 9 3 3 Representing the Collusion by algebra If the two firms collude, they maximize the total profit. Market demand: p a Q a (q1 q2 ) c(Q) cQ Cost functions: The monopolist’s maximizing problem: Max aQ Q 2 cQ 0Q FOC: a 2Q c 0 ac ac Q* q1* q2* 2 and 4 ac p* 2 (a c) 2 1* 2* 8 4 Representing the Competitive model by algebra Market demand: p a Q a (q1 q2 ) Cost functions: c(q1 ) cq1 , c(q2 ) cq2 In the competitive market, p a Q c QCOMP a c q1COMP q2COMP ac 2 p* c 1COMP 2COMP 0 Representing the Stackelberg duopoly game by algebra Stakelberg model: Oligopoly model in which one firm sets its output before other firms do Market demand: p a (q1 q 2 ) Cost functions: c(q1 ) cq1 , c(q2 ) cq2 Suppose firm 1 chooses q1, firm 2 is rational. Hence firm 2 chooses q2 to solve the following maximizing problem: Max 2 aq 2 q 22 q1 q 2 cq2 0 q2 FOC: a 2q 2 q1 c 0 a c q1S q (q ) 2 S 2 S 1 Firm 1 knows that firm 2 is rational, and knows if he produces q1, firm 2 will produce q2S (q1S). Firm 1’s problem is: Max 1 aq1 q12 q1q2S (q1S ) cq1 0 q1 aq1 cq1 q12 cq1 0 q1 2 FOC: a 2q1 12 (a c 2q1 ) c 0 Max 1 aq1 q12 a c q1S a c ac , q2S (q1S ) 2 4 2 a 3 c p S a (q1 q 2 ) 4 2 a 3c a c (a c) c Profit for firm 1: 1S ( p S c)q1S 8 4 2 q1S 2 a 3c a c (a c) c Profit for firm 2: 2S ( p S c)q 2S 16 4 4 5 Representing the monopoly game by algebra Market demand: p a QM Cost functions: c(QM) = cQM The monopolist’s maximizing problem: Max M aQM QM2 cQM 0QM FOC: a 2QM c 0 ac QM* 2 ac p M* 2 2 ac a c (a c) * * * M ( p M c)QM c 4 2 2 Welfare properties of duopolistic markets and comparisons Comparing prices, quantities and profit with algebra Price Monopoly Cournot Stackelberg Bertrand ac 2 a 2c pC 3 a 3c pS 4 p M* pB c Firm 1’s output ac 2 a c q1C 3 ac q1S 2 a c B q1 2 Firm 2’s output QM* Industry output ac 3 ac q 2S (q1S ) 4 ac B q2 2 Firm 2’s profit ac 2 2 ( a c) QC 3 3(a c) QS 4 (a c) 4 (a c) 2 1C 9 ( a c) 2 1S 8 ( a c) 2 9 ( a c) 2 2S 16 Q B (a c) 1B 0 2B 0 QM* q 2C Firm 1’s profit M* 2 In the above analysis, assume a > c, since quantities of output must be positive. p M pC p S p B Q B Q S QC Q M S M leader iC1, 2 Sfollower B 2C – – Comparing Cournot and Stackelberg equilibrium: In the Cournot model, both firms choose quantities simultaneously. In the Stackelberg game, one firm will be the leader and the other will be the follower, they move sequentially, there is always a first mover advantage. p C p S , QC Q S – For Firm 1, ac ac q1C 2 3 2 2 1S (a c) 1C (a c) 8 9 q1S – For Firm 2, q 2C a c q2S (q1S ) a c 2C 3 4 2 ( a c) (a c) 2 2S 9 16 6 Comparing consumer surplus, producer surplus and DWL Welfare is measured in terms of consumer surplus and producer surplus Cournot equilibrium outputs are in between the two extremes of monopoly and perfect competition P DWL under monopoly p M* ac 2 DWL under Cournot duopoly a 2c 3 p COMP p B c pC MC = c DD : MR ac Q 2 * M QC p=a–Q QCOMP Q B (a c) Q 2(a c) 3 Market demand: p = a – Q Marginal cost: c Perfectly competitive market In the perfectly competitive market, firm’s output is welfare maximizing quantity Consumer surplus is maximized No producer surplus as price is equal to MC Total surplus maximized No DWL The result is the same in Bertrand duopoly Monopoly Firm’s output is lower which is not welfare optimal Price is higher than the competitive price and the Cournot price CS falls and PS rises Total surplus is not maximized, and there exists a DWL Cournot duopoly The price and quantity is between perfectly competitive market and monopoly The Cournot equilibrium quantity is still not welfare optimal, it is better than monopoly, but worse than perfectly competitive market. Stackelberg duopoly The price and quantity is between perfectly competitive market and Cournot equilibrium. The Stackelberg equilibrium quantity is still not welfare optimal, it is better than monopoly, but worse than perfectly competitive market. (It’s also better than Cournot equilibrium) 7 Comparing equilibrium price and quantity with iso-output line Output of firm 2 q2 ac COMP Reaction function for firm 1 q1 f 1 (q 2 ) 2(a c) 3 q2 QM* Welfare optimal output q1 q2 a c ac 2 Cournot output q1 q2 ac q 3 C 2 E Reaction function for firm 2 q 2 f 2 (q1 ) Monopoly output q1 q2 2(a c) 3 ac 2 Output of firm 1 q1C