1 Course outline I n Introduction n Game theory n Price setting – monopoly – oligopoly n Quantity setting – monopoly – oligopoly n Process innovation Homogeneous goods

2 Quantity and cost competition n Bertrand versus Cournot n Simultaneous quantity competition (Cournot) n Sequential quantity competition (Stackelberg) n Quantity Cartel n Concentration and competition

3 Price or quantity competition? p1p2p1p2 x1x2x1x2 Bertrand (1883) Cournot (1838)

4 n Bertrand (1883) criticized Cournot’s model (1838) on the grounds that firms compete by setting prices and not by setting quantities. n Kreps and Scheinkman (1983) defended Cournot’s model. They developed a two-stage game with capacities and proved that capacities in a Nash equilibrium are determined by Cournot’s model. Capacity + Bertrand = Cournot p1p2p1p2 k1k2k1k2

5 Cournot versus Stackelberg n Cournot duopoly (simultaneous quantity competition) n Stackelberg duopoly (sequential quantity competition) x2x2 x1x1 x1x2x1x2

6 Homogeneous duopoly (linear case) n Two firms (i=1,2) produce a homogenous good. n Outputs: x 1 and x 2, X= x 1 +x 2 n Marginal costs: c 1 and c 2 n Inverse demand function: n Profit function of firm 1:

7 Cournot-Nash equilibrium n Profit functions: n Reaction functions: n Nash equilibrium:

8 Computing the Cournot equilibrium (accommodation) n Profit function of firm 1 n Reaction function of firm 1 n Nash equilibrium

9 Depicting the Cournot equilibrium x 1 Cournot-Nash equilibrium C x 2

10 Exercise (Cournot) Find the equilibrium in a Cournot competition. Suppose that the demand function is given by p(X) = 24 - X and the costs per unit by c 1 = 3 and c 2 = 2.

11 Common interests n c 1, c 2  Obtaining government subsidies and negotiating with labor unions. n a , b  Advertising by the agricultural industry (e.g. CMA).

12 Exercise (taxes in a duopoly) Two firms in a duopoly offer petrol. The demand function is given by p(X)=5-0.5X. Unit costs are c 1 =0.2 and c 2 =0.5. a) Find the Cournot equilibrium and calculate the price. b) Now suppose that the government imposes a quantity tax t (eco tax). Who ends up paying it?

13 Two approaches to cost leadership n Direct approach (reduction of own marginal costs) - change of ratio between fixed and variable costs -investments in research and development (R&D) n Indirect approach (“raising rivals’ costs”) -sabotage -minimum wages, enviromental legislation

14 Direct approach, analytically n n Direct approach (reduction of your own marginal costs): direct effect strategic effect

15 Direct approach, graphically x 2 x 1 equilibria: increase in production of firm 1 marginal cost reduction of firm 1

16 Exercise (direct approach) n Who has a higher incentive to reduce own costs, a monopolist or a firm in Cournot- Duopoly?

17 Indirect approach, analytically n n Indirect approach (raising rival’s cost): =0 <0 <0 =0 direct effect strategic effect

18 Indirect approach, graphically increase of marginal costs of firm 2 x 2 x 1 equilibria: increase in production of firm 1

19 Reaction curve in the linear case x 1 x 2 Note: alone leads to a price of.

20 Blockaded entry, graphically x 2 x 1 C M firm 1 as a monopolist

21 Blockaded entry n Entry is blockaded for each firm: n Entry is blockaded for firm 2:

22 Blockaded entry (overview) c 2 c 1 duopoly no supply firm 1 as a monopolist firm 2 as a monopolist

23 Cournot – Executive summary n A duopoly will occur only, if entry is blockaded for other firms. n Firms have common and competing interests with respect to demand and cost functions. n There are two approaches to cost leadership. The direct approach is to lower your own marginal cost. The indirect approach is known as “raising rivals’ costs“.

24 Stackelberg equilibrium n Profit functions n Follower’s reaction function (2 nd stage) n Leader’s optimal quantity (1 st stage) n Nash equilibrium:

25 Finding the profit-maximizing point on the follower’s reaction curve Accommodation x 1 x 2 Blockade or deterrence

26 Computing the Stackelberg equilibrium (accommodation) n Reaction function of firm 2: n Profit function of firm 1: n Nash equilibrium with and

27 Depicting the Stackelberg outcome (both firms produce) x 2 x 1 quantities in a Stackelberg equilibrium C S

28 Exercise (equilibria) n Which is an equilibrium in the Stackelberg model? n Are there any additional Nash equilibria ?

29 Cournot versus Stackelberg n Profit function of firm 1 n First order condition for firm 1 direct effectfollower or strategic effect, Cournot: 0, Stackelberg: >0

30 Exercise (Stackelberg) n Find the equilibrium in a Stackelberg competition. Suppose that the demand function is given by p(X) = 24 - X and the costs per unit by c 1 = 3, c 2 = 2. n Possible or not: ?

31 Exercise (three firms) Three firms compete in a homogenous good market with X(p)=100-p. The costs are zero. At stage 1, firm 1 sets its quantity; at stage 2, firms 2 and 3 simultaneously decide on their quantities. Calculate the price on the market!

