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Chapter 5 Business Strategy in Oligopoly Markets EC 170 Industrial Organization 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 EC 170 Industrial Organization 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 EC 170 Industrial Organization 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 EC 170 Industrial Organization 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 EC 170 Industrial Organization The example (cont.) What is the The Pay-Off Matrixequilibrium for this game? The left-hand American number is the pay-off to Morning Evening Delta Morning (15, 15) (30, 70) (70, 30) The right-hand number is the (35, 35) pay-off to American Delta Evening EC 170 Industrial Organization If AmericanThe example If American (cont.) chooses a morning The morning departure chooses an evening The morning departure Pay-Off Matrix departure, DeltaThe departure, Delta is also a dominated is a dominated will choose strategy for American and will so still choose strategy for Delta and evening American can be eliminated. evening again can 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) EC 170 Industrial Organization (35, 35) 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 EC 170 Industrial Organization If Delta The example (cont.) chooses morning TheaPay-Off Matrix However, a morning departure departure, American But ifAmerican Delta will is haschoose nostill a dominated strategy for Delta chooses dominated an eveningstrategy (Evening isAmerican still a dominant strategy. evening departure, American American knows willand choose this so Morning Evening morning chooses a morning departure Morning (18, 12) (30, 70) Delta Evening (70, (70,30) 30) EC 170 Industrial Organization (42, 28) 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 $500 – 120 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: EC 170 Industrial Organization The example (cont.) If Delta prices high The Pay-Off low Matrix If both price highand American then both get 30then American gets passengers. If Delta prices Profit low all 180 passengers.American and perAmerican passengerhigh isProfit per passenger If both price low they each get 90 then$300 Delta gets is $20 passengers. PH = $500 PL = $220 all 180 passengers. Profit per passenger Profit per passenger is $20 is $20 P = $500 ($9000,$9000) ($0, $3600) H Delta PL = $220 ($3600, $0) EC 170 Industrial Organization ($1800, $1800) 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 If both are pricing might lead low boththen to Delta shouldAmerican to change (PL, PHprice ) cannot low then neither wants highbealso price low a Nash equilibrium. to change PH = $500 PL = $220 If American prices There are two Nash high then Delta should equilibria to this version also pricePhigh ($9000,$9000) ($0, $3600) of the$9000) game H = $500 ($9000, “Regret” might Delta cause both to price low PL = $220 ($3600, $0) ($1800, $1800) EC 170 Industrial Organization Nash Equilibrium (cont.) There is no simple (PH, PH) is a Nash waybe to choose between equilibrium. The Pay-Off Matrix There are two(PNash , P ) cannot 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) $9000) H = $500 ($9000, ($0, $3600) Delta PL = $220 ($3600, $0) EC 170 Industrial Organization ($1800, $1800) The only sensible choice for Nash Equilibrium (cont.) consideration of thethat Delta Suppose Delta is PH knowingSometimes, that American The Pay-Off Matrix of moves can help set its price first will follow with PHifand each will Delta can see that it timing sets find the equilibrium This means that earn $9000. theus Nash a high price, then So, American equilibria is (PH, PH) PH, PL cannot be