Price Behavior in a Dynamic Oligopsony: Washington Processing Potatoes - a Comment N Lavoie

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2005 Price behavior in a dynamic oligopsony: Washington processing potatoes - A comment N Lavoie

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Recommended Citation Lavoie, N, "Price behavior in a dynamic oligopsony: Washington processing potatoes - A comment" (2005). American Journal of Agricultural Economics. 99. 10.1111/j.1467-8276.2005.00764.x

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PRICE BEHAVIOR IN A DYNAMIC OLIGOPSONY: WASHINGTON PROCESSING POTATOES -A COMMENT

NATHALIE LAVOIE

In a recent article in this journal, Richards, the CV should not be interpreted in the same Patterson, and Acharya (RPA) evaluate way in a theoretical versus empirical context. whether the Washington State frozen potato processors behave as an oligopsony and de- firmIn theory, i regarding dxj?x howrepresents firm j will the react "conjecture" to an in- of termine the welfare loss associated with this crease in quantity by firm i. Empirically, while market structure. For this purpose, the authors early work gave a behavioral interpretation use the Green and Porter trigger price model to the estimated value of Oi or "conduct pa- of collusion. However, this article contains er- rameter," recent practice has been to interpret rors in the derivation of the industry aver- the conduct parameter as an index of market age conduct parameter and in the derivation power that ignores the (unknown) game that and calculation of the loss in producer wel- firms play (Perloff).2'3 Finally, Corts demon- fare. These errors make the article confusing strated that Bresnahan's middle ground in- and have important implications for the inter- terpretation of the conduct parameter-firms' pretation of the results and associated policy behavior is as competitive as if they held the recommendations. conjecture implied by the estimated value-is The first mistake occurs in the derivation of valid only under a restrictive condition.4 Nev- the values of the industry average conjectural ertheless, validations of the conduct parameter variation (CV) elasticity under different forms approach using direct measures of marginal of firm conduct. CV is defined as cost to compute the "true" value of the con- dX duct parameter have shown that the method (1) i dX= 1 + vi performs reasonably well for low levels of mar- dxi ket power (Genesove and Mullin; Clay and where X is the industry output, xi is firm i's Troesken). RPA model the profit-maximization prob- output, v, = N L', and xj = firm j's output. lem of a typical potato processor in an in- CVs have been the subject of both criticism dustry characterized by oligopsony power. In and confusion in their interpretation.' First, this market structure, the notion of CV comes the nomenclature "conjectural variation" in it- into play because firms are mutually interde- self is confusing because it has been used in the pendent in their actions. While the model is literature and textbooks to describe either Oi, vi (Waterson; Jacquemin), or even 2(Kamien dx, and Schwartz; Brander and Zhang). Second, as 2 The terminology "conduct parameter" has been used generically in the literature to describe the estimated value of either the emphasized by both Bresnahan, and Perloff, CV (0,) or the CV elasticity (X M-L). I will use the term "conduct parameter" generically also. 3 By expressing 0, in elasticity form, its interpretation as a mea- Nathalie Lavoie is assistant professor in the Department of Re- sure of departure from competition becomes clear. The Lerner source Economics at the University of Massachusetts, Amherst. index in this case corresponds to the CV elasticity divided by the The author thanks Mingxia Zhang for verifying the derivation of elasticity of demand. Thus, the CV elasticity can be interpreted equation (4). The author also gratefully acknowledges the helpful as an elasticity-adjusted Lerner index and provides a measure of comments and suggestions of two anonymous reviewers and editor market structure or departure from perfect competition (Perloff; Ian Sheldon. Thanks also go to Tim Richards for his cooperation Corts; Wolfram). by providing the data used and the estimate of the beta parameter. 4 Corts demonstrates that the estimated CV parameter measures However, all errors are the author's responsibility. the marginal, not average, collusiveness of conduct. Thus, market 1 See Carlton and Perloff; Kamien and Schwartz; Bresnahan; conduct inference is limited to cases where behavior in equilibrium Jacquemin; Perloff; and Corts for the discussion of this topic. is identical on the margin, not on average, to a CV game.

