Business Strategy in Oligopoly Markets

Transcription

1 Chapter 5 Business Strategy in Oligopoly Markets

2 Introduction In the majority of markets firms interact with few competitors In determining strategy each firm has to consider rival s reactions strategic interaction in prices, outputs, advertising This kind of interaction is analyzed using game theory assumes that players are rational Distinguish cooperative and noncooperative games focus on noncooperative games Also consider timing simultaneous versus sequential games

3 Oligopoly Theory No single theory employ game theoretic tools that are appropriate outcome depends upon information available Need a concept of equilibrium players (firms?) choose strategies, one for each player combination of strategies determines outcome outcome determines pay-offs (profits?) Equilibrium first formalized by Nash: No firm wants to change its current strategy given that no other firm changes its current strategy

4 Nash Equilibrium Equilibrium need not be nice firms might do better by coordinating but such coordination may not be possible (or legal) Some strategies can be eliminated on occasions they are never good strategies no matter what the rivals do These are dominated strategies they are never employed and so can be eliminated elimination of a dominated strategy may result in another being dominated: it also can be eliminated One strategy might always be chosen no matter what the rivals do: dominant strategy

5 An Example Two airlines Prices set: compete in departure times 70% of consumers prefer evening departure, 30% prefer morning departure If the airlines choose the same departure times they share the market equally Pay-offs to the airlines are determined by market shares Represent the pay-offs in a pay-off matrix

6 The example (cont.) The left-hand number is the pay-off to Delta What is the The Pay-Off Matrixequilibrium for this game? Morning American Evening Delta Morning Evening (15, 15) (30, 70) The right-hand number is the (70, 30) pay-off (35, 35) to American

7 If AmericanThe example If American (cont.) chooses a morning The morning departure departure, Delta The chooses Pay-Off an evening The morning departure Matrix is a dominated departure, Delta is also a dominated will choose strategy for Delta and will so still choose strategy for American and evening evening American can be eliminated. again be eliminated The Nash Equilibrium must therefore be one in which Morning Evening both airlines choose an evening departure Morning (15, 15) (30, 70) Delta Evening (70, 30) (35, 35)

8 The example (cont.) Now suppose that Delta has a frequent flier program When both airline choose the same departure times Delta gets 60% of the travelers This changes the pay-off matrix

9 The If Delta example (cont.) chooses The a Pay-Off morning Matrix departure, American However, a morning departure But if American Delta will has choose is nostill a dominated strategy for Delta chooses dominated an eveningstrategy (Evening is American still a dominant strategy. departure, American American knows this will and choose so chooses morning a morning Morning Evening departure Morning (18, 12) (30, 70) Delta Evening (70, 30) (42, 28)

10 Nash Equilibrium Again What if there are no dominated or dominant strategies? The Nash equilibrium concept can still help us in eliminating at least some outcomes Change the airline game to a pricing game: 60 potential passengers with a reservation price of $ additional passengers with a reservation price of $220 price discrimination is not possible (perhaps for regulatory reasons or because the airlines don t know the passenger types) costs are $200 per passenger no matter when the plane leaves the airlines must choose between a price of $500 and a price of $220 if equal prices are charged the passengers are evenly shared Otherwise the low-price airline gets all the passengers The pay-off matrix is now:

11 The example (cont.) If Delta prices high If both price highand The American Pay-Off low Matrix then both get 30then American gets passengers. If Delta prices Profit low all 180 passengers. American and per American passenger high is If both price low Profit per passenger then $300 Delta gets they each get 90 is $20 all 180 passengers. P H = $500 passengers. P L = $220 Profit per passenger Profit per passenger is $20 is $20 P H = $500 ($9000,$9000) ($0, $3600) Delta P L = $220 ($3600, $0) ($1800, $1800)