will do bestnow by also American an equilibrium pricing high. Delta outcome earns $9000 This means PH = $500 PL = $220 Delta canthat alsoPsee that L,PH if it sets a low price,beAmerican cannot an will do$500 bestequilibrium by pricing$3,000) low. PH = ($9000,$9000) ($0, $3600) ($3,000, Delta will then earn $1800 Delta PL = $220 ($3600, $0) EC 170 Industrial Organization ($1800, $1800) 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 EC 170 Industrial Organization 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(q1 + q2) where q1 is output of firm 1 and q2 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 - Bq1) - Bq2 EC 170 Industrial Organization The Cournot model (cont.) $ P = (A - Bq1) - Bq2 The profit-maximizing A - Bq1 choice of output by firm 2 depends upon the A - Bq’1 output of firm 1 Marginal revenue for Solve this firm 2 is c output MR2 = (A - Bq1)for - 2Bq q22 MR2 = MC A - Bq1 - 2Bq2 = c If the output of firm 1 is increased the demand curve for firm 2 moves to the left Demand MC MR2 q*2 q*2 = (A - c)/2B - q1/2 EC 170 Industrial Organization Quantity The Cournot model (cont.) q*2 = (A - c)/2B - q1/2 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 - q2/2 Cournot-Nash equilibrium requires that both firms be on their best response functions. EC 170 Industrial Organization Cournot-Nash Equilibrium q2 (A-c)/B (A-c)/2B qC2 If firm 2 produces The best response The Cournot-Nash (A-c)/B then firm function for firm 1 is equilibrium is at 1 will choose to q*1 = (A-c)/2B - q2/2 Point C atfunction the intersection Firm 1’s best response produce no output ofIfthe best response firm 2 produces functions nothing then firm The best response 1 will produce thefunction for firm 2 is C monopoly output q*2 = (A-c)/2B - q1/2 Firm 2’s best response function (A-c)/2B qC1 (A-c)/2B (A-c)/B EC 170 Industrial Organization q1 Cournot-Nash Equilibrium q*1 = (A - c)/2B - q*2/2 q2 q*2 = (A - c)/2B - q*1/2 (A-c)/B q*2 = (A - c)/2B - (A - c)/4B + q*2/4 Firm 1’s best response function 3q*2/4 = (A - c)/4B q*2 = (A - c)/3B (A-c)/2B (A-c)/3B C q*1 = (A - c)/3B (A-c)/2B Firm 2’s best response function q1 (A-c)/B (A-c)/3B EC 170 Industrial Organization Cournot-Nash Equilibrium (cont.) • • • • • • • • In equilibrium each firm produces qC1 = qC2 = (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)qC1 = (A - c)2/9 Profit of firm 2 is the same A monopolist would produce QM = (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 EC 170 Industrial Organization Numerical Example of Cournot Duopoly • • • • • • • • • Demand: P = 100 - 2Q = 100 - 2(q1 + q2); A = 100; B = 2 Unit cost: c = 10 Equilibrium total output: Q = 2(A – c)/3B = 30; Individual Firm output: q1 = q2 = 15 Equilibrium price is P* = (A + 2c)/3 = $40 Profit of firm 1 is (P* - c)qC1 = (A - c)2/9B = $450 Competition: Q* = (A – c)/B = 45; P = c = $10 Monopoly: QM = (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 EC 170 Industrial Organization 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 = q1 + q2 + … This + qN denotes output • Demand is P = A - BQ = A - B(q + q2 +firm … +other qN) of 1every than 1 • Consider firm 1. It’s demand curve canfirm be written: P = A - B(q2 + … + qN) - Bq1 • Use a simplifying notation: Q-1 = q2 + q3 + … + qN • So demand for firm 1 is P = (A - BQ-1) - Bq1 EC 170 Industrial Organization The Cournot model (cont.)If the output of the other firms is increased the demand curve for firm 1 moves to the left $ P = (A - BQ-1) - Bq1 The profit-maximizing choice of output by firm A - BQ-1 1 depends upon the output of the other firms A - BQ’ -1 Marginal revenue for Solve this firm 1 is c for output MR1 = (A - BQ-1) - 2Bq q1 1 Demand MC MR1 q*1 MR1 = MC A - BQ-1 - 2Bq1 = c q*1 = (A - c)/2B - Q-1/2 EC 170 Industrial Organization Quantity Cournot-Nash Equilibrium (cont.) q*1 = (A - c)/2B - Q-1/2 How do we solve this As the number of for q* ? 