Amer. J. Agr. Econ. 87(3) (August 2005): 796-801 Copyright 2005 American Agricultural Economics Association Lavoie Comment on Price Behavior in a Dynamic Oligopsony 797 specified for a typical firm, only Table 1. Valuesindustry of dx , 0, and On data for Identical are available-a common difficulty Firms inunder this Different type Forms of Firm Conduct of analysis. When only industry data are available, Bresnahan argues that the aggregate conduct parameter should be interpreted Firm Conduct as the dx, dx 0a industry average conduct. It is in aggregating Perfect collusion 1 N 1 the firms' supply relation to obtain an industry average that an error occurs. CournotThis error competition leads 0 1 to a misspecification of the benchmark Bertrand/perfect values competition N-1 O0 0 of the industry average CV elasticity against which the estimated parameters are compared to assess the degree of departure from competition and the associated welfare loss. Thus, the pretation of the conduct parameter to an "ag- interpretation of the results is gregate affected conduct by thisparameter" (Corts, p. 231). mistake. In fact, the aggregate conduct parameter When firms are not identical (the more gen- (0a) can be interpreted as the industry aver- eral case), aggregating involves weighting each age CV elasticity. The CV elasticity (dX xi) firm's supply relation by its market share and takes the form of 0/N when firms are identical summing across firms (Porter 1983a; Goldberg and Knetter; Wolfram).5 When there are N (and Oi = 0 for all i) because each firm has a identical firms, the market share of each firm market share equal to 1/N. Table 1 summarizes is 1/N and aggregating is done by summing the values taken by 3L, 0, and Oa under differ- the supply relations over all firms and dividing ent forms of firm conduct. In a Cournot setting by N (Perloff; Corts). RPA assume N identi- with identical firms, Oa takes the value of 1/N cal firms with the same marginal cost (cq), the because each firm believes its rivals' quantity is same technology (X, the conversion rate of raw fixed, i.e., dx = 0 and 0 = 1. As shown in the ta- potatoes to french fries), behaving according ble, 0a ranges between 0 (perfect competition) to the same CV (0 defined as in (1)), and fac- and 1 (perfect collusion) and not between 0 ing the market supply curve w(X, z), where zand 2 as claimed by RPA.6 The CV elasticity is a vector of exogenous supply-shift variables. always ranges between 0 and 1.7 RPA then aggregate the first-order condition It is important to correctly specify the values over N firms to obtain the intermediate step: taken by the CV elasticity under the forms of conduct listed in table 1 because those values N can be used as benchmarks to determine the N(p - cq)h - Nw(X, z) - lO i xi = 0 i=1 extent of market power in the industry. For example, when there are five identical firms buying an homogeneous product, an estimated where-q = and j=1 xi = X. Divide byvalue N of Oa greater than 0.2 but less than 1 and rearrange to obtain a similar equation to would imply that the level of market power is equation (RPA5): greater than that implied by Cournot competition but less than under a joint monopsony pX-w(X, z) = CqkX + 0aX.

This equation, however, differs from RPA6 RPA cite Brander and Zhang for the bounds of the industry average CV between 0 and 2. However, Brander and Zhang model in that Oa = = (1 + i dx) whereas an airline duopoly where they actually estimate each firm's conjecture (v,). CV (0 as defined in (1)) does vary between 0 and 2 for a 0RPA - = 1 + k i l,N1 leading N j dx, the authors to duopoly, but not the CV elasticity. incorrectly specify the range of this conduct 7 More generally, when firms are not identical and do not have the same conjectures, 0a = ,N s,20, where s, is the market share parameter. The above definition of 0a, when of firm i, 0, is as defined in (1), and s,O, is the general form of firms are identical and 0i = 0 for all i, is in the CV elasticity (Porter 1983a; Goldberg and Knetter; Wolfram). agreement with the literature, e.g., Waterson; Thus, 0a can be interpreted as the industry weighted average CV

