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Dynamic Price Competition in Homogenous Products Chicago Tradition on Cartels: Friedman 1973, Newsweek on the OPEC Cartel: Cartels involve setting a price in which it would be optimal for somebody to deviate by secret price cutting. Thus, all cartels are unstable, including OPEC, and so there is no need to worry……. However, this fails to recognise that there are some mechanisms under non-cooperative oligopoly models which can hold an equilibrium price up, in spite of the problems of free-riders and secret price cutting….. In general in one-shot games – perfect information - no reputation effects – there are big incentives to deviate and high prices are not sustainable in equilibrium. Hence we turn to repeated games. 1 Dynamic Games Are high prices sustainable in non-cooperative repeated games? Infinite Horizon, Perfect Information, Repeated Game firmi payoff is discounted sum of profits: i = tt where discount factor is 0 < < 1 (higher values give greater weight to the future) Strategy for firmi in repeated game maps prices set by all players in periods 1……t-1 into Pit for firmi in period t Trigger strategy that supports the cooperative outcome as a non-cooperative Nash equilibrium in the repeated game: firmi sets monopoly price in all periods if and only if, no price set in any earlier period of the game is < the monopoly price, otherwise, firmi sets Price = MC. The anticipated one period gain from unilateral deviation from high price is less than the cost of punishment forever (competitive pricing) for certain values of (in homework for 0.5) Thus, all firms will maximise i = tt by setting monopoly price forever, when 0.5 2 Finite Horizon, Perfect Information, Repeated Game Solve Finite Repeated Game in process of backward induction Last period T: anticipated one period gain from unilateral deviation from high price brings about no future punishment. Thus, incentive for representative firm to deviate. All firms thus deviate in final period T, and P = MC Second Last Period T-1: Treat as last period. Perfect information, so all know P = MC in last period T. Thus, anticipated one period gain from unilateral deviation from high price at T-1 brings about no additional future punishment. Thus, incentive for representative firm to deviate. All firms thus deviate in final period T-1, and P = MC Similar for each preceding period So First Period, T=1, we have all firms deviating and setting P = MC Co-operative prices are not sustainable in Finite Repeated Games with Perfect Information 3 Green Porter Model (1984) Introduce uncertainty concerning the nature of demand. If firms observe a low market price, there are two possible stories: 1. firms are deviating from setting a low output (high price), 2. actual demand is low (quotas are set based on anticipated demand). Which is true? Could try to use an observable market signal to distinguish between 1) and 2). However, the environment in which firms operate is actually quite complicated. Underlying Assumptions of the Green Porter Model: 1. Market is stable over time i.e. fluctuations in the demand curve are described by a stationary stochastic process. 2. In this model, there is no route around the signal extraction problem, so ‘cheating’ (firms expanding output) can not be distinguished from a low demand. 3. All information is public, except ‘own output’. So if some other player is producing above its quota, then that is not detectable by other parties. 4. NB: The information which is used to police the arrangement is imperfectly correlated with actions i.e. by observing market price – which is only imperfectly correlated with whether or not ‘cheating’ is taking place. 4 Structure of the Green Porter Model: Is given by the structure of the market…… - n firms - homogenous goods - i(qi, P) is current profit per period of firm i; P = price and qi = sales - As in many models (because there are many potential equilibria) we simplify matters at the outset by restricting the strategy space. X X X X X X X X X X X X All strategy combinations that form equilibria X X X X X Certain types of strategy that form equilibria - The type of strategy used in this model is most widely used simple “Trigger Strategy” - the (restricted) space of strategies we use is as follows : _ qit = if t is ‘normal’ (low output q i , high price – between monopoly and cournot levels) c = q i if t is ‘revisionary’ (higher output, lower price i.e. Cournot) _ qi - assume Cournot behaviour in revisionary periods - the focus of interest is qi - what level of output will profit maximising firms select? - Market Demand: P = P(Qt) . t 5 - Firms watch P . Since they don’t know exactly Qt, they cannot tell whether low P is caused by _ (1) firms strategically expanding output qi above (2) random demand shock resulting in low demand qi or - Trigger Strategy: Switch to Cournot for finite T periods, if ~ P < P (i.e. assume lower observed price is due to firms _ strategically expanding output above q i , though this