1 The firms are identical. As the number firms increases output of q*1 = (A - c)/2B - (N - 1)q*1So /2 in equilibrium they firms of each firmincreases falls have identical (1 + (N - 1)/2)q*1 = (A - c)/2Bwillaggregate output As the number ofof outputs As increases the number q*1(N + 1)/2 = (A - c)/2B firms firmsincreases increasesprice profit q*1 = (A - c)/(N + 1)B tends marginal cost of to each firm falls Q*-1 = (N - 1)q*1 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)2B EC 170 Industrial Organization 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 c1 and of firm 2 Solve this are c2. • Demand is P = A - BQ = A - B(q1 + q2for ) output A symmetric result q1 • We have marginal revenue for firm 1 as before holds for output of • MR1 = (A - Bq2) - 2Bq1 firm 2 • Equate to marginal cost: (A - Bq2) - 2Bq1 = c1 q*1 = (A - c1)/2B - q2/2 q*2 = (A - c2)/2B - q1/2 EC 170 Industrial Organization Cournot-Nash Equilibrium q2 (A-c1)/B R1 q*1 = (A - c1)/2B - q*2/2 The equilibrium As the marginal output cost of firm 2 q*22 = (A - c2)/2B - q*1/2 of firm What happens increases and falls its bestof response q*2 =to (Athis - c2)/2B - (A - c1)/4B firmcurve 1 equilibrium fallsshifts to when + q* /4 2 costs change? the right 3q*2/4 = (A - 2c2 + c1)/4B q*2 = (A - 2c2 + c1)/3B (A-c2)/2B R2 C q*1 = (A - 2c1 + c2)/3B (A-c1)/2B (A-c2)/B q1 EC 170 Industrial Organization Cournot-Nash Equilibrium (cont.) • In equilibrium the firms produce qC1 = (A - 2c1 + c2)/3B; qC2 = (A - 2c2 + c1)/3B • Total output is, therefore, Q* = (2A - c1 - c2)/3B • Recall that demand is P = A - BQ • So price is P* = A - (2A - c1 - c2)/3 = (A + c1 +c2)/3 • Profit of firm 1 is (P* - c1)qC1 = (A - 2c1 + c2)2/9B • Profit of firm 2 is (P* - c2)qC2 = (A - 2c2 + c1)2/9B • Equilibrium output is less than the competitive level • Output is produced inefficiently: the low-cost firm should produce all the output EC 170 Industrial Organization A Numerical Example with Different Costs • Let demand be given by: P = 100 – 2Q; A = 100, B =2 • Let c1 = 5 and c2 = 15 • Total output is, Q* = (2A - c1 - c2)/3B = (200 – 5 – 15)/6 = 30 • qC1 = (A - 2c1 + c2)/3B = (100 – 10 + 15)/6 = 17.5 • qC2 = (A - 2c2 + c1)/3B = (100 – 30 + 5)/3B = 12.5 • Price is P* = (A + c1 +c2)/3 = (100 + 5 + 15)/3 = 40 • Profit of firm 1 is (A - 2c1 + c2)2/9B =(100 – 10 +5)2/18 = $612.5 • Profit of firm 2 is (A - 2c2 + c1)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 EC 170 Industrial Organization 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) - Bq1 But then demand for firm i is P = (A - BQ-i) - Bqi Equate this to marginal cost ci But Q*-i + q*i = Q* A - BQ-i - 2Bqi = ci and A - BQ* = P* This can be reorganized to give the equilibrium condition: A - B(Q*-i + q*i) - Bq*i - ci = 0 P* - Bq*i - ci = 0 P* - ci = Bq*i EC 170 Industrial Organization Concentration and profitability (cont.) P* - ci = Bq*i The price-cost margin Divide by P* and multiply the right-hand side by is Q*/Q* for each firm determined by its own P* - ci BQ* q*i market share and overall = P* P* Q* market demand elasticity The verage price-cost margin But BQ*/P* = 1/ and q*is = si i/Q* determined by industry so: P* - ci = si concentration as measured by the Herfindahl-Hirschman Index P* Extending this we have P* - c H = P* EC 170 Industrial Organization 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 thatthis firms compete demand andin 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 40 units – two firms producing an identical product (spring is 