F Chantreuil

J Cooper

Setting the Initial Allocation of Marketable Emission Permits

INTRODUCTION

Article 17 of the Kyoto protocol allows international emissions trading among the signing parties with quantified emission reduction targets. The precept ofemissions trading is to use the etliciency of the market place to achieve environmental objectives at the lowest possible cost. Under an international emissions trading rule, a country, or a firm, would be able to face its emissions reduction targe! by reducing pollution itself, purchasing reductions from another country, or firm, that was able to achieve excess gains. or sorne combination of bath. This paper focuses on the setting of the reduction targets. Specifically, given that the Kyoto Protocol allows cooperation between countries in achieving emission reductions, we examine the impacts of cooperation between countries on the setting the emission targets.

If the Kyoto protocol is at ail representative of international treaties involving the sharing of sorne burden, the Protocol will use a fairly basic means for the agreeable distribution of burdens across countries. [START_REF] Betram | Tradeable Emission Pertnits and the Control of Greenhouse Gases[END_REF], [START_REF] Epstein | Controlling the Greenhouse Effect[END_REF], and Epstein and Gupta suggest a variety of alternative allocation mechanisms, including allocations based on GNP, real GNP, total population, adult population, land area, and emissions. Countries will naturally support the criterion that give them the smallest reductions. Hahn and Stavins note that several criteria may need to be blended to create international consensus on emission allocations. 4 For example, while developing countries will have relatively little incentive to participate unless they receive economic benefits from an agreement, developed countries wili want to ensure that their allocations are generated in ways that they perceive as equitable. 3 For example, each United Nations member's burden ofthat institution's budget is a scale closely based on their share ofworld gross national product.

DOCUMENTATION ÉCONOMIE RURALE RENNES

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Most proposais for allocating control obligations among nations cali for proportionately higher rates of reduction in emissions by industrialized countries (and among industrialized countries, by the United States) and for substantial reductions in the predicted rates of increase in carbon dioxide eroissions by mûst developing countries.

The economics of agreements on global warming has been theoretically examined using two-country 000cooperative game theory models (e.g., [START_REF] Chen | Negotiating an Agreement on Global Warming: a Theoretical Analysis[END_REF][START_REF] Capian | Winners and Losers in a World with Global Warming: Non-cooperation, Altruism, and Social Welfare[END_REF]. This paper takes a different track and uses cooperative voting game concepts. Cooperative game theory is especially relevant to analysis of the Kyoto Protocol given that it grants permission to the Parties to the Protocol to reach their targets collectively rather than individually, as long as the combined emissions do not exceed the SUffi of their commitments.

Cooperative game theory provides a means to analytically express the basic principals for determining allocation rules over an economic tlpie lt that address the demands of interest groups and of economic efficiency. Consider a three person problem. The difference over the two person case is that coalitions are possible. That means that Iwo players can manipulate the outcome of the game acting together against the third. To take into account the possibility to from coaltions, we appeal to n-persan cooperative game theory for developing models determining initial emission permit allocation, at the country, regional, and Protocol administrator levels,s

Our fDeus is on equity considerations in setting the reduction targets; an allocation based on this economic efficiency criteria may not be particularly relevant at the international level, where equity considerations are a prime concern [START_REF] Hagem | The Design of a Dynamic Tradable Quota System under Market Imperfections[END_REF]. For example, in an international environmental treaty, heavy use of side payments may be not a politically acceptable instrument for distributing permits. Hence, even if subsequent trading leads to a cost-effective outcome whatever the initial allocation, countries will care about the initial allocation.

However, the allocation rules we propose allows part of the burden to be based on equity considerations and the rest on the basis of economic efficiency. For various scenarios regarding the level of bargaining power among the players, we assess the impact ofthese allocation rules on the distribution of the burdens. Protocol has important implications for the level of emissions reduction effects that countries will undertake. In ail existing trading systems, the initial allocation of allowances, which forrns the baseline for trading, has proved to be one of the most contentious issues. One approach is to take emissions level at sorne point in the past and then apply a uniforrn reduction factor to establish allowance. This approach was taken by the European Union (EU) in its initial negotiating position for the Kyoto Protoco!.

THE MODEL

Restated formally, if Qj denotes the reference emissions of a given country j, the emission quantity authorized for this country will be:

qj =1) Qj' with 0<1) <1 (la)
where 1-8 represents the reduction rate that is constant across ail countries.

The total allowances are then (lb)

j j
Obviously, in equity terms, this allocation rule has a superticial appea!. In fact, it does not take into account national circumstances that vary among the different countries, e.g. the number of tirrns, the GDP, the per capita GDP, and the population of each country' The Protocol remains politically controversial and legislative approval is by no means guaranteed (lEA). Hence, it would be use fui for the success of the Protocol to propose rules for sening reduction targets that allows more explicit balancing ofpolitical and economic interests.

To determine the allocation of initial allowances that explicitly accounts for the characteristic of the countries, we propose to use a payoff function, denoted as <p, that derives from an n-person co-operative games construc!. This co-operative games construct implies, implicitly, that the determination of such an allocation can he achieve if ail cOllntries agree to delegate their decision power to an international institution for the definition of the agenda and the type of emission permits market that can be implemented.

[n other words we suppose that ail countries accept the fact that the United Nations Climate Change Commission has to allocate the initial endowments to each country.