Perloff; Corts; and also Wolfram. The aggre- 1,elasticity. under Bertrand/perfect It takes the competition, values ofCournot 0, ENI_ competition, st2(Herfindahl and index), and gation of the supply relationship from the firm perfect collusion, respectively. It can be seen that 0a=0/N is a spe- level to an industry level changes only the inter- cial case of the general model and results from the assumptions of identical firms with identical conjectures. In this special case, the industry average CV elasticity (08) is the same as each firm's CV elasticity. See also Muth and Wohlgenant for the derivation 5 Note that Porter (1983a) uses 0i to represent the firm's andCV interpretation of the aggregate conduct parameter under two elasticity rather the CV defined in equation (1). special cases. 798 August 2005 Amer. J. Agr. Econ. or perfect cartel. than predicted Porter by the noncollusive (1983a); Cournot Brander and Zhang; Deodhar scenario where and 0a = 0.2 whenSheldon; N = 5, the num- Genesove and Mullin; Wolfram; ber of major players Sexton; in the industry andaccording Clay and Troesken are examples to RPA, and it in fact ofrepresents articles behavior close compar- ing or testing estimated to a joint monopsony.9 conduct While 0a > 1, under theparameters against theoretical collusive benchmarks regime, is not a problem orin itself giving be- them an "equivalent number cause the estimate of is probably symmetric not statistically Cournot firms" interpretation different from (i.e.,one, Porter N(1983b) = shows 1/0a). "in Given that the trigger general price the optimal quantitymodel in cooperative of pe- Green and Porter and the one of RPA assume reversion to riods will exceed that which would maximize a single-shot Cournot-Nash equilibrium dur- expected oint net returns in any single period" ing punishment periods, it is imperative to (p. 314).1 This logic would imply that the con- compare the estimated level of market power duct parameter would normally be strictly less under reversionary periods with this theoret- than 1, even in collusive regimes. ical benchmark to evaluate the consistency It is a source of concern that such high de- of the results with the conceptual model.8 grees of collusion are estimated under both From now on, I use the notation 0a defined regimes and, consequently, the results do not above. conform well to the trigger price strategy of RPA (personal communication) indicate collusion put forth by the authors. However, that Oa was not restricted in their estimation to if one believes the estimated conduct param- lie within any conceptual bounds. Thus, while eters, then the estimated degree of departure the empirical estimates of 0a are not affected from competition indicates the presence of a by this conceptual error, there are important powerful cartel and would likely warrant an implications for the interpretation of these es- antitrust investigation. timates of market power. The mistake in the definition of the bench- The authors estimate the conduct parame- mark values of the industry average CV elastic- ters in the collusion regime to be 1.038 and ity also has important implications for the in- 0.861 in the punishment regime. Note that terpretation of the magnitude of welfare loss in under the authors' derivation of the indus- RPA's table 2.11 Given the extent of departure try average CV elasticity, 0RPA = 1.038 would from competition implied by RPA's results, it is be roughly equivalent to Cournot competi- surprising that their estimate of producers' loss tion in the collusive regime. In contrast, their due to imperfect competition ($0.369 million/ economic model, following Green and Porter, month) represents only 1.6% of the aver- assumes that firms revert to Cournot competi- age shipment value during the sample pe- tion in the punishment regime. Under the cor-riod (when the supply flexibility (p) is 2.16). rect interpretation of the industry average This CV percentage loss in producer surplus (PS) elasticity, 0a, the estimates of the conduct ispa- small relative to the theoretical prediction rameter under both the collusive and punish- that can be derived. In deriving the theoreti- ment regime mean a much higher degree cal ofpredictions, I have also found a mistake in market power than implied by Cournot com-equation (RPA18). In what follows, I rederive petition. Specifically, in collusive periods, (RPA18) Oa to develop theoretical predictions for = 1.038 m 1.0 indicates that potato processors the percentage loss in PS due to oligopsonistic perfectly collude to maximize their joint profit. power of potato processors. Even in the punishment regime (0a = 0.861), the departure from competition is much larger 9 It should also be noted that those estimates of CV elasticity are also large in the context of previous empirical research. Sexton 8 In collusive periods, the theory provides an expected range for and Lavoie's survey of the literature indicates that the measured the estimated value of the conduct parameter, i.e., greater than departures from competition in the food processing industry have the value expected under the punishment period, but smaller than mostly been small with CV elasticities often below 0.2. This re- the value expected under static joint profit maximization (Porter sult is true even in highly concentrated industries such as the meat 1983a, Porter 1983b). In punishment periods, the theory provides processing industry where Azzam and Pagoulatos estimated the a specific expected value for the conduct parameter, i.e., the value buyers' CV elasticity to be 0.223. See also table 1 of Sheldon and of the CV elasticity under the Bertrand-Nash equilibrium when Sperling, which summarizes market power and Lerner index esti- price is the strategic variable, or the value of the CV elasticity un-mates in the food and related industries. der the Cournot-Nash equilibrium when quantity is the strategic 10 Intuitively, colluding at a quantity higher than the monopsony variable. Price is the strategic variable in Porter's (1983a) model, quantity reduces the incentives to cheat on the agreement. The and he explicitly compares the estimated value of the conduct pa- gains to cheating decrease as the colluding quantity increases for rameter under cooperation with both the Cournot benchmark and a given trigger price and length of punishment period. the expected range of this parameter to evaluate the consistency "1 Note that with 0a e [0;1], the last three columns of RPA's table 2 of the results with the conceptual model. are not relevant. Lavoie Comment on Price Behavior in a Dynamic Oligopsony 799