12 Nash Equilibrium There is no simple (cont.) way to choose between (PH, PH) is a Nash these equilibria. even so, the Nash concept equilibrium. Matrix (PHThe, PL)Pay-Off cannotbut be (PL, PL) is aequilibria Nash has eliminated half of the outcomes as If both are pricing a Nash equilibrium. equilibrium. and familiarity highcustom then neither wants If American prices American If both are pricing might lead both to to change low then Delta should low then neither wants (PL, PHprice ) cannot be high also price low a Nash equilibrium. to change PH = $500 PL = $220 If American prices There are two Nash high then Delta shouldequilibria to this version also pricephigh ($9000,$9000) ($0, $3600) ($9000, of the$9000) game H = $500 Regret might cause both to Delta price low ($3600, $0) ($1800, $1800) PL = $220

13 Nash Equilibrium (cont.) There is no simple (PH, PH) is a Nash way to choose between equilibrium. The Pay-Off Matrix, P ) cannot be There are two(p Nash H L (Pat a Nash L, P L) iswe these equilibria, but least have If both are pricing equilibria to thisa version Nash equilibrium. equilibrium. eliminated half of the outcomes as high thenofneither wants the game If American prices American If both are pricing possible equilibria to change low then Delta would (PL, PH) cannot be low then neither wants want to price low, too. a Nash equilibrium. to change PH = $500 PL = $220 If American prices high then Delta should also pricephigh ($9000,$9000) ($0, $3600) ($9000, $9000) H = $500 Delta PL = $220 ($3600, $0) ($1800, $1800)

14 The only sensible choice for Delta is PH knowingsometimes, that American consideration of thethat Delta Suppose The Pay-Off Matrix timing of moves can canhelp set its price first will follow with P and each will Delta can see that Hif it sets find the equilibrium This means that earn $9000. theusnash a high price, then So, American equilibria is (PH, PH) will do bestnow by also AmericanPH, PL cannot be pricing high. Delta an equilibrium earns $9000 This means PH = $500 PL = outcome $220 Delta can that alsopsee that L,PH if it sets a low price, American cannot be an will do$500 best by pricing$3,000) low. PH = ($9000,$9000) ($0, $3600) ($3,000, equilibrium Delta will then earn $1800 Delta PL = $220 ($3600, $0) ($1800, $1800)

15 Price Leadership Implicit Collusion Price Leader (Barometric Firm) Largest, dominant, or lowest cost firm in the industry Demand curve is defined as the market demand curve less supply by the followers Followers Take market price as given and behave as perfect competitors

16 Price Leadership

17 Oligopoly Models There are three dominant oligopoly models Cournot Bertrand Stackelberg They are distinguished by the decision variable that firms choose the timing of the underlying game But each embodies the Nash equilibrium concept

18 The Cournot Model Start with a duopoly Two firms making an identical product (Cournot supposed this was spring water) Demand for this product is P = A - BQ = A - B(q 1 + q 2 ) where q 1 is output of firm 1 and q 2 is output of firm 2 Marginal cost for each firm is constant at c per unit To get the demand curve for one of the firms we treat the output of the other firm as constant So for firm 2, demand is P = (A - Bq 1 ) - Bq 2

19 The Cournot model (cont.) P = (A - Bq 1 ) - Bq 2 $ The profit-maximizing choice of output by firm 2 depends upon the output of firm 1 Marginal revenue for firm 2 is Solve this for output A - Bq 1 A - Bq 1 MR 2 = (A - Bq 1 ) - 2Bq 2 MR 2 MR 2 = MC A - Bq 1-2Bq 2 = c q 2 c q* 2 q* 2 = (A - c)/2b - q 1 /2 If the output of firm 1 is increased the demand curve for firm 2 moves to the left Demand MC Quantity

20 q* 2 = (A - c)/2b - q 1 /2 The Cournot model (cont.) This is the best response function for firm 2 It gives firm 2 s profit-maximizing choice of output for any choice of output by firm 1 There is also a best response function for firm 1 By exactly the same argument it can be written: q* 1 = (A - c)/2b - q 2 /2 Cournot-Nash equilibrium requires that both firms be on their best response functions.