Hence, the problem of emissions right allocation can be set in the form of a simple game in characteristic function form (N,V),\ i.e., with side payments, where N is the set of players (i.e. countries) and V the characteristic function of the game'. In the climate change negotiation context, this side payments assumption expresses the possibility for countries to form blocks that will meet the aggregate emission level of the countries forming the block. The characteristic function sums up ail possible utility sets of every coalition S ç N . For example, if population is the relevant criterion, we need to be able to calculate it for ail possible coalitions. If PO(S) represents the population of coalition S we have the following simple game with the characteristic function V(S)

For ail S (S { l if PO(S)? f3 PO(N) eN, V )= - 0 otherwise (2)
with 0 < f3 < 1. For example, a value of f3 =0.5 means that a coalition Scan obtain the total emissions allowances if its population is equal or greater that 50 percent of the United Nations population PO(N) .

Given this framework, the Shapley allocation approach is particularly use fui to solving the model (see Roth Ed., 1988 for Shapley's paper, which was first published in 1953 and for a survey on extension works; Mas-Colell,

Whinston, and Green). This normative concept attempts to describe a fair way to allocate gains from cooperation,

given the strategie realities captured by the characteristic form. The Shapley value in our case represents the final distribution of initial allocation of emission permits between ail countries. A lengthy discussion of Shapley values is outside the scope ofthis paper. Briefly, the Shapley value summarizes the complex possibilities facing each player i (i.e. country) in game (N,V) by a single number Cfi,(N, V) representing the value to i ofplaying the game. Thus the value of game (N, V) is an n xl vector in which each element represents the "expected value" to a player of playing the game, where Cfi, (N, V) represents the expected payoff to player i under a randomization scheme on ail coalitions S she can join. For a simple two player case, the egalitarian solution is represented by the expression

Cfi, (N,V )-Cfi2 ({I}, V) =Cfi 2 (N,V )-Cfi, ({2 },V), where Cfi, (N,V )+Cfi2 (N, V) =V(N)
. This relationship says is that in the egalitarian Shapley value solution, player 1 gets the same utility out of the presence of player 2 as the latter gets out of the former. Extending this concept to a multiple player game, the general formula is (see e.g., Mas-Colell, Whinston, and Green):

Cfi,(N,V)= L, s!(n-s-I)![V(SU{i})_V(S)) ieN n! iES ( 3
)
where s is the number of players in a coalition S. The basic principle (marginality principle) behind the share Cfi,(N,V) is that when a player joins a coalition she receives the marginal amount [V(SU{i})-V(S)). The probability that a random ordering of coalition SeN forms as the union of i and its predecessors equals the probability that i is in the s'" place, which is X multiplied by the probability that S -{i} forms when we randomly select s -[ members from N -{i}, which is s! (n -s -I)! . For any given random ordering ofplayers, we calculate the marginal contribution ofevery player i to its set ofpredecessors in this ordering.

Consider the simple game denoted in (2) belWeen five producers (a, b, c, d, e) whose population amounts .

( of P,suppose that in the vote vector, a player has a weight of 0.55 (55%). For p =0.5, it has ail the power. As p increases in the range 0.55 < P< l , the power ofthis player decreases, and when P=l , ail the players have the same power. The relative impact of changing P is data set specific.

The Shapley value can address the distribution of initial endowments between countries, but, most of the time and this is certainly true for the global climate change problem, negotiations held not only between Heads of each delegation, but also between Heads of State from their capitols. Perhaps the best illustration of this phenomenon is that while the President of the United States has signed the Kyoto Agreement, the treaty has not been ratified by the US. Senate. In fact, it is clear that those in industry most opposed to deaJing with the climate change have thoroughly worked the political system to cast doubt on the science; and emphasize the possible negative economic impacts of the Kyoto Protocol. Obviously, the Shapley value is not the appropriate co-operative game theory model for determining initial emission permit allocation, at the country, regional, and Protocol administrator levels. The Shapley value can address the distribution of initial endowments between countries, over which the members of each country (firm, sub-county, ... ) would bargain with each other to determine the division of the share received by their country. The main question now is how can we capture bargaining within countries. Put differently, how can we determine allocation rules that address the demands of interest groups and of economic efficiency. Considering the previous five countries example, we \Vant to be able to compute the power sharing when, for example, countries a and b act together. Co-operative game theory provides a means to analytically express the basic principals for that purpose. To take into account that the negotiations held at several levels, we assume that fictitious delegated are elected to represent each country and each region. In that case, the set of players is denote asN ={l....i, ... ,n} which represents the set of firms (for example). The regions and the countries they belong to are denoted by the level structure B ={B' ,B'}, where B' ={C" ...,CnJ is the set of ail countries and B' ={R" ...,R g } the set of ail regions that describe N 's a priori coalition structure. Given this coalition structure framework. if we assume that in each country j, C j E B' , a delegate is selected to represent the coalition, the bargaining situation is a problem of how to divide the emission permits and can be formally represented by the quotient (M, V) =(N, U) / B' , where (M, V) is agame with a set of players (country representatives) M={l, ...,j,...,m} and ilS characteristic function is given by :

V(S)=U(UC) forall SEM (4)

)eS } Thus a reasonable expectation for the j''' country is the amount <p;(M, V), which is the element in the Shapley value corresponding to player j in game (M, V), and would be the value normally expected by this country.

Theo, in each countries, the emission permits this country receives must be divided among regions and firms.

