duopolio de la sal-rees

8/7/2019 Duopolio de la sal-Rees

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THE ECONOMICJOURNALJULY 1993

The Economic Journal, 103 (July) 833-848. Royal Economic Society 1993. Published by BlackwellPublishers, 108 Cowley Road, Oxford OX4 iJF. UK and 238 Main Street, Cambridge MA 02142, USA.

COLLUSIVE EQUILIBRIUM IN THEGREAT SALT DUOPOLY*Ray Rees

This paper sets out to test two interesting lines of recent development inoligopoly theory. The first, arising out of the analysis of infinitely repeatedgam es, suggests conditions u nd er w hich collusive outcomes can be suppo rted asnon-cooperative equilibria by appropriate threat strategies. The secondconsiders the natu re of equilibrium in a homogeneous duopoly in which firmsset prices subject to fixed capacity constraints. Both these bodies of theory arediscussed more fully in thenext section.The data used for the tests are given ina report on the UKMonopolies andMerger Commission (MMC) inquiry into price behaviour in theUK marketfor white salt.^ In this market two firms produ ce an essentially homogeneouscommodity with blockaded entry and fixed capacities. The report providesdetailed data on prices, outputs and (marginal) costs as well asa great deal ofmore qu alitative information which is valuable in interpreting these data. Theinformation in the report is derived directly from the working of a real-worldoligopoly. Its main drawback is that it relates only to five years, and does notallow standard econometric methods to be applied, in part icular to theestimation of a demand function.Nevertheless, this paper hopes to demonstrate that some quite strongconclusions can still be dra w n, inpart icular on the extent to which the variouspossible equilibrium concepts proposed by the theoretical literature canexplain the ap pa ren t n ature ofthe equilibrium in this case. Th e wealth of detailgiven in the report seems too good to ignore, even if it cannot support astandard econometric investigation.There is a correspondence between the two types of model with which thispaper is concerned and the positions taken by theM M C and the firms that

* Earlier versions of this pap er hav e been presented at seminars at the U niversities of Birm ingham , B ristol,East Anglia, and Swansea, theEuropean University Institute, Florence, the Institute of Economics andStatistics, University of Oxford, and Northwestern University, Evanston, 111. I amgrateful to participantsin those seminars for many helpful comments, as well as to James Fr iedman, Rolf Fare, Shawna Grosskopf,Dan Kovenock, ValLambson, Venk Sadanand, Mike Waterson and two referees. None of these of course


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834 THE ECONOMIC JOURNALwere the subject of the inquiry. The theory of price-setting duopoly undercapacity constraints assumes that firms act non-cooperatively, making noattempt, whether tacit or explicit, toagree upon their choice ofprices. Thefirms in the M M C inquiry claimed tha t they had in fact not colluded, and tha t. the market outcome was fully consistent with 'competitive' behaviour. Byexamining whether thepredictions of the price-setting model match whathappened in this market, we have simultaneously a test of the model and alsoof whether the firms' claims can be accepted.

While skating carefully around the word 'collusion' , the MMC concludedthat the firms had 'severely restrained price competition'.^ The basis for thisjud gem en t appears to have been some evidence on comm unication b etween thefirms, the fact that over a long period prices had been virtually identical andchanged more or less simultaneously, and finally a view of what the outcomeshould have been had the firms in fact competed. This view was not based onthe predictions ofthe models considered h ere, and it is indeed q uestion able th atit could be supported by any generally accepted positive model of the market,but later in this paper we argue that the MMC's judgement was essentiallycorrect.Given then that the behaviour of the firms can be taken to be collusive, thequestion arises of whether this can be explained by recent developments in theanalysis of repeated games. In the next section we present brief outlines oftherelevant theories and identify the sense in which they will be tested in thispaper .