21 Cournot-Nash Equilibrium (A-c)/B (A-c)/2B q C 2 q 2 If firm 2 produces The best response The Cournot-Nash (A-c)/B then firm function for for firm 1 is equilibrium is at is 1 will choose to q* q* 1 = 1 (A-c)/2B -- q 2 /2 Point C at the intersection 2 /2 produce no output of If the firm best 2 produces response nothing functions then firm The best response 1 will produce the function for for firm 2 is is C monopoly output q* q* 2 2 = (A-c)/2B -- q 1 1 /2 /2 Firm (A-c)/2B 2 s best response function Firm 1 s best response function q C 1 (A-c)/2B (A-c)/B q 1

22 Cournot-Nash Equilibrium (A-c)/B (A-c)/2B (A-c)/3B q 2 Firm 1 s best response function C q* 1 = (A - c)/2b - q* 2 /2 q* 2 = (A - c)/2b - q* 1 /2 q* 2 = (A - c)/2b - (A - c)/4b + q* 2 /4 3q* 2 /4 = (A - c)/4b Firm 2 s best response function q* 2 = (A - c)/3b q* 1 = (A - c)/3b (A-c)/3B (A-c)/2B (A-c)/B q 1

23 Cournot-Nash Equilibrium (cont.) In equilibrium each firm produces q C = 1 qc 2 = (A - c)/3b Total output is, therefore, Q* = 2(A - c)/3b Recall that demand is P = A - BQ So the equilibrium price is P* = A - 2(A - c)/3 = (A + 2c)/3 Profit of firm 1 is (P* - c)q C = (A - 1 c)2 /9B Profit of firm 2 is the same A monopolist would produce Q M = (A - c)/2b Competition between the firms causes their total output to exceed the monopoly output. Price is therefore lower than the monopoly price But output is less than the competitive output (A - c)/b where price equals marginal cost and P exceeds MC

24 Numerical Example of Cournot Duopoly Demand: P = 100-2Q = 100-2(q 1 + q 2 ); A = 100; B = 2 Unit cost: c = 10 Equilibrium total output: Q = 2(A c)/3b = 30; Individual Firm output: q 1 = q 2 = 15 Equilibrium price is P* = (A + 2c)/3 = $40 Profit of firm 1 is (P* - c)q C 1 = (A - c)2 /9B = $450 Competition: Q* = (A c)/b = 45; P = c = $10 Monopoly: Q M = (A - c)/2b = 22.5; P = $55 Total output exceeds the monopoly output, but is less than the competitive output Price exceeds marginal cost but is less than the monopoly price

25 Cournot-Nash Equilibrium (cont.) What if there are more than two firms? Much the same approach. Say that there are N identical firms producing identical products Total output Q = q 1 + q 2 + This + q N denotes output Demand is P = A - BQ = A - B(q of every 1 + q 2 firm + other + q N ) than firm 1 Consider firm 1. It s demand curve can be written: P = A - B(q q N ) - Bq 1 Use a simplifying notation: Q -1 = q 2 + q q N So demand for firm 1 is P = (A - BQ -1 ) - Bq 1

26 The Cournot model (cont.) P = (A - BQ -1 ) - Bq 1 $ The profit-maximizing choice of output by firm 1 depends upon the output of the other firms Marginal revenue for firm 1 is Solve this for output A - BQ -1 A - BQ -1 MR 1 = (A - BQ -1 ) - 2Bq 1 MR 1 MR 1 = MC A - BQ -1-2Bq 1 = c q 1 c q* 1 q* 1 = (A - c)/2b - Q -1 /2 If the output of the other firms is increased the demand curve for firm 1 moves to the left Demand MC Quantity