Obviously, the payoff a player (i.e. a firm) receives depends crucially on the definition of the bargaining relationships between regions and between firms. To address this topic, in the following subsections, we propose three bargaining and payoff principle scenarios that are based on the same bargaining relationship among countries but that bargaining scenarios can vary among regions and among producers. The scenarios depend on the capacities of threat (bargaining power) of some regions over other regions within the same country or on the capacity of threat of a firm toward other firms within the same region. Section 2.1 presents a payoff function 'l', for a base scenario in which we consider only the amount each producer can obtain on his own. Section 2.2 presents a payofffunction '1'2 that captures the "Iobbying game" between regions as played out in United Nations. Section 2.3 de fines a payoff function '1'3 motivated by the subsidiarity principle. In these three scenarios, to determine the final distribution of initial endowments in a manner that take ioto account interest firms of various types, various regions, and various countries, we assume a three-step process. In the firs! step, the countries bargain with each other to determine the division of the surplus. ln the second step, the regions belonging to the same country bargain with each other over the allocation received by their country. Finally, the producers of a given region divide among themselves the share the region receives. However, because the Shapley value formula in (3) does not take into account the fact that the producers are organized a priori into level structure B, the model must be extended for determining the sharing of emission permits.

Nnll threat and egalitarian principle

Since in this minimum information game we only account for the amonnt a player can obtain himself (that is his value in the characteristic function) and the amount the coalition to which he belongs to can obtain, this player has "no power" to negotiate \Vith other players in the same coalition. Hence the term "'"uH threar". The lenn "egalitarian principle" is a technical one. For example, since US is not a winning coalition al the international level, the value of the characteristic function for the US regions is always the same (zero in this case) so the division of the emission permits US receives is an egalitarian one. As in the five countries example, no player has no greater opportunity than another player to form a minimal winning coalition. Hence every player has the same power, and the symmetry axiom of the Shapley value implies that ail players will obtain the same share. In other words, this first allocation rule supposes that each region and each firm accept passively the emission permits allocation proposed by the United Nations.

Fonnally, the tirst bargaining procedure within countries originates when we simply take iota account the amaunt U(K) that every coalition ofregions K (such as K ç Ci' K E B') can obtain on its own. For this game, we can define the subgame (NCi ,WC) in country Ci' where N c J represents the set of regions in country Ci . The characteristic function ofthis subgame is given by :

c(K)=U( ) for ail , i' KE B (5) (6) (7)
Equation ( 5) says that the empty set is worth nothing and (7) says that the amount a coalition K (a region) can itself obtain in the subgame, defined on the country that K belongs to, is the same amount K can obtain in the initial game. Given these equations, a reasonable expectation for the region Rh C C j is the amaunt <Pli (Nc

J ' Wc) ),
which is the Shapley value ofplayer h in the subgame (N c J ,Wc).

We can use the same reasoning to divide the amount received by the region Rh C Ci among the firms of this region. Thus, each firm i E Rh C Ci can obtain the amount <p; (NR, ' W R , ), which is the Shapley value of firm in the subgame defined on the region Rh C Ci.

For this bargaining game, we can define a payoff function 'P' , in which the share a firm i E Rh C Ci will receive is (see Chantreuil 1999):

'P;'(N,U)= 2: g!(rh-~-l)![U(Gu{i})-U(G)] GeR" rh' iv:G 1 [ k'(c -k -1)' ] +~K~j • i Cl! •[U(KuRh)-U(K)]-U(Rh) R"v:K +_1[_1[2: s!(m-;-l)![u(suC i )-U(S)]-u(cJ]J rh Cj m. ( 8
)
where m denotes the number of countries, s. k, and g, are the number of players in every coalition of countries S, every coalition ofregions K, every coalition offirms G, respectively. ci represents the number ofregions in the country Ci and rh the number offirms in the region Rh•

Consider the example of the five countries with population criterion. Ifwe take into account the fact that players a 1

and b act together, the payoffvector using the allocation rule 'P will be -, -, -, -, -. 12 12 6 6 2

Strong threat and the quotient game lobbying principle

The payoff function in this section uses more information than in the first, given that here we need to know the amaunt a region can obtain by forming a coalition with other countries, an amaunt that is different for each country.

Hence, the degree of bargaining power varies among the countries, which produces the demand for lobbying activities. This bargaining procedure within countries consists in accounting for the amaunt U(K)that every coalition K (such as K ç; Ci' K E E') can obtain itself and the amounts U(K U C q u ... u Cm! that K could obtain ifit would replace country Ci and fonn a coalition with one or more of the remaining countries of BI.

A region can threaten to leave a coalition on the basis of being able to gain more elsewhere. Of course this is not a real threat and is never carried out but il cao be used to compute the relative power of each region in a given country, and as such, it captures much of the "Iobbying game" of regions at the international leve!.

Formally, for any K C Ci' and K' its complement relative to Ci' we define a restricted game (MIC i / K, VCjl K) as representing the quotient game (M, V) when K replaces the country Ci in B'. where MIC} / K represents the set of players when country Ci is replaced by K. Given this function, a reasonable expectation for K is the Shapley value <PK (MIC i / KI) of player K in this restricted game. This amount also represents the relative payoff, in game (N,V), of K ifit would replace the country Ci and bargain with the m -1 other countries.