I. THEORETICAL BACKGROUNDConsider a market with two firms producing homogeneous outputs in a singletime period, and independently choosing prices subject to equal, constantmarginal costs and exogenously given capacity constraints. Edgeworth (1897)showed that if each firm's capacity is less than market demand at aprice equalto the given marginal cost, the Bertrand result that equilibrium price equalsmarginal cost no longer holds. If the market situation is repeated over asequence of periods, price will vary cyclically between well-defined upper andlower limits,/>ft and/>j. The upper limit/(^ is the price which maximises a firm'sprofit given tha t it is undercut by its competitor. The firm with the lower priceproduces at capacity, thehigher-priced firm is then faced with a residualdemand with respect to which it finds the most profitable price/);,. The lowerlimit/)j is the price which yields a firm the same profit n* when it is the lower-priced firm and produces to capacity, as when it is the higher priced firm andsets /ft. In general />, exceeds marginal cost. If, however, we insist that theanalysis must relate to only one time period, i.e. to a ' one-shot game' ,then Edgeworth essentially shows that no equilibrium price exists in thismodel.


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1993] COLLUSION IN THE SALT DUOPOLY 835equilibrium in mixed strategies. Beckman (1965) andLevitan and Shubik(1972) derived these equilibrium mixed strategies for specific examples of themodel, the main difference between them being in the assumptions made aboutthe rationing process. When the firms setdifferent prices, some assumptionmust be made as to how the residual demand facing the higher-priced firm isdetermined, or equivalently, how buyers wishing to be supplied by the lower-priced firm are rationed. Beckman assumed a form of random rationing.Levitan and Shubik assumed efficient rationing: the lower-priced firm suppliesthose buyers with hig her w illingness to pay.* For concreteness, we focus he re onthis latter case. Then the equilibrium outcome in this type of market ispredicted to be as follows: there is agiven int erval of prices which is defined bythe Edgeworth upper and lower bounds p ^ ^ and j&,. Firms choose pricesrandomly from this interval, and the equilibrium probability distributionsregulating these choices are such that each firm has the same expected profitn* whatever the price pair chosen. It follows that there is a zero probabilitythat the firms will choose eq ual prices, and tha t if the market situation isrepeated after a period, each firm's price changes randomly (within the giveninterval) over time.*

An interesting extension of these results with particular relevance to themarket studied in this paper has recently been made by Deneckere andKovenock (1992). They allow the (still exogenously given) capacity levels ofthe firms, as well as their (constant) marginal costs, to differ, and consider thequestion of the endogenous non-cooperative determination of the identity of aprice leader in this model. That is, firms engage in a game of timing of priceanno uncem ents, an d the equilibrium of the game determines which firm is theprice leader and which the follower. Their result is that the firm with largercapacity will be the price leader, while the smaller firm will follow with a pricejust below that of the leader, and will produce at full capacity. Thus the priceset by the lead er isp^, the upper bound of the Edgeworth interval, and it earnsthe same profit n* as in the mixed strategy equilibrium. O n the other hand thesmaller firm earns higher profit und er price leadership th an u nd er sim ultaneou schoice of (mixed strategy) prices, since it is producing tocapacity at a pricegreater than />,.

The theories then give quite definite testable predictions about the kind ofprice behaviour we should observe in this type of market. It is argued in thenext section t ha t the m arket for white salt is the typ e of m arke t for wh ich thesemodels can apply, and therefore can be used to test these theories.For a thorough discussion of the economics of these rationing schemes see Dixon (1987),* Cap acity is here taken to be exogenous, Krep s and Schein kma n (1983) allow capacity levels to be chosenendogenously, in a two stage game . At the second stage firms play aprice-setting game with fixed capacities.

At the first stage they choose capacities in the light of their effects on the equilibrium at the second stage.Th e interesting result is tha t capacities are chosen to be such tha t ou tputs and price are precisely those givenby the Cou mo t equilibriu m of the model. This result is further generalised by Osbo rne an d Pitchik (1986),