27 Cournot-Nash Equilibrium (cont.) q* 1 = (A - c)/2b - Q -1 /2 How do we solve this Q* -1 = (N - 1)q* 1 As the The firms for q* number are 1? of identical. firms increases As the number output of q* 1 = (A - c)/2b - (N - 1)q* 1 So /2 in equilibrium they of each firms firm increases falls (1 + (N - 1)/2)q* will have identical 1 = (A - c)/2b aggregate output As outputs q* 1 (N + 1)/2 = (A - c)/2b As increases the the number number of of firms firms increases increases price profit q* 1 = (A - c)/(n + 1)B tends of to each marginal firm falls cost Q* = N(A - c)/(n + 1)B P* = A - BQ* = (A + Nc)/(N + 1) Profit of firm 1 is P* 1 = (P* - c)q* 1 = (A - c) 2 /(N + 1) 2 B

28 Cournot-Nash equilibrium (cont.) What if the firms do not have identical costs? Once again, much the same analysis can be used Assume that marginal costs of firm 1 are c 1 and of firm 2 are c 2. Solve this for output Demand is P = A - BQ = A A - B(q symmetric 1 + q 2 ) result q 1 We have marginal revenue holds for firm for 1 output as before of MR 1 = (A - Bq 2 ) - 2Bq firm 2 1 Equate to marginal cost: (A - Bq 2 ) - 2Bq 1 = c 1 q* 1 = (A - c 1 )/2B - q 2 /2 q* 2 = (A - c 2 )/2B - q 1 /2

29 (A-c 1 )/B (A-c 2 )/2B q 2 R 1 R 2 Cournot-Nash Equilibrium q* 1 = (A - c 1 )/2B - q* 2 /2 The equilibrium As the marginal output cost of firm of firm 2 q* 2 2 = (A - c 2 )/2B - q* 1 /2 increases falls its What and best of happens response q* 2 = to (A this - c 2 )/2B - (A - c 1 )/4B firm curve 1 equilibrium fallshifts to when + q* 2 /4 the costs right change? 3q* 2 /4 = (A - 2c 2 + c 1 )/4B q* 2 = (A - 2c 2 + c 1 )/3B C q* 1 = (A - 2c 1 + c 2 )/3B (A-c 1 )/2B (A-c 2 )/B q 1

30 Cournot-Nash Equilibrium (cont.) In equilibrium the firms produce q C 1 = (A - 2c 1 + c 2 )/3B; q C 2 = (A - 2c 2 + c 1 )/3B Total output is, therefore, Q* = (2A - c 1 - c 2 )/3B Recall that demand is P = A - BQ So price is P* = A - (2A - c 1 - c 2 )/3 = (A + c 1 +c 2 )/3 Profit of firm 1 is (P* - c 1 )q C 1 = (A - 2c 1 + c 2 )2 /9B Profit of firm 2 is (P* - c 2 )q C 2 = (A - 2c 2 + c 1 )2 /9B Equilibrium output is less than the competitive level Output is produced inefficiently: the low-cost firm should produce all the output

31 A Numerical Example with Different Costs Let demand be given by: P = 100 2Q; A = 100, B =2 Let c 1 = 5 and c 2 = 15 Total output is, Q* = (2A - c 1 - c 2 )/3B = ( )/6 = 30 q C = (A - 2c + c )/3B = ( )/6 = 17.5 q C = (A - 2c + c )/3B = ( )/3B = 12.5 Price is P* = (A + c 1 +c 2 )/3 = ( )/3 = 40 Profit of firm 1 is (A - 2c 1 + c 2 ) 2 /9B =( ) 2 /18 = $612.5 Profit of firm 2 is (A - 2c 2 + c 1 ) 2 /9B = $312.5 Producers would be better off and consumers no worse off if firm 2 s 12.5 units were instead produced by firm 1