Using the measure of the relative payoff of each region of the country C} , we can define the subgame (Nc J ' W CI )

of country Ci by its characteristic function given in ( 5), ( 7) and by: Thus, each region R" ç; C j can obtain the amount <P,,(Ncj,W c ) which is the Shapley value ofplayer h in the receive substantial attention in the mainstream economics literature, equity concems do not receive their due in the resource economics literature. Certainly, from a pure economics standpoint, equity tend not to be a strong mechanism for making allocations, and we prefer to he efficient and present allocations that maximize consumer plus producer surplus. Realistically however, political realities can require equity concems to he of important, or even prime concem. The Shapley value fonnat we use for our co-operative games solutions is efficient in the c1ass of equity allocations'.

As an example of equity criterion, consider equation ( 2) for the case where the characteristic function is defined assuming that population is the relevant criterion. Note that this definition is based on the basic voting theory principle "one man, one vote". More often than not, population is mentioned as a basis for emission permits allocations and this base is consistent with the egalitarian criterion that induces a proportional allocation ta population. Our framework expands this criterion. Since the concept we use (the Shapley value) distribute emission pennits between countries in a way that satisfied the weighted power majority of countries, we can argue that this concept is characterized by what Rose and Stevens called the "consensus equity". In other words, at least in the idealized context of an analytic framework, the allocation rule we propose make the international bargaining process fair and promote a solution that is politically stable. Of course, since countries with large population have bigger bargaining power than others, the Shapley value is also tied ta the egalitarian criterion.

Hence, the Shapley value can address the distribution of initial endowments belWeen countries in a manner that induced the faimess of the international negotiation process. But the negotiations were held not only between Heads of Delegation in Kyoto, but also between Heads of State from their capitols. In fact, the discussions on the flexible mechanisms could not be concluded by the time the Conference ended. Il is c1ear that lobbies opposed ta dealing with the c1imate change have thoroughly worked the political system.

We propose three co-operative game concepts ta capture the bargaining process within countries. The three Shapley-based CS (cooperative solution) values we propose distribute emission pennits satisfying the weighted power ofeach regions, or firms. In that sense, these values are also characterized by consensus equity. The ditference belWeen these three allocation rules come from the outcome that might arise. Actually, the outcome of the first allocation rule 'f, (the null threat and egalitarian principle in section 2.1) is characterized at the domestic level by the egalitarian criterion when the outcome of the second one 'P 2 ( the strong threat and the quotient game lobbying principle in section 2.2) depends exclusively on the bargaining power of each region we can consider.

The third allocation rule 'P 3 (the subsidiarity principle in section 2.3) is the more appropriate for the introduction of flexible mechanisms as part of the control of the buildup of global wartning gases in the atmosphere.

First of ail, it makes the international bargaining process fair and also promotes solution that is politically stable at the international leve!. Secondly, it makes the domestic bargaining process (and the bargaining process at each level :

Federal govemment, State govemments and local govemment, etc.) fair and promote also a solution that is politically stable. Finally and most importantly, the allocation rule based on the subsidiarity principle allows the use of different types of control mechanism at different level ofnegotiation process. In other words, subject to the agreement reached at the international level, each national program can he based on an efficient and fair allocation rule and subject to the agreement reached at the national level, each local program can also be based on a rule that addresses the requirement of efficiency and fairness.

The possibility for countries to fortn blocks that will meet the aggregate emission level of the countries fortning the block motivates this co-operative game theory background. [n this framework, perhaps surprisingly, the notion of faimess and power are very closed. The key concept of these allocation rules is that the outcome an individual cao obtain depends on her bargaining power. Tn general, finns have more influence at the regional level than at the country level, and even less so at the intemationalleve!. If the relative power of large to small producers at regional and country levels is lower than their relative power at the intemationallevel, then small ftrms willlikely prefer scenario 2.2 to 2.3. By the same reasoning, large firtns will prefer 2.3 to 2.2, and certainly, 2.1 is their least preferable scenario.

1

  INRA.ESR, rue Adolphe Bobierre. CS 61103, 3501 t, Rennes cedex, France. 2 Economie Research Service (United States Department of Agriculture), t800 M Street, NW. Washington OC, 20036•5831, USA.

  7119)respectlvely to5, 15, 20, 25, and 35. If P=0.5 , then the Shapley value of this game is -, -, -, -, -. 30 60 5 5 20 Note that the Shapley value is the same for country c and d, even though the population of country d is larger. This results describes a fundamental concept behind the Shapley value: since player d has no greater 0pp0rlunity than c to fonn a minimal winning coalition. he must have the same share as player c in a bargaining game. In contrast, the "vote vector" result ---payoffs strictly proportional to each person's share of the total population, i.e. no country has ( 5 15 20 25 35) majority power on his own ---is --, --, --, --, --. As an example of the implication of the choice 100 100 100 100 100

4AS an example, Hahn and Stavins note that the Canadians proposed the use of population and GNP combined as allocation criteria whcn crc reduction obligations wcrc being considered in the development of the Montreal ProtocoJ. Considering the emissions reduction problem, sorne argue that no single nation should initiate a directed course

  of action until there is a global framework with worldwide warrant. Others argue that a global response is, in effect, just a sequence of national responses, and that it is incumbent upon individual nations to begin taking steps reduce their own emissions now. The Kyoto Agreement shows that in reality we will have to go down both paths

simultaneously. Nevertheless, sorne countries have not signed the Agreement, not because they oppose sening a

	global limit on carbon emissions, but because they would Iike developed nations to pay the cost of reducing
	emissions. The perception in sorne developing countries is that they did not cause the current mess and should not
	have to pay for il. At the core of the developing country view is the notion of faimess. Is it fair, sorne ask, for the
	countries with far lower GDP and per capita GDP to be asked to take on obligations to deal with a global problem
	caused thus far by the emissions !Tom the developed world?