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836 THE ECONOMIC JOURNALT he models jus t discussed are essentially 'one-shot games': they areconcerned w ith deriving a Nash equilibrium in a single play ofthe price-settinggam e. How ever, if we move to the empirically more relevant view ofthe m arketas an infinitely repeated game, then it is well-known that repeated plays of the

one-shot Nash equilibrium also represent a Nash equilibrium of the repeatedgame. However, the important point is that other Nash equilibria are possible,and in particular those that yield the firms more profitable outcomes than thosein the one-shot non-cooperative equilibrium. The basic idea underlying thework of Fried m an (1971), Abreu (1986, 1988) and Fudenberg and Maskin(1986) among others, is that these more profitable outcomes in the one-shotgame may be sustained as non-cooperative Nash equiUbria of the repeatedgame by threats of appropriate punishments for deviation. The intuition isclear. If a firm deviates from an agreement to collude in one period, it couldbe punished in later periods, and the threat of this exante may be enough tosustain collusion. However, going beyond intuition, a number of issues have tobe considered. What form can or should punishment take and will it besufficient in fact to offset these gains since it causes future losses which have tobe discounted to be comparable with immediate gains from deviating?Moreover, since punishment will often hurt the punishers, for example apunitive price war reduces profits to all firms, will threats to carry out suchpunishment in fact be credible?

A formal answer to these questions is given by Abreu's theory of ' simplepenal codes' , which has been applied to the case of price-setting capacity-constrained oligopoly by Lambson (1987, 1991). Suppose that firms agree,tacitly or explicitly, on a particular price and allocation of outputs for eachperiod. They also agree on a t ime path of prices that will be applied as apunishment for a deviation from the agreed price by a firm, where thispunishment path may depend on exactly which firm deviates. A punishmentpath is credible if it is in each firm's interest not to deviate from it in the eventtha t it has to be imposed. An agreed price and output allocation is sustainableif it would not pay any firm to deviate from it given the credible punishmentpath that would then be imposed. An interesting aspect ofthe punishment pathis its 'stick and carro t ' na ture . In the first stage of punishment, price is cut toinflict loss of profit, but this is followed by a second stage of reversion to themore profitable price and output allocation. It then pays a firm that has justdeviated to accept its punishment, since failure to do so leads to reimpositionof the punitive phase of the punishment path and postponement of the returnto the more profitable cooperative phase. If a firm that did not deviateoriginally refused to participate in punishing the firm that did, then it itselfwould become a deviant and have the appropriate punishment path inflictedon it. In this theory the requirement of credibility is formally embodied in theconcept of subgame perfect equilibrium. The strategy of adhe ring to the agreed


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^99 3] COLLUSION IN THE SALT DUOPOLY 837actually observe implem entatio n of the punish m ent strategies - the ob servedmarket equilibrium would be the agreed price and output allocation.Any particular price and output allocation may or may not be sustainableby Abreu's punishment strategies or simple penal code. This depends on thefirms' discount factors and the structure of the market - the demand and costfunctions the firms face. Those deter m ine the extent ofth e gains from devia tion,the losses of profit that can be infiicted through punishment, and the presentvalue of future losses relative to imm ediate gains from deviation . F or ourpresent purposes, we are interested in the question: if we were to accept thatfirms in the white salt market behaved collusively, whether tacitly or explicitly,is this consistent with the models of Abreu and Lambson? We would concludethat it was, if the actual allocation turned out to be sustainable by Abreu-typepunishment strategies, while if the actual allocation turned out to be notsustainable (at reasonable discount rates), we would have to reject the theoryand look for some alternative explanation of collusion. Note that this is a one-sided test of the theory. It would also be interesting to find a market in whichcollusion did not take place, and to examine whether more profitableallocations than the actual one would be sustainable, in which case we couldagain reject the theory.* This will however have to be left for further work.

I I . THE MARKET FOR VV^HITE SALTThis section sets out briefiy some saHent facts about the salt market.^

Production. Salt production in the United Kingdom consists essentially of theextraction and processing of a non-renewable natural resource. However,reserves are so large relative to consumption that the resource rent is effectivelyzero and we can regard salt as a manufactured commodity. Water is pumpeddown into salt strata lying underground, this dissolves the salt to form brine,which is then pumped to the surface and transported through a pipeline to,initially, a purification plant. Here chemicals are added to remove unwantedminerals, then the purified brine is pumped to an evaporation plant. Six largeboilers, known as effects, are arranged in sequence, brine is pumped into thefirst, the water is boiled off and the salt precipitated, and the waste steam ispassed into the second effect where it is used to heat more brine, and so on.After the evaporation process 'undried salt' is produced, with the consistencyof wet sand. Part of this output is shipped immediately to chemical plants,mainly for use in production of caustic soda and chlorine. The remainder isdried, and then shipped, in bulk or in bags, again to chemical plants for use in