may not be the case….) ~ ~ - Choice variables: qi, P , T . Thus, { q*, P , T} is an equilibrium satisfying the condition that no firm wishes to deviate (i.e. Nash Equilibrium) - Let the discount factor be 0 < < 1 (higher values of give greater weight to future profit) Mechanism: Calculate the Payoff (NPV of future profits) from deviating, when everyone plays the above strategies Need to worry about different future paths pricing may take ….. _ Even if no-one else deviates (expands qi > q i ) - I might deviate and trigger Cournot revisionary period for T finite periods - I might not deviate, but low demand triggers Cournot for T finite periods 6 ~ P and T are given, but I decide on the level qi to set, to maximise NPV payoffs future earnings ) (Earnings this period + discounted Let Vi(qi)= NPV of i’s profit stream if qi is used in normal periods _ (issue will be, should I set qi = q i or set qi > V i (qi ) _ q i ?) i (qc ) i (qi ) i (qc ) 1 1 ( T ) (qi ) ~ probability of breakdown (i.e. P < P ) = (qi) Vi(qi) = T t i i (qi ) (1 (qi ))V (qi ) (qi ) (qc ) TV i (qi ) t 1 i no trigger( probability (1 ( qi )) earn V i ( qi ) ( discounted ) from now on trigger( with probability ( qi )) earn cournot ( discounted t ) profits for T periods V i ( qi ) ( discounted T ) from when go back to normal Discounted future earnings = discounted payoffs if no Cournot reversion (with probability 1 - (qi)) + discounted Cournot payoffs for T periods if breakdown (with probability (qi)) + discounted payoffs from the point that we go back to normal Solving for Vi(qi), we obtain (as written earlier): 7 V i (qi ) i (qc ) i (qi ) i (qc ) 1 1 ( T ) (qi ) deviant must trade off more profit today, with higher (qi). Thus the “cartel”, on average, gets lower profit _ The decision to deviate (set qi > q i ) involves selecting qi to maximise Vi(qi) dV i (qi ) F.O.C. sets dq 0 i The optimal q* chosen takes into account: the expected gains from one period deviation of qi by one unit, and the expected costs of triggering breakdown. Note that the expected costs of deviating include the loss of profit for T periods (cournot strategy played) And the fact that a breakdown may happen by accident (low demand), and thus the future benefit you forego is one you only get sometimes – this reduces the expected cost Whether the maximising firm sets the co-operative output level _ * q , or deviates and sets qi> q i , depends on the values of { q , _ i ~ P , T} * ~ There are many { q , P , T} triples that form a Nash Equilibrium, such that the F.O.C. requirement holds so that no firm will want to deviate along the equilibrium path of the game i.e low output (and high price) is feasible and no-one wants to deviate under non-cooperative dynamic oligopoly 8 ~ e.g. low P , needs high T to be a sufficient deterrent to deviation….. The more severe the punishment (longer T and/or more competitive behaviour during revisionary period) and the greater the weighting given to future profits (), the lower the _ output q (and higher the price) that can be sustained under dynamic non-cooperative oligopoly. In making a decision about the level of the ~ trigger price P and the length of time for reversion to Cournot T, firms trade off current profits from deviation and future _ losses from Cournot relative to q i . ~ For values of { q , P , T}, there is a Nash Equilibrium – nobody finds it worthwhile to deviate from low output (high price), and this is common knowledge. * ~ Does this mean, if players observe P < P , they can agree to ignore it, knowing that it can’t have been caused by a deviant? No – since removing the punishment does not discipline the firms, and so you get unilateral incentives to deviate….. Green Porter Predictions 1. Interprets Revisionary Periods as ‘Price Wars’ 2. ‘Price Wars’ should occur sometimes 3. ‘Price wars’ should happen when demand is low. 4. Firms should not cheat (in equilibrium, ‘price wars’ happen only due to demand shocks) 5. output during normal periods exceeds the monopoly level, but is lower than Cournot 9 Rotemberg-Saloner (1986) Homogenous Goods 2 price setting symmetric firms, infinite game No uncertainty i.i.d. Demand shock: at each period can be low (D1(p)) or high (D2(p)) with probability ½ . Assume D2(p) > D1(p) p In each period, state of demand is known before choose p Thus, discounted profits of each firm from any two prices is given by: 1 D2 ( p 2 ) 1 D1 ( p1 ) V T ( p1 c ) ( p2 c) 2 2 2 2 t 0 D ( p )( p1 c) D2 ( p 2 )( p 2 c) 1 1 4(1 ) Can we enforce a (non-cooperative) agreement? Is there {p1*,p2*}in which deviating from a price ps when demand is in state s is not privately optimal? Assume firms set pm in each state of demand Assume maximal punishment : if observe p<pm: p=mc and zero profits forever Incentives to deviate? Highest in high demand period, so consider these…. Maintain high prices if profit from deviating < profit from cooperating 1m 2m V If monopoly in all states : (1 )4 10 Gain from deviating in state of High demand 2: m 2 2m 2 2m 2 Thus, for pms to be sustainable: Benefits deviating (discounted) costs of punishment 1m 2m 2m V 2 (1 )4 or, re-writing 2 2m 0 3 2m 1m Since 2m > 1m, 0 is between ½ (1=2) and 2/3 (1 = 0). i.e. cooperative outcomes are sustainable in non-cooperative oligopoly where 0 such that ½ < 0 < 2/3 When demand is high, the temptation to undercut is important. The punishment is an average of high and low profit (so less severe than if high demand were to persist with certainty) What if between ½ and 0? Can not support monopoly prices in high demand periods. Then choose (p1,p2) to max firms expected payoffs subject to the incentive (no undercutting) constraints: 1 ( p ) ( p ) 4 1 1 2 2 max (1 ) p1, p2 s.t . and 1 ( p1 ) 1 4 1 ( p1 ) 2 ( p2 ) (1 ) 2 ( p2 ) 1 4 1 ( p1 ) 2 ( p2 ) 2 (1 ) 2 11 Re-writing the two constraints as 1(p1) K2(p2) 2(p2) K1(p1) where K / (2-3) 1 Intuitively, second constraint is the binding one (high demand). So for any p1, choose p2 to maximise subject to it. But this solution gives an objective function which increases in p1 up to p1m , so set p1 = p1m and then choose p2 subject to 2(p2) = K1(p1m). So charge p1m in low demand, and p2< p2m in high demand (note: this does not mean necessarily price levels in one period are higher compared to another – depends on what the demand function and thus what monopoly price is each period) Rotemberg and Saloner: No uncertainty Rational comparison of gains from deviating to losses of punishment Harder to support monopoly pricing in good times than bad, since incentive to deviate is higher (i.i.d. assumption important here – assumes good times not known to be followed by even better times….) Consistent with ‘Countercyclical Pricing’ Revisions in prices interpreted as ‘Price War’ ‘Price Wars’ occur in Booms (unlike Green-Porter, where ‘price wars’ occur in low demand periods) 12 Haltwinger and Harrington (1991) Replace i.i.d. demand shifts with predictable demand movements (e.g. business cycle, seasonal fluctuations …) Thus, different periods differ in returns to deviating (as with Rotemberg and Saloner) But here, since different periods have different futures, they also differ with respect to the loss due to punishment. Homogenous Goods n Price setting symmetric firms, infinite game Deterministic Demand Cycles ^ Demand curves increase (at every p) until t , and then decrease until cycle is complete. Maximal Punishment: if firm deviates, then we get reversion to zero profits forever Firms sustain max joint profits subject to the constraint that the price path is supportable by a subgame perfect equilibrium. Thus, punishment must > value of deviation for each period P(t ) p( ) c D( p( )); / n t t 1 n 1 p(t ) c D( p(t )); t / n D(t ) t here refers to the period in the cycle discounted future loss from deviating in period t from the cooperative price path (foregone future higher profits) one time gain from deviating 13 The equilibrium they derive depends on the value of 1) if ,1 (i.e is large enough), firms maintain pm ^ forever, and whether this is pro- or counter-cyclical depends on the form of the sequence of {D(p,t)}. 2) if 0, n 1 n i.e. is low enough, then the p = c forever (can not sustain cooperative prices. Note that, for a high enough value of n this is actually a likely event) 3) there is a range of values where we will only not maintain monopoly outcomes at one point in the cycle, and that point is after the peak. i.e. the point at which cooperative outcomes can not be maintained is always when demand is falling If lowered further, then there would exist many more such points over the cycle where cooperative outcomes could not be sustained However, for the same level of demand, the point when demand is falling will always loose the ability to maintain cooperative outcomes faster than the point at which demand is rising Two forces at work Higher demand makes it more profitable to cheat Falling demand makes punishment from deviating smaller Thus, it is when demand is high and falling that monopoly prices can not be maintained 14 Note : This is all relative to the monopoly price, which in turn depends on how demand curves shift over the cycle (e.g. if they become more elastic when demand grows, prices will be countercyclical…) When prices fall < pm, this does not mean profits fall (no price war or punishment in this sense). Haltwinger and Harrington Current price depends on current demand and on expectations of future demand Gain to deviating from established pricing rule varies over the cycle, and is highest when demand is strongest (discounted) loss from deviation varies over the cycle, and is lowest when demand is anticipated to be falling in immediate future for the same level of demand, prices will always be lower during periods of falling demand than during rising demand. Thus, it is possible that prices may be procyclical during booms, and countercyclical during recessions 15 Porter (1983) A Study of Cartel Stability – the JEC 18801886 JEC – a railroads freight cartel controlling eastbound freight from Chicago (preceded Sherman Act 