This point of view is natural, since the initial distribution of emissions commitments under the Kyoto

  Thisrestricted game is the fonnal representation of a bargaining situation which involves K and the other countries. Ils

	characteristic function is given by
	VCIK(S)=V(UC -K')foraIlSç;MICi/K	(9)

J

qeS q

The regional level refers to coalitions that countries may form in the marketing of permits Altematively, the analysis can be done at a more mîcro•level at the producer, rcgional (sub•country), and country levels within the group of countries participating in the protocol

Equations la and 1b are in faet slight simplification taken for c1arity as in the proposed reduction targels under the Kyoto PrOlocol, the three ~ssible obligatÎons a arc possible: 0.95 for Annex 1counlries, 0.92 for most countries. and 0.93 for the V.S.The sidc payment assumption implies the existence of commodities that are liocarly transferable. In other words, the ulility functions for the individuals can he chosen so that the rate oflransfer ofutility among any two ofthem is 1: 1. Hence, the total utility obtainable by a coalition S can he divided among the memhers ofthis coalition in any number ofpossihle ways.

For a discussion orthe crticiency orthe Shapley value in making allocations, sce Eatwel1, Milgate and Newman (1989), p. 24 and p. 213.

To determine the division of the amount received by the region Rh among the firrns ofthis region, we use the same argument. Each firm i E Rio C C j can obtain the amount (j)i (N•• ,W•.J, which is the Shapley value ofplayer i in the subgame defined on region Rio'

Given this subgame, we can define a payoff function 'P 2 in which the share a firm i E Rh C C j will receive is given by the following formula [START_REF] Chantreuil | Axiomatics oflevel structure values[END_REF] :

With the five countries game example, if we take into account the fact that players a and b act together, the payoff 2 (13111) vector using the allocation rule \fi will be -, -, -, -,-.

24 24 6 6 2

The subsidiarity principle

Finally, we can define a third payoff function that assumes that the problem of the United Nations is only to determine the emission permits allowance for each country. This assumption can be motivated by the principle of subsidiarity, which basically means that the United Nations does not make decisions at the individual leve!. [nstead, the country itself has to solve problems at this leve!. [n this case, as discussed in section 2, the payoff vector we are looking for corresponds to the Shapley value of the quotient game (M, V) played by the delegates of each country.

The share every country jE M will receive is given by:

Once this payoffs vector is defined, the United Nations consider the problem solved at the International leve!. Then, with respect to the principle of subsidiarity, each state can choose its own emission pennits allocation process regardless of what the others do. We can set this problem of the division of the gain among the regions of a given II country in the fonn of a simple game. Hence, the share a region will obtain corresponds to the Shapley value of the game defined on the country of interest.

Using the same argument for the allocation of emission pennits within cach region, we can define a payoff function '1'3 in which the share a finn i ER" c C j will receive is given by (see [START_REF] Mathurin | Application de la théorie des jeux à l'analyse économique de la coopération internationale: illustrations par l'étude du cas de la politique agricole commune[END_REF]:

where (N R, ,VI<,) is the simple game defined on the region R" and (Nc j ,V Cj ) is the simple game defined on the country C j . With the five finn game example, if we take into account the fact that players a and b act together, the 3 (1 111) payoffvector using the allocation rule '1' will be 0, -, -, -, -.

6 662

DISCUSSION

ln order to control the global waming gases phenomenon, most of the UNFCC participants have signed an agreement sening a target level not to exceed the year 2007. Although ail countries agree to set a global Iimit on carbon emissions, sorne have not signed the agreement. The main disagreement refers to the global system of tradeable carbon dioxide pennits, qualified as being immoral and unfair by a number of developing countries.

Unfortunately, there is no consensus on the best definition of faimess, or equity, but the negotiation process can be facilitated if countries understand the full ramifications of various alternatives (cf. [START_REF] Rose | Will a global warning agreement be fair to developing countries?[END_REF].

Nevertheless, there is a range of research works in social choice and welfare theory, equity theory and co-operative game theory dealing with the defmition of criteria such as equity and faimess. While efficiency-equity tradeoffs


Yves Lespinasse

The role of plant breeders in organic fruit production

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.


Alexandre Gohin

Hervé Guyomard

Measuring market power for food retail activities: French evidence

Introduction

The estimation of market power has been a prominent component of empirical industrial organisation over the past fifteen years. There are now many papers in which the methods of New Empirical Industrial Organisation (NEIO) have been applied to evaluate the degree of market power of a specific industry on the output market on the basis of demand and cost functions and hypotheses concerning the strategic interactions among firms. Following the pioneering work of [START_REF] Gollop | Finn interdependencies in oligopolistic markets[END_REF], and [START_REF] Appelbaum | Testing price taking behavior[END_REF][START_REF] Appelbaum | The estimation of the degree of oligopoly power[END_REF], many studies consider the case of a single output industry characterised by an oligopolistic structure in the output market and use the "conjectural-variation" or "conjectural-elasticity" modelling approach where firms choose their output levels given their beliefs, i.e., their conjectural variations, about rivais' reactions to their output choice. This basic modelling framework has been extended to include the multioutput structure of the considered industry [START_REF] Gelfand | Entry barriers and multiproduct oligopolies: Do they forbear or spoil?[END_REF][START_REF] Schroeter | Measuring market power in multi-product oligopolies: The US meat industry[END_REF][START_REF] Wann | Imperfect competition in multiproduct food industries with applications to pear processing[END_REF], the possibility that the considered firms exert market power simultaneously on both the output and input markets [START_REF] Schroeter | Estimating the degree of market power in the beef packing industry[END_REF][START_REF] Azzam | Testing oligopolistic and oligopsonistic behaviour: An application to the US meat-packing industry[END_REF][START_REF] Wann | Imperfect competition in multiproduct food industries with applications to pear processing[END_REF][START_REF] Murray | Measuring oligopsony power with shadow prices: U.S. markets for pulpwood and sawlogs[END_REF], or the existence of policy regulations [START_REF] Rude | The impact of trade liberalisation on the Canadian dairy processing sector[END_REF][START_REF] Oxley | Public research effects on the Canadian food processing industry: a dynamic optimisation approach[END_REF].