^ To put this more precisely, consider the set of all markets, and the subsets of markets (a) which satisfyAbreu's conditions for the sustainability of an agreed allocation by credible threats, and (A) in whichcollusion is observed. I interpret Abreu's theory to say that these subsets are equal. All that this paper cando, in considering just one market, is to show that their intersection is not empty, if Abreu's conditions are


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838 THE ECONOMIC JOURNALproduction of sodium and chloride, but also to food manufacturing and animalfeed p repa ration plants, and tan ning and dyeing works. Less than 10 % of totalsalt output is sold for cooking or table use.

Concentration. There are effectively just two producers: British Salt, (BS), aself contained but wholly-owned subsidiary of an industrial engineering andcontracting group, Stavely Industries; and ICI Weston Point, (WP), a smallpa r t of the Mond division of the large chemicals conglomerate ICI.Fortunately for this study WP is a self-contained accounting unit selling lessthan 5 % of its ou tpu t to other IC I plants. Imports an d a num ber of very smallsalt works account for around 3 % of the m arket and so in the rest of this studywill be ignored. We treat BS and WP as single-plant profit maximising firms.BS takes on average about 55 % of the UK market and WP the remainder .

Capacity. Ea ch firm is subject to amax imum capacity constraint, which is 824kilotonnes (kte) pa for BS and 1095 kte pa for WP . O ver th e years 1 980-4 th erewas considerable excess capacity: BS averaged less than 75% capacityutilisation, while W P's U K sales alone am ou nted only to 45 % of capa city, onaverage, though its export sales, made at a much lower profit, brought itscapacity utilisation rate up to around 65%. The degree of excess capacityappears to have been caused by an unanticipated decline in demand since thecapacity was first installed in the early 1970s.

Entry. Though salt strata suitable for extraction are common in the UnitedKingdom, a combination of planning controls and high transport costs seemsto rule out production outside the Cheshire area inwhich both BS and ICI 'splants are located. The main users are located quite closely to the salt plants,while at the prevailing prices imports were not regarded as a threat because ofthe high cost of transport and transshipment relative to value. The major saltstrata in Cheshire areowned by the incumbent firms. Moreover, there aresignificant economies of scale and as we ha ve ju st seen significant excesscapacity in the market. In the rest of this study therefore we assume that themarket behaviour of the incumbents has been infiuenced by the threat of newentry only to the extent that the possibility of imports places an upper boundon the price that can be set.Costs. The MMC report suggested that variations inoutput by BS can beachieved w ithou t significantly affecting energy usage per un it of ou tpu t (para4-10, M M C (1986)) an d, since this is the main v ariable in pu t, we translate thisinto the assumption that over the relevant rarfge of outputs average variablecost of production {ave) is constant as output varies and so equals marginalprodu ction cost. W P, which has a somewhat different technology than BS, hasa more complex cost structure. Reductions in output below capacity are mostefficiently coped with by reducing the number of effects in operation, and thisraises ave in a stepwise way.' See Fig. i. The MMC report gives an indication


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1993]

C O L L U S I O N I N T H E S A L T D U O P O L Y

*

11111

4-Efrect- 5-Effect

-.- 6-Effect

Vte \aac2

MC MC

1,095 kte/p.a.Fig. I. Cost Structure for WP.

1,095 kte/p.a.

of the heights of these steps but does not give the precise output levels at whichthe steps occur. In the period under study WP operated along the middle step.In addition to production cost, the other component of variable cost isdistribution cost, consisting mainly of transport costs. We assume these areconstant per unit of output. Marginal cost MC is then the sum of ave andaverage distribution cost. Finally, we define as average avoidable cost (aac) afirm's MC plus 'f ixed produc tion costs ' per unit of ou tpu t. Th e latter,consisting mainly of labour, management and maintenance costs, do not varyw ith outp ut, b ut are incurred if and o nly if the plant is operat ing: aac is thereforezero if output is zero and the plant is shut down, aac^ denotes BS's aac at itscapacity ou tput, and similarly SaCg is WP's capacity aac and takes into accountWP's lower average variable production cost at capacity, due to six-effectoperation. Since all these costs play an important role in what follows, it isuseful to sum ma rise the full range of inform ation in T ab le i.