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 EC 170 Industrial Organization 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 – q2 = 0 – q2 = 100 - 2p2 – q2 = 0.5(100 - 50) = 25 if p2 > p1 = $25 if p2 < p1 = $25 if p2 = p1 = $25 EC 170 Industrial Organization Bertrand competition (cont.) • More generally: Demand is not continuous. There is a jump at p2 = p1 p2 – Suppose firm 1 sets price p1 • Demand to firm 2 is: q2 = 0 if p2 > p1 p1 q2 = 100 - 2p2 if p2 < p1 q2 = 50 - p1 if p2 = p1 • The discontinuity in demand carries over to profit 100 - 2p1 50 - p1 EC 170 Industrial Organization 100 q2 Bertrand competition (cont.) Firm 2’s profit is: p2(p1,, p2) = 0 if p2 > p1 p2(p1,, p2) = (p2 - 10)(100 - 2p2) if p2 < p1 p2(p1,, p2) = (p2 - 10)(50 - p2) if p2 = p1 Clearly this depends on p1. For whatever reason! Suppose first that firm 1 sets a “very high” price: greater than the monopoly price of $30 EC 170 Industrial Organization What price Atshould p2 = (cont.) pfirm Bertrand competition 1= 2 So, if p1 falls to $30, $30, firm 2 If p1 = $30, then set? firm 2 should just With p1 > $30, Firm 2’s profitgets looks like this: half of 2 will only earn a undercut p1 a bit andthe firm monopoly What if firm 1 Firm 2’s Profit positive profit by cutting its The monopoly get almost all the profit prices at $30? price to $30 or less price of $30 monopoly profit p2 < p1 p2 = p 1 p 2 > p1 $10 $30 EC 170 Industrial Organization p1 Firm 2’s Price Bertrand competition (cont.) Now suppose that firm 1 sets a price less than $30 Firm 2’s profit looks like this:As long as p1 > c = $10, Firm 2 should What price aim Of2’scourse, Firm Profit firm just to undercut should firm 2 1 will then set firm now?1 undercut firm 2 p < p1 so on Then firm 2and should also2 price at $10. Cutting price below cost gainsWhat the whole but loses if firmmarket 1 money every customer p2 = p1 priceson at $10? p 2 > p1 $10 p1 $30 EC 170 Industrial Organization Firm 2’s Price Bertrand competition (cont.) • We now have Firm 2’s best response to any price set by firm 1: – p*2 = $30 if p1 > $30 – p*2 = p1 - “something small” if $10 < p1 < $30 – p*2 = $10 if p1 < $10 • We have a symmetric best response for firm 1 – p*1 = $30 if p2 > $30 – p*1 = p2 - “something small” if $10 < p2 < $30 – p*1 = $10 if p2 < $10 EC 170 Industrial Organization The best response Bertrand competition (cont.) The best response function for These best response functions look like this function for firm 1 p2 firm 2 R 1 R2 $30 The equilibrium The Bertrand isequilibrium with both has firms bothpricing firms charging at marginal $10 cost $10 $10 $30 p1 EC 170 Industrial Organization 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 EC 170 Industrial Organization 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. QC = 63.42 - 3.98PC + 2.25PP MCC = $4.96 QP = 49.52 - 5.48PP + 1.40PC MCP = $3.96 There are at least two methods for solving this for PC and PP EC 170 Industrial Organization Bertrand and Product Differentiation Method 1: Calculus Profit of Coke: pC = (PC - 4.96)(63.42 - 3.98PC + 2.25PP) Profit of Pepsi: pP = (PP - 3.96)(49.52 - 5.48PP + 1.40PC) Differentiate with respect to PC and PP respectively Method 2: MR = MC Reorganize the demand functions PC = (15.93 + 0.57PP) - 0.25QC PP = (9.04 + 0.26PC) - 0.18QP Calculate marginal revenue, equate to marginal cost, solve for QC and QP and substitute in the demand functions EC 170 Industrial Organization Bertrand competition and product differentiation Both methods give the best response functions: The Bertrand PP PC = 10.44 + 0.2826PP Note that these equilibrium is PP = 6.49 + 0.1277PC are at upward their sloping intersection These can be solved for