The expression for the marginal outlay x (MO) curve is12

(2) MO = (1 - a) [?XP + Oa (p + 1) pX. S IF Ot) . Note that this specification also implies that + Oa ranges between 0 (perfect competition) and 1 (monopsony), because Oa can be interpreted as a weight between the industry supply curve and marginal cost curve in determining the quantity purchased (Melnick and Shalit; " a" Sexton and Lavoie). Moreover, two terms are missing in (RPA17), the equation that defines 0) the difference in PS between competitive and oligopsonistic outcomes. It should read

1 1 0?

(3) p+1I PSdiff = w(c -( P + 1

cO Wc Wc P Oap + 1 p(Oap + 1) wc (p + 1)(Oap + 1) W 1) X P(0a-p + 1) " Thus, the expected loss in PS when there are II . - x Ix shifts in behavioral regime corresponds to

E O.0 00+ ( s P we P ri (4) PSdiff =p 1 -) T -T

LE a- 0 1P +1 gl,a- a-

1 p1+1 0

a E k .U: o o E 0

o and Four differs alternative from analytical(RPA18) byexpressions the factor for P.13 0 ,--00 the relative loss of producer welfare due to E oo a imperfect competition can be derived by dividing the expression for absolute producer loss ei 3 in equation (3) by the expressions for (a) the Cu oH