32 Concentration and Profitability Assume that we have N firms with different marginal costs We can use the N-firm analysis with a simple change Recall that demand for firm 1 is P = (A - BQ -1 ) - Bq 1 But then demand for firm i is P = (A - BQ -i ) - Bq i Equate this to marginal cost But c i Q* -i + q* i = Q* A - BQ -i - 2Bq i = c i and A - BQ* = P* This can be reorganized to give the equilibrium condition: A - B(Q* -i + q* i ) - Bq* i - c i = 0 P* - Bq* i - c i = 0 P* - c i = Bq* i

33 Concentration and profitability (cont.) P* - c i = Bq* i The price-cost margin Divide by P* and multiply the right-hand for each side firm by is Q*/Q* P* - c i = BQ* determined by its own q* i market share and overall P* P* Q* market demand elasticity The verage price-cost margin But BQ*/P* = 1/η and q* i /Q* = s i so: P* - c i s = i P* η Extending this we have P* - c P* = H η is determined by industry concentration as measured by the Herfindahl-Hirschman Index

34 Price Competition: Bertrand In the Cournot model price is set by some market clearing mechanism Firms seem relatively passive Check that with An alternative approach is to assume that this firms demand compete and in prices: this is the approach taken by Bertrand these costs the Leads to dramatically different results monopoly price is Take a simple example $30 and quantity is 40 units two firms producing an identical product (spring water?) firms choose the prices at which they sell their water each firm has constant marginal cost of $10 market demand is Q = 100-2P

35 Bertrand competition (cont.) We need the derived demand for each firm demand conditional upon the price charged by the other firm Take firm 2. Assume that firm 1 has set a price of $25 if firm 2 sets a price greater than $25 she will sell nothing if firm 2 sets a price less than $25 she gets the whole market if firm 2 sets a price of exactly $25 consumers are indifferent between the two firms the market is shared, presumably 50:50 So we have the derived demand for firm 2 q 2 = 0 if p 2 > p 1 = $25 q 2 = 100-2p 2 if p 2 < p 1 = $25 q 2 = 0.5(100-50) = 25 if p 2 = p 1 = $25

36 q 2 = 0 if p 2 > p 1 p 1 Bertrand competition (cont.) More generally: Suppose firm 1 sets price p 1 Demand to firm 2 is: p 2 Demand is not continuous. There is a jump at p 2 = p 1 q 2 = 100-2p 2 if p 2 < p 1 q 2 = 50 - p 1 if p 2 = p 1 The discontinuity in demand carries over to profit 100-2p q p 1

37 Firm 2 s profit is: Bertrand competition (cont.) π 2 (p 1,, p 2 ) = 0 if p 2 > p 1 π 2 (p 1,, p 2 ) = (p 2-10)(100-2p 2 ) if p 2 < p 1 π 2 (p 1,, p 2 ) = (p 2-10)(50 - p 2 ) if p 2 = p 1 Clearly this depends on p 1. Suppose first that firm 1 sets a very high price: greater than the monopoly price of $30 For whatever reason!

38 What price Bertrand competition At should p So, if p (cont.) 1 falls to $30, 2 = p firm 1 = 2 $30, firm If With p 1 > $30, Firm 2 s profit looks set? p firm 2 should just like 1 = 2 $30, then gets this: undercut p 1 a bit and firm half 2 will of only earn a Firm 2 s Profit What if firm 1positive the get almost all the The profit monopoly by cutting its prices at $30? monopoly price monopoly profit price to $30 of $30 or less profit p 2 < p 1 p 2 = p 1 p 2 > p 1 $10 $30 p 1 Firm 2 s Price

39 Bertrand competition (cont.) Now suppose that firm 1 sets a price less than $30 Firm 2 s profit looks like this: As long as p 1 > c = $10, Firm Of 2 s course, Profit firm Firm What 2 should price aim 1 will then should just to undercut firm 2 undercut firm 2 set firm now? 1 p 2 < p Then firm 2 and should so on also price 1 at $10. Cutting price below cost gains What the whole if firm market 1 but loses money prices on at $10? every customer p 2 = p 1 p 2 > p 1 $10 p 1 $30 Firm 2 s Price