Table iEirms' Marginal and Average Avoidable Costs

av emeaa e

BSWPBSWPBSWP

19806-306-029-81

12-7712-6114-46

Year19818-077-3912-11

14-2215-0715-68

Souree: M M C

19828-129-4912-03

147414-7216-28(1986).

19839-21

10-8213-6716-7717-0718-49

19849-0711-47

13-3616-1417-0117-72


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840 THE ECONOMIC JOURNALthis paper. We should at this point therefore enter a qualification. We shallthroughout conduct the analysis as if there is only one output. However, thereare at least three: undried and dried salt sold in bulk, and dried salt sold inbags. The last two outputs niust be som ewh at costlier to produce because of theadditional drying and/or bagging costs. It is impossible to disaggregate the costdata among these three outputs (for example no separate figures are given onbulk and bagged dried salt sales). However, for each firm the proportions oftotal output accounted for by each type of salt remained fairly stable over thisperiod. For WP, undried salt varied apparently randomly between 35 % and41 % of total outp ut and for BS between 30% and 37 %. Thus we assume thatno significant systematic bias results from treating output as homogeneous.This is helped by the fact that, as we see below, the two firms made identicalpercentage increases in the prices of all types of salt over this period.

Prices. In a fascinating section of the report (paras 5-25-5-41, MMC (1986)),the MMC lists the dates and amounts of the seventeen changes to list pricesmade by the two firms between Ja n ua ry 1974 and Ja nu ar y 1984. The increasesare always either exactly or virtually identical. From 1980 each firm made thesame percentage increases across all grades of salt, prior to this increases va riedacross grades. In each case one firm announced its price increases and thesecond firm followed within a month and usually within two weeks. Of the 13price increases announced from 1974-80, BS led 8 times and WP led 5 times.In each of the years 1981-4, WP was the leader. Typically the leader wouldinform the follower of its planned price increase a month before it came intoeffect, and the latter would then inform the leader of its proposed (identical)price change within that period (Table 5-8 of MMC (1986)) .In their evidence to the MMC on this m atter, the firms denied collusion^ andthe exchange of any information other than of proposed price changes" (paras8-8-8-17, 8-56-8-74, MMC (1986)). They made the point that in a competitivemarket prices would be identical and would move closely together. They alsoargued that it is not enough to consider only list prices, since there iswidespread discounting to buyers and so actual prices paid could well havemoved differently. To test this latter point the MMC examined the discountstructure of each seller. Until 1980 the rebate scales of the firms had beenidentical . Furthermore, for the majority of buyers discounts have beeninsignificant, amounting to less th an i % of the list price. For a few very largebuyers, BS's discount structure after 1980 implied a price per tonne of roughly0-25% below that of W P . Moreover, the MMC sampled a group of buyers toidentify the values of differences in prices they had been quoted by the twosellers. These differences average about 0-5 % of the price, with the highest at

' Prior to the Restrictive P ractices Act, 1956, a formal agreement to set common ex works and deliveredprices for producers and common resale prices for merchants had been in force for more than twenty years.The re was also an aggregated rebate scheme under which buyers received a discount based on aggregate


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1993] COLLUSION IN THE SALT DUOPOLY 84ITable 2

Cap acity Utilisation, Market Share, Prices and Profits

I.

I I

III .IV .

Capacity utilisation (%)BSWP (U.K. output/capacity)WP (total output/capacity)Shares of U.K. market (%)BSW PROC (%)BSW PRate of Price Increase (%)Firm initiating

1980

8554755446463319-4BS

Souree: MMC

1981

714760

534745327-5W P

(1986).