1890, and so was explicit). Cartel took weekly stock of sales Cartel reported official prices and market share quotas weekly in the “Chicago Railway Review” However, clearing arrangements allowed Market demand highly variable (some 70% of annual business was undertaken by steamships when Lakes openend), so actual market shares depended on actual prices (could be different from official rate) and the realisation of the demand shock Porter (1983) believed there was an internal enforcement mechanism, which was a variant of a trigger price strategy, used by the JEC to maintain collusion - We observe price and quantity movements over time. Are they due to (exogenous) shifts in the demand and cost functions? Or are they due to price wars? - Porters Main Objective: Establish the existence of price wars JEC gathered and disseminated weekly information to member firms 16 TQG – total quantity of grain recorded as shipped by JEC members – varies dramatically over period GR - index of grain rate prices of the JEC PO - dummy variable = 1 when the “Railway Review” reported that a price war was occurring (though conflicts with other indices of when a price war was occurring that were available for that period) PN – Porters estimate of when there was a price war Various changes in industry structure over the period 2 entrants to the railroad industry 1 exit from the cartel opening and closing of alternative means of transport (the Great Lakes) various seasonal effects Thus, assumptions behind the ‘repeated game’ are suspect. Paper allows for the change in structure to cause exogenous changes in the various cartel prices (but only prices in punishment phases) 17 Porter’s Model: Demand Equation ln Qt = 0 + 1 ln Pt + 2 Lt + 1t Lakes is the main outside option Lt = 1 Great Lakes open to shipping (all seasons, save Winter) = 0 Otherwise Supply Equation Recall, we saw in the previous topic that the general F.O.C. for firms is given as dP P Q MC dQ (where = 0 for competitive industry; = 1 for collusive industry; = 1/N for cournot industry) N firms, asymmetric with respect to costs ci(qi) = aiqit + Fi i = 1,….,N Thus, Marginal Revenue for firm i: it MRi p1 MCi (qit ) ai qit 1 1 Homogenous good, so p is same for each firm 18 Define market-share weighted parameter: N t it sit i 1 Conduct is allowed to vary over time (this is the essence of the Green-Porter model – varies between normal and revisionary behaviour). Adding up MR condition over the N firms, and solving for the quantities, we obtain the industry marginal revenue conditions: t 1 MR pt 1 DQ t 1 N where D ai1 1 1 i 1 The implied Supply Equation is therefore: ln pt = -ln (1+t/1) + ln D + ( -1)ln Qt We identify t by putting on some structure about how it varies. Porter assumes there are only two regimes: one that is collusive, and one that is a price war 19 He estimates the following: ln pt = 0 + 1 ln Qt +2 St + 3 It + 2t 0 + 1 log Qt +2 St represents the price in punishment periods St = set of market structure dummies that accommodate entry/exit It = dummy = 1 during collusive regime Theory predicts: higher during collusive regime, and therefore 3 should be positive (since 1 is negative) When the It are known, identification is as in Bresnahan When It not known, they are estimated using a straight maximum likelihood Data and Results: GR - $/100 pounds shipped (average of self-reported prices TQG – total quantity of grain shipped PO – cheating dummy = 1 if collusion is reported by Railway Review (not really used) ^ PN – estimated cheating dummy ( I t ) DM1-DM4 - structural dummies 20 Table 3: Results Collusion Dummies indicate collusive price 40% - 50% higher than price in the punishment phase TSLS: IV procedure where Porter instruments for GR and TQG. Cooperative prices > prices in punishment phase BUT, Porter reports that these cooperative prices < jointprofit maximising prices (when absolute value of elasticity should = 1) Does this imply that cost of maintaining a collusion too high? Or at least, too high when environment varied from period to period? Lakes: Dummy = 1 when one could ship on Great Lakes Figure 1: GR, PO, and PN series Punishment phase does correspond to price wars, but price wars seem to vary in duration and magnitude Revisions to price wars happened more regularly in later periods after the new entry (and hence, when there are more cartel members) Model implies that price wars should occur when there is unanticipated low realised demand. Porter does not find this in the demand errors. Could be due to several missing variables from demand system that may have dominated the behaviour of those errors and known to the agents at the time (not to the econometrician today – eg price of freighter traffic on the Great Lakes). There 21 is some, not strong, historical evidence that price wars tended to occur after unexpected demand shifts. Summing Up: 1. Green and Porter (1984) prediction that price wars should occur sometimes. This is tested by Porter (1983) - the paper seems to document the existence of an omitted