40 Bertrand competition (cont.) We now have Firm 2 s best response to any price set by firm 1: p* 2 = $30 if p 1 > $30 p* 2 = p 1 - something small if $10 < p 1 < $30 p* 2 = $10 if p 1 < $10 We have a symmetric best response for firm 1 p* 1 = $30 if p 2 > $30 p* 1 = p 2 - something small if $10 < p 2 < $30 p* 1 = $10 if p 2 < $10

41 Bertrand competition (cont.) The best response These best response function functions for look like this The best response firm 1 function for p 2 firm 2 R 1 $30 $10 R 2 The equilibrium The Bertrand is equilibrium with both has firms both pricing firms charging at marginal $10 cost $10 $30 p 1

42 Bertrand Equilibrium: modifications The Bertrand model makes clear that competition in prices is very different from competition in quantities Since many firms seem to set prices (and not quantities) this is a challenge to the Cournot approach But the Bertrand model has problems too for the p = marginal-cost equilibrium to arise, both firms need enough capacity to fill all demand at price = MC but when both firms set p = c they each get only half the market So, at the p = mc equilibrium, there is huge excess capacity This calls attention to the choice of capacity Note: choosing capacity is a lot like choosing output which brings us back to the Cournot model The intensity of price competition when products are identical that the Bertrand model reveals also gives a motivation for Product differentiation

43 An Example of Product Differentiation Coke and Pepsi are nearly identical but not quite. As a result, the lowest priced product does not win the entire market. Q C = P C P P MC C = $4.96 Q P = P P P C MC P = $3.96 There are at least two methods for solving this for P C and P P

44 Bertrand and Product Differentiation Method 1: Calculus Profit of Coke: π C = (P C )( P C P P ) Profit of Pepsi: π P = (P P )( P P P C ) Differentiate with respect to P C and P P respectively Method 2: MR = MC Reorganize the demand functions P C = ( P P ) Q C P P = ( P C ) Q P Calculate marginal revenue, equate to marginal cost, solve for Q C and Q P and substitute in the demand functions

45 Bertrand competition and product differentiation Both methods give the best response functions: P C = P P P P The Bertrand Note equilibrium that these is P P = P C are at upward their intersection sloping These can be solved for the equilibrium $8.11 prices as indicated $6.49 B R C R P $10.44 $12.72 P C

46 Bertrand Competition and the Spatial Model An alternative approach is to use the spatial model from Chapter 4 a Main Street over which consumers are distributed supplied by two shops located at opposite ends of the street but now the shops are competitors each consumer buys exactly one unit of the good provided that its full price is less than V a consumer buys from the shop offering the lower full price consumers incur transport costs of t per unit distance in travelling to a shop What prices will the two shops charge?

47 Bertrand and thewhat spatial model if shop Xm marks the Assume that shop 1 sets 1 raises price? location ofprice the p1 and shopits 2 sets Price Price marginal buyer price p 2 one who is indifferent between p 1buying either firm s p2 good p1 x m Shop 1 xm All consumers to the Shop 2 xm moves to the left of xm buy left: fromsome consumers And all consumers shop 1 switch to shop to 2the right buy from shop 2

48 Bertrand and the spatial model p 1 + tx m = p 2 + t(1 - x m ) 2tx m = p 2 - p 1 + t x m (p 1, p 2 ) = (p 2 - p 1 + t)/2t There are n consumers in total This is the fraction of consumers who buy from firm 1 How is x m determined? So demand to firm 1 is D 1 = N(p 2 - p 1 + t)/2t Price Price p 1 p 2 x m Shop 1 Shop 2