Year1982

7943655842

533014W P

1983

694059574352248W P

1984

674164554553245W P

2-2% and the modal value close to zero (Table 5-14, MMC (1986)). Theproposition th at buyers perceived p rice uniformity is supp orted by the fact t ha taround 78 % of buyers had not changed their sources of supply over the fiveyears previous to the enqu iry (para 5-13, M M C (1986)).Profits. The accounting rates of return on capital employed (ROC), net ofdepreciation, and at historic cost, are shown for the two firms inTa ble 2, whichalso gives some othe r imp ort an t m arke t information. O ver the same period, thecomparable rate of return for all large quoted companies varied between 9 %a n d 1 3 % , and of companies in the chemicals and man-made fibres industriesbetween 7% and 16 % . However, in the remainder ofthis paper we consideronly profits defined as revenues less variable and fixed production anddistribution costs. The reason is of course that the capital costs were essentiallysunk and did not vary either with the level of output or the shutdown decision.Profits are the short run quasi-rents which the firms are assumed to maximise.

III. COMPETITION, PRICE LEADERSHIP, COLLUSION AND JOINTPROFIT MAXIMISATION

T h e da ta on costs, capacities and prices given by the repo rt we take to be ' ha rddata ' . Though they are subject to interpretation, the numbers themselves arethose the firms themselves would have had to work with. We can givereasonably firm answers, on the basis only of these data and, in some cases,general assumptions on demand, to the three questions with which we areconcerned. Did the firms behave non-cooperatively as in the Edgewor th-


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842 TH E ECON OMIC JO UR NA Lcooperative equilibrium involves firms operating at below capacity andchoosing mixed strategies in prices.^" Clearly, both firms were producing at lessthan capacity. If they had been choosing prices according to mixed strategies,then the probability that every time they chose prices those prices would beidentical, is zero. Yet on each of the 17 times prices were set in the period1974-84 prices were in fact identical. T hu s we could reject the EL S m odel, evenif we had no knowledge of the extent to which the firms actually exchangedinformation on proposed price changes, and thu s could be said to be co rrelatin gstrategies.

A somewhat stronger case could be made for the Deneckere-Kovenocktheory of price leadership. The theory predicts that the larger firm would be theprice leader. This was true in each year 1981-4. In the seven years previous tothat, leadership varied between the two firms, but we have cost data only for1980-4. In the Deneckere-Kovenock model, the smaller firm could be priceleader if its marginal cost is sufficiently higher than that of the larger firm, andonly in 1980 can we certainly say that this was not true, so that BS's priceleadership in tha t year contradicts the theory. Th e theory also predicts that thefollower will price 'just below' the leader, and, though this is not consistentwith th e dat a on list prices, the evidence on discounts given by the M M C couldper hap s be interp reted as jus t consistent with this. Ho wev er, the c rucialm isma tch is in respect of cap acity utilisation. In the De nec kere -K ove noc kprice leade rship equilibriu m , the follower sells at full capa city. T his w as clearlynot the case in the white salt market.Thus, in this market at least, the predictions of the ELS and Deneckere-Kovenock theories are not confirmed. The main reason, we would claim, isthat they are derived from one-shot non-cooperative equilibria.In its evidence to the M M C , BS stated tha t 'if it raised prices by a lesseramount than [WP], and [WP] failed to lower its own price to the same level,there would be an immediate transfer of business to itself... This would lead toa long-term retaliation by [WP] who would seek to take customers from BritishSalt ' . (MMC (1986), para 28-11). This statement shows that the firms clearlyshare the intuition underlying the idea of collusive equilibrium supported bythe threat of retaliation, which is hardly surprising, simple as it is.W e now ha ve to see if the outcom e in this m arke t is consistent with the m oreformal th eory. W e assume th at th e actua l prices and profits in each of the years1980-4 correspond to collusive allocations, and we wish to test whether thesecan be sustained by credible threats. Following Lambson (1987), we have thecriteria for:(i) Sustainabiiity: Let nf denote the one-period profit firm i= 1,2 earnsunder the agreement, nf the maximum profit it can earn by reneging on thisagreement, T^ a punishment path of prices that will be imposed in the period


