Industrial Organization or Imperfect Competition Consumer Search and Entry deterrence I

1. Industrial Organization or Imperfect CompetitionConsumer Search and Entry deterrence I Univ. Prof. dr. Maarten Janssen University of Vienna Summer semester 2011 Week 8 (May 19, 20)

2. Endogenous Sequential Search • Two types of consumers: fraction λ fully informed, fraction 1-λ bears search cost s for each additional search; Max. willingness to pay v for both groups (is high) • After each search, consumers can decide whether or not to continue searching • Perfect recall of prices • How to decide whether to start searching? • First search is for free; or not • N Firms choose prices as before • Symmetric Nash equilibrium where • Static game, despite sequential search • Consumer search behaviour is optimal given strategy of firms • Firm pricing behaviour is optimal given strategy of other firms and consumers

3. Optimal search rule • Suppose F(p) is firms’ pricing strategy and p’ is price consumers have observed. • Buy now yields v-p’ • Continue searching yields v – s– (1–F(p’))p’ - F(p’)E(p│p < p’) • Price ρ that makes consumer indifferent between two options is ρ = E(p│p < ρ) + s/F(ρ) • Claim: largest price in support of F(p) cannot be above min ρ • Suppose it were, consumers will continue to search; will find lower price with probability 1 • Thus, F(ρ) =1 and ρ = s + E(p)

4. Characterization of F(p) and ρ • Write down profit function for p < ρ ≤ v • Π(p) = { λ(1-F(p))N-1 + (1- λ)/N } p • Π(ρ) = (1- λ)ρ/N • F(p) = 1 – [ (1- λ)(ρ-p)/λNp ]1/(N-1) • E(p) = ∫ pf(p) dp = ∫ p dy (by using the change of variables y = 1 - F(p)) • Ep = ρ ∫ dy/[1+bNyN-1], where b = λ / (1- λ) • Reservation price ρ = s/ {1 - ∫ dy/[1+bNyN-1] } • Can be larger than v if s is large enough.

5. Definition of entry deterrence • Incumbent’s choice of business strategy such that it can only be rationalized in face of threat of entry • Two different mechanisms often contemplated: • Building up capacity • Studied in both Cournot and Stackelberg context • Choice of prices to signal (low) cost structure • Context of game with asymmetric information • First, discuss briefly Cournot and Stackelberg models • Then extensions to entry deterrence • Later, pricing choices

6. Capacity Expansion and Entry Deterrence • Central point: For predation to be successful—and therefore rational—the incumbent must somehow convince the entrant that the market environment after the entrant comes in will not be a profitable one. How this credibility? • One possibility: install capacity • Installed capacity is a commitment to a minimum level of output

7. Cournot Model 2 (or more) firms Market demand is P(Q) Firm i cost is C(q) Firm i acts in the belief that all other firms will put some amount Q-iin the market. Then firm i maximizes profits obtained from serving residual demand: P’ = P(Q) - Q-i

8. P(q1) P(q1, Q-i =10) Market demand P(Q)=P(q1,Q-i=0) P(q1, Q–i =20) q1 Demand and Residual Demand

9. Cournot Reaction Functions • Firm 1’s reaction (or best-response) function is a schedule summarizing the quantity q1 firm 1 should produce in order to maximize its profits for each quantity Q-i produced by all other firms. • Since the products are (perfect) substitutes, an increase in competitors’ output leads to a decrease in the profit-maximizing amount of firm 1’s product ( reaction functions are downward sloping).

10. Cournot Model The problem Max{(P(qi+Q-i) qi – C(qi)} defines de best-response (or reaction) function of firm i to a conjecture Q-ias follows: P’(qi+Q-i)qi + P(qi+Q-i) – C’(qi) = 0 Q-i Firm i’s reaction Function r1 qi qiM qi*(qj) qj Q-i=0

11. Cournot Equilibrium • Situation where each firm produces the output that maximizes its profits, given the the output of rival firms • Conjectures about what the others produce are correct. • No firm can gain by unilaterally changing its own output

12. q2 r1 Cournot equilibrium q2M=30 r2 q1M=30 q1 Cournot Equilibrium • q1* maximizes firm 1’s profits, given that firm 2 produces q2* • q2* maximizes firm 2’s profits, given firm 1’s output q1* • No firm wants to change its output, given the rival’s • Beliefs are consistent: each firm “thinks” rivals will stick to their current output, and they do so!

13. Properties of Cournot equilibrium • The pricing rule of a Cournot oligopolist satisifes: • Cournot oligopolists exercise market power: • Cournot mark-ups are lower than monopoly markups • Market power is limited by the elasticity of demand • More efficient firms will have a larger market share. • The more firms, the lower will be each firm’s individual market share and monopoly power.