variable on the supply side, which he interprets as “price wars” 2. However, he does not model what drives it. There is no explanation of why price wars start or how long they last (vary in duration and magnitude) 3. Green and Porter (1984) prediction that price wars should happen when demand is low. Porter (1983) regresses price war occurrence on indicator variables and finds nothing. As mentioned above, the power of this test is low due to lack of data. 22 4. Porter (1983) allows for change in industry structure (entry and exit) – but (i) does not tackle the issue of how much the existence and success of a cartel induces change in structure and (ii) assimilates the two new entrants into the cartel without much of a fight 5. Green and Porter (1984) prediction that in a noncooperative oligopoly, firms should not cheat – in equilibrium price wars occur only due to demand shocks. This is not tested by Porter (1984). Ellison (1994) considers this. 6. Mariuzzo and Walsh (2006) include Lake prices rather than just a dummy; and allow for a deterministic cycle as in Haltwinger and Harrington (1991) 23 Borenstein and Shephard (1996) – Dynamic Pricing in Retail Gasoline Markets Not a study of an established cartel Objective: Demonstrate Collusion AND Examine its Form - is pricing of retail gasoline consistent with predictions of Halwinger-Harrington (1991) type models? Looks for reduced form implications that are consistent with the data (1986-1992) Haltwinger-Harrington: harder to support collusive prices if, all else equal, future demand is lower 1. Collusive margins will respond to anticipated changes in cost and demand 2. Controlling for current demand, margins will respond positively to expected increase in near-term demand (punishments are likely more effective so can support a higher price) 3. Controlling for current input prices, margins will respond negatively to expected increase in input prices (punishments are less effective and we can’t support higher prices) Retail gasoline: - differentiated product market (mostly by location) - known seasonal changes in demand and input prices (primary input is wholesale gasoline) 24 - many ‘related’ firms in each market, which doubt whether the joint profit maximising price can be sustained (without side payments between firms, which is illegal) - Data are by city (so abstract from intracity competition) - Figure 2 shows seasonal in quantities – shows distinct seasonal pattern, so there are periods when future demand is expected to be higher than current demand and vice-versa - Figure 1 shows seasonal in price - terminal price is the closest they have to a wholesale price, so margins are roughly proportional to the difference between the terminal price and the retail price (only roughly, as there are different types of contracts between retailers and suppliers so margins can depend on the nature of the vertical contract). - (Note that the terminal price series is much more erratic than the quantity series, making it difficult to see a seasonal in the margins. This is the market with OPEC - various political and collusive considerations are important in determining the terminal price) Basic Equation: Marginit = 1Nvolit + 2expvolchgit+1 + 3terminalit + 4exptermchgit+1 + controls +it Controls account for the impact of past terminal prices, past retail prices, city and time effects Nvol = state volume / state mean volume of retail sales in the sample period 25 Assumes (absent incentives for collusion) retail price would be a distributed lag of past terminal and retail prices about an equilibrium determined by volume and city effects. Haltwinger-Harrington following: “collusive” theory predicts the 2 > 0 (if anticipated demand , punishments are likely more effective so can support a higher price) AND 3 < 0 (if anticipated terminal prices , punishments are less effective and we can’t support higher prices) The data: average monthly prices in ~ 60 cities over 5 year period (1986-1992) Predict volume changes with separate equation for each city of the form: Nvolt = f(past Nvolt-1) + f(past retail pt-1) month dummies+f(time) High fit (0.80 – 0.95) mainly due to the seasonal Predict terminal prices similarly - city-by-city regression as a function of month, past terminal p and past crude prices. Fit is only 0.3 – 0.6. Terminal or input prices vary in a much less predictable way than volume. 26 Table 2: Results (correcting for endogeneity) 2 > 0 AND 3 < 0 Margins (not price) are increasing in quantity sold (Nvolt), and by about the same amount as margins increase with expected volume changes Note: average margin = (retail – terminal price = ~ 10.6 cents) / (average terminal pricet = ~ 73 cents pergallon) Numbers not very large (effect of a one deviation change in the expected volume on margin, calculated at the mean, is about 0.26 cents – and similar for impact of terminal price change) but they are significant Results consistent with Haltwinger-Harrington theory of collusions (and with previous studies of retail gasoline) 27