the equilibrium $8.11 prices as indicated RC RP B $6.49 $10.44 EC 170 Industrial Organization PC $12.72 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? EC 170 Industrial Organization Xm Bertrand and the spatial model What if shop 1 raises marks the Assume that shop 1 sets price? location ofprice the p and shopits 2 sets 1 Price marginal buyer— price p 2 one who is indifferent between p’1buying either firm’s good Price p2 p1 x’m Shop 1 xm All consumers to xthe Shop 2 m 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 EC 170 Industrial Organization is the fraction Bertrand and This the spatial model of consumers who p1 + = p2 + t(1 buy from firm 1 m 2tx = p2 - p1 + t m How is x xm(p1, p2) = (p2 - p1 + t)/2t determined? txm xm) There are n consumers in total So demand to firm 1 is D1 = N(p2 - p1 + t)/2t Price Price p2 p1 xm Shop 1 Shop 2 EC 170 Industrial Organization Bertrand equilibrium Profit to firm 1 is p1 = (p1 - c)D1 = N(p1 - c)(p2 - p1 + t)/2t p1 = N(p2p1 - p12 + tp1 + cp1 - cp2 -ct)/2t Solve this Thistoispthe best for p1 Differentiate with respect 1 response function N for +firm 1 =0 (p2 - 2p t + c) p1/ p1 = 1 2t p*1 = (p2 + t + c)/2 This is the best response function for firma 2 What about firm 2? By symmetry, it has similar best response function. p*2 = (p1 + t + c)/2 EC 170 Industrial Organization Bertrand and Demand p2 p*1 = (p2 + t + c)/2 R1 p*2 = (p1 + t + c)/2 2p*2 = p1 + t + c R2 = p2/2 + 3(t + c)/2 p*2 = t + c c+t (c + t)/2 p*1 = t + c (c + t)/2 EC 170 Industrial Organization c+t p1 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 EC 170 Industrial Organization Stackelberg Equilibrium: an example • Assume that there are two firms with identical products Both firms have constant marginal costs ofbe: $10, • As in our earlier Cournot example, let demand – P = 100 - 2Q = 100 - 2(q1 + q2) i.e., c = 10 for both firms • Total cost for for each firm is: – C(q1) = 10q1; C(q2) = 10q2 • Firm 1 is the market leader and chooses q1 • In doing so it can anticipate firm 2’s actions • So consider firm 2. Demand is: – P = (100 - 2q1) - 2q2 • Marginal revenue therefore is: – MR2 = (100 - 2q1) - 4q2 EC 170 Industrial Organization Equate This ismarginal firm 2’s revenue Stackelberg equilibrium (cont.) Solve this equation withresponse marginal cost best for output function MR2 = (100 - 2q1) - 4q2 But firm q12knows q2 what q2 is going MR = (100 - 2q1) - 4q2 = 10 = c Firm 1 knows that to be this is how firm 2 q*2 = 22.5 - q1/2 From earlier example (slide 22) we know will reactSotofirm firm11’s can Demand for firm 1 is:that 22.5 is the monopoly output. This is an output choice anticipate firm 2’s P = (100 - 2q2) - 2q1 important result. The Stackelberg leader 22.5 reaction the same output as a monopolist would. P = (100 - 2q*2) -chooses 2q1 But 2 is not excluded P = (100 - (45 - q1)) -marginal 2q1 firm revenue Equate S from the market 11.25 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 = 11.25 EC 170 Industrial Organization 2 22.5 45 q1 Stackelberg equilibrium (cont.) Aggregate output is 33.75 Leadership benefits q2 Firm 1’s best response So the equilibrium price is $32.50 the leader firm 1 but Leadership benefits 45 function “like” Firm 1’s profit is (32.50 - 10)22.5 R1 harms theisfollower consumers but firm Compare firm2’s 2 this with p1 = $506.25 reduces aggregate the Cournot Firm 2’s profit is (32.50 - 10)11.25 profits equilibrium 22.5 p2 = $253.125 C We know (see slide 22) that the 15 S Cournot equilibrium is: 11.25 qC1 = qC2 = 15 R2 q1 The Cournot price is $40 45 15 22.5 Profit to each firm is $450 EC 170 Industrial Organization 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 EC 170 Industrial Organization