While there are numerous applications of this approach to various manufacturing industries (in particular, food industries), and more recently to export markets (see, e.g., Karp andPerloff, 1989, 1993 ;Deodhar andSheldon, 1995, 1997), the retail industry has received only very limited attention in this context. This is hardly justifiable since the retail industry is particularly important for studies of welfare. The objective of this paper is then to estimate the degree of imperfect competition in the French food retail industry using a structural econometric model based on the formulation and estimation of a multioutput cost function for this industry, a set of supply functions for the "oligopsoned" inputs, i.e., the wholesale goods, and a set of demand functions for the "oligopoled" outputs, i.e., the final goods.

The theoretical framework adopted in this paper draws heavily on [START_REF] Schroeter | Measuring market power in multi-product oligopolies: The US meat industry[END_REF] who developed and estimated an economic mode] for measuring market power in a quantity-setting oligopoly engaged in the joint production of demanded-related goods. The French food retail industry technology is restricted to be of fixed proportions between each final good and the corresponding wholesale good, but additional factors of production are employed in variable proportions. The assumption of fixed proportions implies that the conjectural elasticities are identical in the input and output markets (Schroeter). This theoretical framework is applied to a time series of aggregate data for the French food retail industry. As it is often the case in empirical industrial organisation work, firm-level data are not available. The model is thus estimated at the industry level and we briefly discuss the conditions to be maintained in order to ensure a consistent aggregation of firm-specific functions and equilibriurn conditions to industry-wide counterparts. Applying the "conjectural-elasticity" approach to the French food retail industry is also compounded with data problems, in particular the lack of available data for prices and quantities of additional factors of production. We also discuss this issue. We finally present and interpret the results, especially the conduct parameters, i.e., the conjectural elasticities, and the degree of oligopsony-oligopoly power for the three goods we consider, i.e., fresh milk and dairy products, meat products and other food products. The final section concludes.

Theoretical framework

Consider a non-competitive retail industry in which N firms produce, i.e., distribute, M homogeneous final goods. At least some of the N firms offer the M goods while the others may specialise in the distribution of some of them. To put these final goods at consumers' disposai, a retail firm j buys the corresponding wholesale goods and employs a set of additional factors of production to produce the bundle of services which is incorporated into the wholesale goods. Each firm j exercises some market power in purchasing wholesale goods and in selling final goods, but is a price taker in the market for additional factors of production.

The relationship between the wholesale good input and the final good output is assumed to be one of fixed proportions. Without loss of generality, units of measurement are defined so that input and output quantities can be represented by the same variable, i.e., Q/ for the quantity of the "input-output" i which is used and produced by the jth firm. Accordingly, Q; is the vector of "input-output" quantities which are used and produced by the jth firm. Additional factors of production, Xf, k = I, ... ,K, are employed in variable proportions. lt follows that the total cost of distribution for the jth firm, CTi (Qi , w, ri, CF i ), may be defined as:

M (I) cri (Qi, w, ,,, cFi) = I w;.Q/ + ci (Qi, 11) + cFi i = I
where ri is the price vector of additional factors of production, w is the purchasing price vector of wholesale goods, Ci (Qi,11) are variable costs of additional factors of production, and CFi are fixed costs. Let the wholesale market supply curve facing the retail industry for the ith wholesale good be given by: where Y is a vector of exogenous variables, and as,(.) / àw, > O.

Let the final market demand curve facing the retail industry for the ith final good be given by:

(3) Q = D, (p,Z) where p is the price vector of final goods, Z are exogenous factors, and aD, (.) / aP; < 0 . Profits for the jth retail firm are given by:

M M (4) 1t 1 = LP;-Q/ -L w,.Qi -C 1 (Q 1 , 11)-CF 1 i= I i=I
The problem for the }th firm is then to choose the optimal quantities Q( , i:.::: 1, ... , M , which maximise its profit (4) given the nature of its environment defined by equations ( 2) and (3). From (3), one notes that the M final goods are assumed to be demand related which implies that all final good quantities defined at the industry level enter each of the M inverse final demand functions. But, from (2), one notes that the M wholesale goods are assumed to be supply independent which implies that the inverse wholesale supply function for good i does not depend on aggregate quantities of other wholesale goods. Assuming an interior solution for all quantities, profit maximisation under oligopoly-oligopsony yields the following firstorder conditions:

1
where Em 1 = (8pm I aQ).(Q, I Pm) is the industry elasticity of the inverse final demand for the mth final good with respect to the quantity of the /th final good, 0{; = (ôQ I ôQ/).(Q/ I Q,) is the }th retail firm's conjectural elasticity of market quantity for the /th good with respect to the quantity of the ith good used and produced by this firm, and Y mm= (àwm I ôQm).(Qm I wm) is the industry elasticity of the inverse wholesale supply for the mth wholesale good with respect to the quantity of this wholesale good.