ac 3 QM* ac 2 q1 q1 COMP 2(a c) 3 ac (monopoly output) 2 a c (competitive output), the optimal response for firm 1 is 0 When q2 = 0, the optimal response for firm 1 is QM* When q2 = q1 When q1 = 0, the optimal response for firm 2 is QM* When q1 = q1 C ac C ac 2 a c , the optimal response for firm 2 is 0 Iso-output line: different combinations of q1 and q2 give the same amount of total output at same price level Since price level depends on the total output, as the total output level is constant over all the output combinations on the same iso-product line, price level is constant on an iso-product line. Point E is the Cournot equilibrium Cournot equilibrium quantity is on an iso-output line strictly between the monopoly line and the welfare optimal line At Cournot equilibrium, price and quantity are between the monopoly and welfare optimal levels The outcome for society between the monopoly and welfare optimal levels 8 Numerical Example: Let there be 2 firms, A and B, in a market of the same good MC = 2 for both Firm A and Firm B The demand function of the market is given by P 26 q A q B Cournot Model Scenario 1: Cournot equilibrium Firm A’s profit maximizing problem: Max A (26 q A q B )q A 2q A qA FOC: 24 2q A q B 0 q q *A 12 B (Reaction function for firm A) 2 Firm B’s profit maximizing problem: Max B (26 q A q B )q B 2q B qB FOC: 24 2q B q A 0 q q B* 12 A (Reaction function for firm B) 2 Solving the two reaction functions for the Cournot equilibrium: q*A qB* 8 and p* 10 Profit for firm A p * q *A 10(8) 2(8) 64 Profit for firm B p * q B* 10(8) 2(8) 64 Scenario 2: Cartel If Firm A and Firm B collude, they will act as a monopoly and will maximize the joint profit. Their joint maximization problem: Max (26 Q)Q 2Q Q FOC: 24 2Q 0 Q* = 12, q *A q B* 6 p * 14 Profit for firm A p * q *A 14(6) 2(6) 72 Profit for firm B p * q B* 14(6) 2(6) 72 The total profit Cartel is higher (monopoly profit = 72 + 72) than the total profit in Cournot equilibrium (total profit = 64 + 64). 9 Cartel and stability Cartel is not stable. We could show that both firms will have incentive to depart from the collusion. In the end, they will act independently with the equilibrium as in the case of oligopoly (Cournot equilibrium). In the Cartel, q *A q B* 6 . Both firms will have incentive to increase production for a higher profit, given the other firm follow the cartel. Scenario 3: One of the firm deviates Suppose Firm B follows the cartel and produces q B* 6 . According to the Reaction function of Firm A, q q *A 12 B 9 2 p* = 26 – (qA + qB) = 26 – 6 – 9 =11 Profit for firm A p * q *A 11(9) 2(9) 81 Profit for firm B p * q B* 11(6) 2(6) 54 Firm B will also have incentive to deviate from the cartel too. Scenario 4: Both of the firms deviate If both firm A and B deviate and q *A 9 , q B* 9 , p* = 26 – 9 – 9 = 8 Profit for each firm = 54 From the above example, we could show that the cartel is not stable, both of them will deviate and it end up in the Cournot equilibrium again. We could analysis the scenario by game theory and represent it with a payoff matrix. (In fact, it is a Prisoner’s dilemma game) Comparison of equilibrium Price Firm A’s output Firm B’s output Industry output Firm A’s profit Firm B’s profit Cournot p* 10 q*A 8 qB* 8 Q = 16 A 64 B 64 Cartel p * 14 q*A 6 qB* 6 Q = 12 A 72 B 72 One firm (A) deviates Both firm deviate p* 11 q*A 9 qB* 6 Q = 15 A 81 B 54 p* 8 q*A 9 qB* 9 Q = 18 B 54 B 54 Profit under Cartel is the highest, however, as the cartel is not stable, firms will deviate and end up in Cournot equilibrium. (Profit for each firm 72 > 64) 10 Stackelberg Model Suppose firm 1 chooses q1, firm 2 is rational. Hence firm 2 chooses q2 to solve the following maximizing problem: Max B (26 q A q B )q B 2q B qB FOC: 24 2q B q A 0 q AS q (q ) 12 2 * B S A Firm 1 knows that firm 2 is rational, and knows if he produces q1, firm 2 will produce qBS (qAS). Firm 1’s problem is: Max A [26 q A q BS (q AS )]q A 2q A qA FOC: 26 2q A 12 q A 2 0 q*A 12 , qB* 6 and p * 8 Profit for firm A: A ( p* c)q1* 72 . Profit for firm B: B ( p* c)q2* 36 Bertrand Model p* MC 2 . p 26 q A q B , q A q B 12 , A B 0 Monopoly The monopolist’s maximizing problem: Max (26 qM )qM 2qM qM FOC: 26 2qM 2 0 qM* 12 , p* 14 and M 144 11