14. Concentration measures • Different industries have very different structures and also different behaviours • SCP paradigm • Structure (cost, entry conditions, number of firms) • Conduct (prices, product differentiation, advertising,etc.) • Performance (Lerner index (P-MC)/P, profit, welfare, etc.) • Concentration measures try to provide indication of conduct and/or performance on the basis of structural features • Preference for one number representation • Use this for regression analysis (e.g. Lerner index on concentration measure)

15. Different concentration measures • C4 is sum of four largest market shares • Can’t be used in highly concentrated sectors such as in mobile telephony • No difference between four firms with 25% market share and monopolist • Why 4? • Market shares of 5th, 6th etc. largest firm has no effect • HHI uses all information: sum of all squared market shares • Larger market shares get more weight

16. “Justifying” HHI

17. Changes in marginal costs

18. Q2 r1 B C Increasing Profits for Firm 1 A D Q1M Q1 Another look at Cournot decisions • Firm 1’s Isoprofit Curve: combinations of outputs of the two firms that yield firm 1 the same level of profit

19. CournotEquilibrium Profits at Cournot equilibrium Q2 Firm 2’s Profits r1 Q2M Q2* Firm 1’s Profits r2 Q1M Q1* Q1

20. Cournot versus Bertrand I • Predictions from Cournot and Bertrand homogeneous product oligopoly models are strikingly different. Which model of competition is “correct”? • Kreps and Scheinkman model two stages • firms invest in capacity installation • then choose prices. • Solution: firms invest exactly the Cournot equilibrium quantities. In the second stage they price to sell up to capacity. • We discussed this implicitly when discussing capacity constraint Bertrand competition

21. Cournot versus Bertrand II • Cournot model is more appropriate in environments where firms are capacity constrained and investments in capacity are slow. • Bertrand model is more appropriate in situations where there are constant returns to scale and firms are not capacity constrained

22. StackelbergModel • 2 (or more) firms • Producing a homogeneous (or differentiated) product • Barriers to entry • One firm is the leader • The leader commits to an output before all other firms • Remaining firms are followers. • They choose their outputs so as to maximize profits, given the leader’s output.

23. Q2 Follower’s Profits Decline r1 Stackelberg Equilibrium Cournot Equilibrium Q2* Q2S r2 Leader’s Profits Rise Q1M Q1* Q1S Q1 Stackelberg Equilibrium

24. Stackelbergsummary • Stackelberg model illustrates how commitment can enhance profits in strategic environments • Leader produces more than the Cournot equilibrium output • Larger market share, higher profits • First-mover advantage • Follower produces less than the Cournot equilibrium output • Smaller market share, lower profits

25. Stackelberg Mathematics I Linear Demand and No production cost Stackelberg Follower’s Profit Stackelberg Follower’s Reaction Curve:

26. Stackelberg Mathematics II Stackelberg Leader’s Profit Or, Optimal Output Leader: Is credibility used somewhere?

27. Stackelberg with Fixed Entry Cost: Follower Q2 Follower’s Profits are High Reaction Curve with Entry cost Follower’s Profits are Low With Entry Cost: follower’s profits in the market can be too low to recover entry cost Q1

28. Follower’s decision with entry cost f Stackelberg Follower’s Profit (with α=β=1) Stackelberg Follower’s Reaction Curve: qF = (1-qL)/2 If πF ≥0, i.e., if (1-qL)2/4 ≥ f or qL≤ 1 - 2√f Otherwise qF = 0

29. Stackelberg with Entry Cost: Leader Q2 r1 Stackelberg Equilibrium r2 Q1S Q1 Optimal output

30. Stackelberg with Low Entry Cost: Leader Q2 r1 Stackelberg Equilibrium r2 Q1S Q1 Entry deterrence is not optimal (accommodated entry)

31. Stackelberg with High Entry Cost: Leader Q2 r1 Stackelberg Equilibrium r2 Q1S Q1 Monopoly Output is enough for entry deterrence

32. When do the different cases occur? • Leader’s profit of entry accommodation is 1/8 (as p = ¼ and its output is ½); follower’s profit is 1/16 – f. • Leader’s profit of entry deterrence is 2√f(1-2√f) (as p = 2√f and [total] output is 1- 2√f); • choosing minimal output level to deter • Entry deterrence profitable if 2√f(1-2√f) > 1/8, i.e., iff √f > ¼(1- ½√2) • 0 < √f < ¼(1- ½√2) is too costly • ¼(1- ½√2) < √f < ¼ entry deterrence in proper sense (distort output decisions compared to monopoly decision) • √f > ¼ monopoly output to deter entry

33. Is entry deterrence in Stackelberg context always bad? • Welfare (TS) if entry takes place is ½ - 1/32 – f • Total output is ¾; price is ¼ • Welfare (TS) if entry is deterred is ½ - 2f • Total output is 1-2√f; price is 2√f • Thus, TS is higher under entry deterrence if f < 1/32 • Entry deterrence is individually optimal for incumbent and takes place if (1- ½√2)2/16 < f < 1/32 • Thus, entry deterrence is sometimes optimal from a TS point of view (entry can be excessive)