At this stage, the two following remarks are in order. First, industry elasticities of the inverse wholesale supply for the mth wholesale good with respect to the quantity of the /th wholesale good, l -:t:-m , are by assumption equal to zero. In other words, we have y mi = 0 for l -:t:-m. Second, since the relationship between the wholesale good input i and the final good output i is assumed to be one of fixed proportions, the output or final good market conjectural elasticity of firm j for the !th good with respect to the quantity of the ith good and the input or wholesale good market conjectural elasticity of firm J for the !th good with respect to the quantity of the ith good coincide. If, in addition, we assume that market crossconjectural elasticities equal zero, i.e., 0{; = 0, i -:t:-l, equation (5b) reduces to:

From ( 6), it appears that the conjectural elasticity 9{; is the crucial conduct parameter. It lies between zero when the behaviour of the considered firm is competitive and one for a monopoly-monopsony behaviour. In the first case, the right-hand side term of ( 6) is null and this equation reduces to the usual condition that final good output price equals total marginal cost. At the other extreme, if this parameter equals one, equation ( 6) defines the optimality conditions for a final good monopoly -wholesale good monopsony. In that second case, total marginal cost equals perceived net marginal revenue where the latter includes cross-output market effects via cross-quantity elasticities of inverse final demand functions.

To summarise, we assume a homogeneous product, quantity-setting game in which retail firms have conjectural variations which allows us to distinguish between collusion, Cournot-Nash competition and price taking. The proposed analytical framework cannot thus be used to capture the possibility of oligopolistic-oligopsonistic price-setting behaviour since with homogeneous goods, the latter collapses into the competitive equilibrium. [START_REF] Gasmi | Econometric analysis of collusive behavior in a soft-drink market[END_REF] extend the traditional conjectural variation model to the case of differentiated products with two control variables, price and advertising. [START_REF] Carter | Price or quantity competition? Oligopolistic structures in international commodity markets[END_REF] follow the approach of Gasmi et al. to test the competing hypotheses of price versus quantity setting in the case of the Japanese market for imported beef. More generally, [START_REF] Corts | Conduct parameters and the measurement of market power: the impossibility of astructural inference[END_REF] argues that the traditional conjectural variation model fails to measure market power accurately since "without stipulating the true nature of the behaviour underlying the observed equilibrium, no inference about the extent of market power can be made from analysis of the observed variables". One must therefore bear in mind that any conclusions that can be drawn from our analysis rests on the assumption of a homogeneous product, quantity-setting game and the premise that the conjectural variation model allows us to identify and measure market power.

Empirical implementation

Aggregation issues

Because our application uses aggregate data, it is useful to consider the problems raised by aggregation in the multiinput-multioutput case. These issues have been largely discussed in the literature (see, e.g., Appelbaum; Schroeter and Azzam; Wann and Sexton; Murray) and they are consequently only briefly presented in this paper. For cost functions to be well defined at the industry level, the retail firm total cost function ( l) must be of the Gorman polar form with nonjointness in production, i.e.,

M M (7) CTj (Qj , w, Tl, CFj ) = L W; .Q/ + Gj (ri)+ L H;(TJ). Q( + CFj i =I
From ( 7), it follows that the total marginal cost of a final good i is constant across retail firms j, j = l, ... ,N. For a given firm j, it does not depend on output i level neither on quantities of other final goods produced by this firm, i.e.,

The second aggregation issue concems interpretation of the conjectural elasticities. Following Appelbaum, and Wann and Sexton, we assume that at equilibrium conjectural elasticities are the same for all retail firms, i.e., 0{; = 0/i 'ï!j = 1, ... ,N. As noted by Wann and Sexton, this second assumption can be achieved without loss of generality since the assumption of constant total marginal costs of distribution has been maintained in order to ensure consistent aggregation of costs to the industry level.

Multiply equation ( 6) by Q(, sum over all retail firms j and <livide by industry quantity Q. 0 , one yields:

0.. ~ • • (9a) P; -W; -H;(Y]) = -(Q;~ ).[~Em;•Pm •Qm -y ;;•W;. Q.]
or, equivalently,

M Q: (9b) P; = W; + H;(Y])-0;;.~(Q/).Emi •Pm +0;; • Y;; • W;

Empirical mode! specification

Equation ( 9b) is used as a basis for testing the significance of market power of retail firms in bath the wholesale good and final good markets. To identify the various parameters entering this equation, i.e., 0;;, Em; and Y;;, i = 1, ... , M, m = 1, ... , M , the estimation procedure must combine the information contained in equation ( 9b) with that of supply fonctions for wholesale goods and demand functions for final goods. In other words, the complete aggregate model is made of equations ( 2), ( 3) and (9b ). For each wholesale good, we specify the input supply function (2) faced by the retail industry as a simple linear form, i.e., where t is a time trend, and a ; , b, . and c; are parameters to be estimated. From (10), own price elasticities of supply may easily be computed as:

As empirical specification for the final demand set, i.e., for equations (3), we use a Linear Expenditure System (LES). The system of expenditure equations for the M final goods is thus defined as (see, e.g., Johnston et al., 1984):