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1993] COLLUSION IN THE SALT DUOPOLY 843follovi^ing a violation ofthe agreement by firrn i,P^(TJ the present value at theda te pu nish m eht begins of profits to firm i along this path , r > o the per-periodinterest rate and = (i +r )" ^ the discount factor. T he n the agreed allocationis sustaina ble if at each time t

nf-nf ^ nf/r-Smr,) i=i,2. (i)T his says tha t the one-period gain from dev iating at time t is less than thepresent value at t of the future loss of profit from having the punishment pathinflicted ne xt perio d ra th er th an enjoying th e collusive profit forever. P rov idedthe punishment path is credible, satisfaction of (i) ensures that the threat offuture punishment will deter a one-shot violation of the agreement."(ii) Credibility: Let nf den ote th e profit in some given period t that firm i willmake on a prescribed punishment path^^ nf^ the maximum profit it couldmake at t if i t reneged on the punishm ent pat h in that p eriod, and Vf the presentvalue at t+i of profit the firm would earn from adhering to that prescribedpunishment path from t+i onw ard. T hen that punishm ent p ath is credible if

T h e righ t-ha nd side of (2) gives the present value at t ofthe difference in profitsbetween continuing along the prescribed punishment path from t+ i on, andhaving a punishment path for a deviation imposed a.tt+i from its beginning.T he left-hand side gives the one-shot gain from dev iating from the prescribedpunishment path. If this inequality is satisfied, itdoes not pay firm i to deviatefrom the prescribed p unishm ent p ath and so the threat of imposing that pa this credible.^*

T o test w heth er these cond itions can be satisfied in the mark et un de r studywe first need tospecify a time period and associated interest rate. We take 3months and 10% respectively as reasonable assumptions.^* Next we need tospecify the exact nature of the punishment price paths. In general, a pa thwh ich can satisfy ( i) an d (2) for some set of intere st rates is not un iq ue , bu t th efollowing specification has some intuitive appeal:If either firm deviates, in the following three periods both firms set price ataac2 and then they revert to the initial allocation.Since on this (sym metric) pu nish m ent p ath price falls to W P 's actu al aac, itmakes no profit in the pu nish m ent phase , while BS makes a small profit becauseits aac is somew hat lower. T he pun ishm ent strategy corresponds to a 'pr ice

" Abreu (1988) shows that if deviation is unprofitable for one period it will never be profitable.Strictly we should write TT^^, ( = i , . . . J = 1,2 since profits may well vary along apunishment path, andthe path may depend onwhich firm deviated, but noconfusion should result from keeping the notationuncluttered here." Simply rearranging the condition as Trf+ SV^ir,) ^7rf + SV^ shows that we could equivalently

interp ret the condition as saying it is better to continu e along the given punishm ent p ath tha n to deviate thisperiod and have punishment begin anew next period.T he longer the tim e period, the m ore profitable does reneging becom e, since the longer the period for


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844 THE ECONOMIC JOURNALw a r ' in which prices are slashed to the break-even level (at actual output) forthe higher cost firm.To quantify the effects of pu nis hm en t on the firms' p rofits aswell as the gainsfrom one-shot deviations from the punishment path we require someassumption about market demand. As a first app roxim ation, we assume zeroelasticity of demand at any prices below the agreed price. Since, if this weretrue at prices abov e the agreed price, the latter could not be profit maximising,we are implicitly assuming a kink in demand at the actual price, possibly dueto the threat of imports.Finally, we need to assume how total ma rket dem and will be shared betweenthe firms along a punishment path. Since they set the same prices, it seemsreasonable to assume that their market shares are as in the actual allocation.Thus , effectively we assume that along a punishment path the firms wouldproduce the same outputs as those they actually produced, but at much lowerprices and profits. For each of the years 1980-4, we then calculate the valuesofthe quantities entering into conditions (i) and (2), given the punishmentstrategies jus t described. The results^* are given in Table 3, and show that thespecified punishment path was credible in each year, and could sustain theactual allocation. Table 3Gains andLosses from Deviation and Punishment

1980I98I198219831984

BS367964800

1.3771.631

WP2,0152,9013.3403.3973.633

BS3.3474.1725.1435.0416.035

WP3.7594,1484,0063.6213.645

BS256376276494468

(000)' -

duopolio de la sal-rees

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