49 Bertrand equilibrium Profit to firm 1 is π 1 = (p 1 - c)d 1 = N(p 1 - c)(p 2 - p 1 + t)/2t 2 π 1 = N(p 2 p 1 - p 1 + tp 1 + cp 1 - cp 2 -ct)/2t Differentiate with respect This to is p the best response 1 function N π 1 / p 1 = (p 2t 2-2p for 1 + firm t + c) 1 = 0 Solve this for p 1 p* 1 = (p 2 + t + c)/2 This is the best response What about firm 2? By symmetry, function for it has firm a 2 similar best response function. p* 2 = (p 1 + t + c)/2

50 Bertrand and Demand p* 1 = (p 2 + t + c)/2 p* 2 = (p 1 + t + c)/2 p 2 R 1 2p* 2 = p 1 + t + c = p 2 /2 + 3(t + c)/2 c + t p* 2 = t + c p* 1 = t + c (c + t)/2 R 2 (c + t)/2 c + t p 1

51 Stackelberg Interpret in terms of Cournot Firms choose outputs sequentially leader sets output first, and visibly follower then sets output The firm moving first has a leadership advantage can anticipate the follower s actions can therefore manipulate the follower For this to work the leader must be able to commit to its choice of output Strategic commitment has value

52 Stackelberg Equilibrium: an example Assume that there are two firms Both with firms identical have constant products As in our earlier Cournot example, marginal let demand costs of be: $10, i.e., c = 10 for both firms P = 100-2Q = 100-2(q 1 + q 2 ) Total cost for for each firm is: C(q 1 ) = 10q 1 ; C(q 2 ) = 10q 2 Firm 1 is the market leader and chooses q 1 In doing so it can anticipate firm 2 s actions So consider firm 2. Demand is: P = (100-2q 1 ) - 2q 2 Marginal revenue therefore is: MR 2 = (100-2q 1 ) - 4q 2

53 Equate This ismarginal firm 2 s revenue Stackelberg equilibrium (cont.) Solve this equation with marginal cost best response for output function MR2 = (100-2q1) - 4q2 But firm q12knows q2 what q2 is going MR = (100-2q1) - 4q2 = 10 = c Firm Firm11knows knowsthat that to be this how firm 22 q*2 = q1/2 thisisis22) how firm From earlier example (slide we know will react totofirm firm 1 s react firm 1 s So 1 can Demand for firm 1 is:that 22.5 is the monopolywill output. This iscan an So firm 1 output choice output choice anticipate firm anticipate firm2 s 2 s P = (100-2q2) - 2q1 important result. The Stackelberg leader 22.5 reaction reactionwould. the same output as a monopolist P = (100-2q*2) -chooses 2q1 But 2 is not excluded P = (100 - (45 - q1)) -marginal 2q1 firm revenue Equate S from the market P = 55 - q1 with cost Solvemarginal this equation R Marginal revenue for firm 1 is: for output q1 MR1 = 55-2q1 55-2q1 = 10 q*1 = 22.5 q*2 = q1

54 Stackelberg equilibrium (cont.) Aggregate output is So the equilibrium price is $32.50 Firm 1 s profit is ( )22.5 π 1 = $ Firm 2 s profit is ( )11.25 π 2 = $ We know (see slide 22) that the 15 Cournot equilibrium is: q C = 1 qc = 15 2 The Cournot price is $40 Profit to each firm is $450 q 2 R 1 Leadership benefits Firm the leader 1 s best firm response 1 but Leadership function is like benefits harms the follower consumers 2 s but firm 2 reduces the aggregate the Cournot profits equilibrium C S Compare this this with with equilibrium R q 1

55 Stackelberg and Commitment It is crucial that the leader can commit to its output choice without such commitment firm 2 should ignore any stated intent by firm 1 to produce 45 units the only equilibrium would be the Cournot equilibrium So how to commit? prior reputation investment in additional capacity place the stated output on the market Finally, the timing of decisions matters