12 This expression simplifies to MO = PXP + Oap PXP, where 3 o is a constant in the equation for inverse supply, and p replaces -q cz 0._.t in RPA-a typo. To avoid confusion, readers should also note the e4 0 typo in the definition of p on p. 266. As in Huang and Sexton, p a represents a supply flexibility and should be defined as q , not 1. 3 The omission of the factor P in (RPA18) cannot by itself ex- plain low measures of welfare loss. If RPA omitted the factor P in their calculation of producers' welfare loss, the correct numbers in table 2 of RPA would be lower, thus only reinforcing my obser- vation that the welfare losses are small compared to the theoretical predictions. 800 August 2005 Amer. J. Agr. Econ. competitive PS, (b) In thesummary, oligopsonistic RPA estimated PS, (c) conduct pa- the competitive producerrameters revenue, within aand Green (d) theand Porter trigger oligopsonistic producer price framework revenue. These of collusionanalyt- to determine ical expressions appear the level in theof marketfirst row power of ta- in the Washing- ble 2. All expressions ton State are apotato function processing of p and industry. Errors in 0a. Thus, they can the be evaluatedbenchmark at thevalues estimated of the industry average value of p (2.16) conductand under parameter a collusive affect (Oa the = interpretation of 1.038) and a punishment their results. (0a = Specifically,0.861) regime. I show that the es- Regardless of the timated measure values used, of the the relative conduct parameter im- loss in PS is much ply larger a much than larger 1.6%, degree as cal- of market power in culated by RPA. Ithe presume potato thatprocessing the reference industry than indicated revenue used by byRPA RPA. ("the In averagefact, the monthly results indicate that un- value of producer der shipments") collusive periods, represents potato the processors max- oligopsonistic producer imize their revenue. joint However, profit as theif they were acting theoretical prediction as a monopsony. suggests that Even the under per- the punishment centage loss in PSregime, should the be conduct between is 250%close to perfect collu- and 314% relative sion to withthe oligopsonistic 0a = 0.861. Such pro- a high level of de- ducer revenue, orparture at least from $58.66 competition million per should imply large month. The predictions welfare presented losses for in potatotable 2 producersare relative to also consistent with what those would of Sexton be attained who shows, under perfect compe- using simulations tition. based I also show that theon relative linear measure of demand and supply equations, welfarethat loss calculatedthe byloss RPA is significantlyin PS represents an important percentage lower than the theoretical of predictionsthe forcompetitive this PS even at modest departures level of departure from competition. from competition. Note that the theoretical Thus, if the reader accepts thepredictions estimated val- de- pend on the estimated ues of the conduct values parameters, the of results p of and 0a, and the functional form RPA suggest assumption significant producer welfare for loss the supply of processing potatoes. due to the presence ofHowever, a monopsony-like cartel the relative welfare loss calculations in the potato processing also industry. Givendepend such on the value of P, the value anticompetitive of behaviorthe andproxy associated loss for the competitive price of in processingproducer welfare, an antitrust potatoes investigation (wc), and the reference measure would seem to be warranted.of producers' However, some revenue. The value of the readersproxy may not readily is acceptespecially this conclusion important for the calculation without aof clearer welfareexplanation of the apparent losses. Specif- ically, lower values inconsistencies of noted wc here between than the empir- that implied by the model would ical results andgenerate the underlying theory. lower In this absolute and relative welfare case, further loss research should than reinvestigate that the predicted by theory. 14 degree of imperfect competition in the Wash- ington processing potato industry.

14 I find that the value of w, implied by the model is much higher than the value of the proxy used by RPA. RPA proxy the com- [Received October 2003; petitive price of processing potatoes (w,) by scaling downward the fresh market potato price series by 23% to take into account accepted May 2004.] a conversion ratio of raw to processed potato of 0.5. The average monthly price of fresh potatoes is $4.75/cwt (according to the data provided by RPA), thus the average monthly value of w, is References $3.66/cwt. According to the data provided by RPA, the average monthly shipments of processed potatoes is 4.738 million cwt. Pre- sumably, those shipments represent oligopsony quantities (Xm). Knowing that the quantity determined by oligopsonists is found Azzam, A., and E. Pagoulatos. "Testing Oligopolis- by equating the perceived marginal outlay expression (2) with tic and Oligopsonistic Behavior: An Applica- marginal value product (we in RPA's setup), we can get an idea tion to the U.S. Meat Packing Industry." Journal of the magnitude of w, implied by the model using the estimated values for p (0.539), p (2.16), and oa under punishment (0.861) and of Agricultural Economics 41(1990):362-70. collusion (1.038). Those calculations reveal that the magnitude of Brander, J.A., and A. Zhang. "Market Con- wc implied by the model is between $44.37 and $50.31 per cwt, duct in the Airline Industry: An Empirical which is more than ten times higher than the values used by RPA ($3.66/cwt on average). Thus, a possible explanation for the low Investigation." Rand Journal of Economics magnitude of welfare loss compared to the theoretical prediction 21(1990):567-83. is the difference between the average value of the proxy for wc used by RPA and the value implied by the model at the estimated Bresnahan, T. "Empirical Studies of Industries parameter values. with Market Power." In R. Schmalensee and Lavoie Comment on Price Behavior in a Dynamic Oligopsony 801

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