32 Blockaded entry p x 1 blockaded entry for firm 2 M

33 Reaction functions in the case of blockaded entry

34 Profit function of firm 1 in the case of blockaded entry of firm 2

35 Deterring firm 2’s entry p x 1

36 Deterrence pays,

37 Deterrence does not pay

38 Blockaded and deterred entry I n Entry is blockaded for each firm: n Blockaded entry (firm 2):

39 Blockaded and deterred entry II n Deterred entry (firm 2): – Entry is not blockaded if – Deterrence pays if  Deterrence if

40 Blockade and deterrence firm 1 as a monopolist c 2 c 1 duopoly no supply blockade firm 2 as a monopolist deterrence

41 Exercise (entry and deterrence) Suppose a monopolist faces a demand of the form p(X)=4-0.25X. The firm’s unit costs are 2. a) Find the profit-maximizing quantity and price. Is entry blockaded for a potential entrant (firm 2) with unit costs of 3.5? b) How about unit costs of c 2 =1? c) Find firm 1’s limit output level for c 2 =1. Should the incumbent deter entry?

42 Deterrence and sunk costs I We now introduce quasifix costs of 3: p(X)=4-0.25X

43 Deterrence and sunk costs II n b) Entry blockaded ? Comparison is not sufficient

44 Deterrence and sunk costs III n c) Should firm 1 deter?

45 Deterrence and sunk costs IV  deterrence pays

46 Deterrence and sunk costs V

47 Deterrence Deterrence and sunk costs VI Accommodation Blockade

48 Strategic trade policy  1  2 x dx fx dx f s n Two firms, one domestic (d), the other foreign (f), compete on a market in a third country. n The domestic government subsidizes its firm’s exports using a unit subsidy s. n The subsidy grants the domestic firm an advantage that is higher than the subsidy itself (Brander / Spencer (1981, 1983)).

49 Exercise (Strategic trade policy) n In the setting just described, assume and p(X)=a-bX. n Since the two firms sell to a third country, the rent of the consumers is without relevance and domestic welfare given by n Which subsidy s maximizes domestic welfare?

50 n Direct effect of subsidy for domestic welfare is zero. n Strategic effect: Solution (Strategic trade policy) - interpretation <0 s  Cournot-Nash- equilibria (firm d Stackelberg leader)

51 Strategic trade policy - problems n The recommendation depends on whether there is price or quantity competition. n „One can always do better than free trade, but the optimal tariffs or subsidies seem to be small, the potential gains tiny, and there is plenty of room for policy errors that may lead to eventual losses rather than gains.“ Trade Policy and Market Structure; Helpman/Krugman, S. 186

52 Stackelberg – Executive Summary n Time leadership is worthwhile: in a Stackelberg equilibrium the leader realizes a profit that is higher – than the follower’s and – his own in a Cournot equilibrium. n Costs of entry (even in the form of identical quasifix costs) make the follower’s deterrence easier. n Strategic trade policy may conceivably pay.

53 Example: The OPEC Cartel n The best known cartel is the OPEC, which was formed in 1960 by Saudi Arabia, Venezuela, Kuwait, Iraq and Iran. Each member nation must agree to an individual output quota, except for Saudi Arabia, which adjusts its production as necessary to maintained high prices. n In 1982, OPEC set an overall output limit of 18 million barrels per day (before 31 million). n Production quota at 28 million barrels per day effective July 1, 2005.

54 The quantity cartel n The firms seek to maximize joint profits n Optimization conditions n Compare monopoly with two factories.

55 The cartel agreement n The optimization condition is given by n Each firm will be tempted to increase its profits by unilaterally expanding its output. n In order to maintain a cartel, the firms need a way to detect and punish cheating, otherwise the temptation to cheat may break the cartel.

56 Cartel quantities x 2 x 1 C S K quantities in a symmetric cartel

57 Exercise (cartel quantities) n Consider a cartel in which each firm has identical and constant marginal costs. If the cartel maximizes total industry profits, what does this imply about the division of output between the firms? Intermediate Microeconomics; Hal R. Varian

58 Cartel – Executive Summary n If all firms keep the cartel agreement, they can increase their profits compared to Cournot competition. n Nevertheless cartels are unstable from a static point of view. n However, cartel agreements may be stable from the point of view of repeated games.

59 The outcomes of our models quantity price a monopoly (M) and cartel (K) Cournot (C) Stackelberg (S) perfect competition (PC) p M p C p S p PC = c X M X C X S X PC

60 Antitrust laws and enforcement, Germany n laws – Gesetz gegen unlauteren Wettbewerb (1896) – Gesetz gegen Wettbewerbsbeschränkungen (GWB), (1957) n enforcement – Bundeskartellamt

61 Exercise: Calculate C 2 for C k concentration ratio l 2 firms with equal market shares, l 3 firms with shares of 0.1, 0.1 and 0.8 or l 3 firms with shares of 0.2, 0.6 and 0.2 ? monopoly: perfect comp.: Setup: Definition:

62 GWB, §19 (3) n One firm is called „market dominating“ if C 1 >1/3. n A group of firms is called „market dominating“ if

63 The Herfindahl (Hirschman) index n Definition: n Exercise: Calculate H for l 2 firms with equal market shares, l 3 firms with shares of 0.8, 0.1 and 0.1 or l 3 firms with shares of 0.6, 0.2 and 0.2 ?

64 n firms in Cournot competition n Total industry output: n Firm i’s profit function: n Firm i’s marginal revenue :

65 Lerner index of market power n First order condition: n Lerner index for one firm: n Lerner index for the industry:

66 Exercise (Replication) In a homogenous good market there are m identical costumers and n identical firms. Every costumer demands the quantity 1-p at price p. The cost function of firm j is given by a) Calculate the inverse market demand function! b) Calculate the reaction function of firm j and the total market output and p C in the symmetric Cournot- equilibrium! Hint: Use c) Now the number of firms and costumers is multiplied by Calculate again p C and MC j ! Prove that for the gap between price and marginal costs converges to zero! Theorie der Industrieökonomik; Bester