M (12) Pm• Qm =Pm .dm+ em.(R -LPm•dm) m = 1, ... , M m= I M
where R = LPm•Qm, and dm and em are parameters to be estimated. m=I For the system of equations represented by ( 12), uncompensated own and cross pnce elasticities are, respectively:

(13a) Ômm = {l / Emm) = -1 + (1-em).(dm / Qm) (13b) Ômi = (l / Em;) = -em.[(P;.d;) / (pm .Qm)]
The final empirical issue concems specification of functions H; ( ri) . Since the prices ri of additional factors of production are not available in the database, we heroically assume that the total marginal cost of distribution for each final good i may simply be defined as the sum of the purchasing price of the corresponding wholesale good, w; , and a linear function of a time trend, t . In other words, we assume that H; ( 11) = J; + g;. t, V i = 1, ... , M , where J; and g; are parameters to be estimated. It is clear that this specification is one of the main weak points of our analysis. Nevertheless using some possible alternatives, like an index of wages defined at the national level instead of a time trend, leads to the same conclusions conceming market power estimates of the French food retail industry.

Data

For purposes of empirical analysis, the French food retail industry is assumed to produce three final goods, i.e., dairy products ( i = 1 ), meat products ( i = 2 ) and an aggregate of other food products ( i = 3 ). The latter includes non processed agricultural products. Data for estimation are supplied by the Institut National de la Statistique et des Etudes Economiques (INSEE). They are annual and cover the 1977-1993 period. Final good implicit price series (1980=1) are derived by dividing expenditures in current French francs by expenditures in constant Francs. Marketing margins are directly available from input-output tables. Unit marketing margins for the three considered goods can be calculated by dividing marketing margins by corresponding quantities. Using final good implicit price series, one can then define wholesale good implicit price series.

Econornetric mode/ specification

Input supply equations (10) may be used to yield an estimate of the industry elasticity of the inverse suppl y for each wholesale good, i.e., y;;. Similarly, the system of expenditure equations ( 12) may be used to obtain an estimate of own and cross industry elasticities of inverse demands for each final good, i.e., emm and Em;. A two-step procedure estimation may then be used by directly incorporating these parameters into equations (9b) which are simultaneously estimated to obtain an estimate of the three industry conjectural elasticities, i.e., 0;;, i = 1, ... , M = 3. Given the potential problems associated with this two-step estimation procedure (see, e.g., [START_REF] Love | Econometric analysis of imperfect competition and implications for trade research[END_REF], we prefer to jointly estimate suppl y equations ( 10), final demand equations ( 12) and optimality conditions (9b) as a system of simultaneous equations. The errors are assumed to be additive and jointly normally distributed with zero mean and constant variance-covariance matrix. To avoid singularity of the latter, one of the expenditure equations in the sub-system of final demand is deleted from the estimated mode!. In practice, the third expenditure equation corresponding to other food products is omitted. The empirical mode! consisting of three supply equations, two expenditure equations and three first-order conditions is estimated using the iterative Three-Stage Least Squares (3iSLS) procedure, which [START_REF] Hausman | An instrumental variable approach to full information estimators for linear and certain nonlinear econometric models[END_REF], e.g., showed to be asymptotically equivalent to Full Information Maximum Likelihood (FIML) and which provides consistent and asymptotically efficient estimates. We treat all explaining variables (except the time trend) as endogenous variables and we use one-year lagged variables as instruments. As noted by, e.g., Appelbaum, the problem with the instrument variables method is that it may be sensitive to the choice of instruments. Nevertheless it is reassuring to note that 3iSLS and FIML estimates do not differ substantially and lead to the same conclusions concerning market power estimates of the French food retail industry.

Empirical results and discussion

The parameter estimates and t-ratios, as well as the conventional R 2 (calculated as one minus the residual sum of squares to the total sum of squares in each equation) and the Durbin-Watson statistics are given in Table 1. The estimated equations fit the data quite well, as indicating by the R 2 coefficients all in excess of 0.96 except for the supply function of other food products ( R 2 = 0.86 ). The t-ratios indicate that ail but three parameters are statistically significant at least at the five per cent level. Furthermore the three insignificant parameters are constant estimates in marginal cost functions. Parameter estimates for the linear expenditure sub-system show that the marginal budget shares are positive and that the minimum consumption levels for the three commodities are positive, ranging from 3 7 215 for dairy products to 156 201 for other food products. The three income elasticities are positive. Dairy products and other food products have estimated income elasticities that are greater than one (1.15 and 1.16, respectively, in average over the estimation period), suggesting that some commodities within these groups are luxuries. On the contrary, meat products have estimated income elasticities that are less than one, 0.56 in average over the estimation period. The three income elasticities have remained fairly stable over the whole period. Compensated and uncompensated own price elasticities of final demand are negative. In average over the period, uncompensated own price elasticities are -0.42 for dairy products, -0.28 for meat products and -0. 79 for other food products. The uncompensated own price elasticities for dairy products and meat products have experienced an increase (in absolute value) over the estimation period, from -0.30 in 1978 to -0.49 in 1993 for dairy products, and from -0.21 in 1978 to -0.32 in 1993 for meat products. The uncompensated own price elasticity for other products has remained stable. As expected, all compensated cross price elasticities of final demand are positive. Uncompensated cross price elasticities of final demand are ail negative indicating that the three goods are gross complements. The three estimated supply functions are increasing in prices and very inelastic as would be expected, i.e., 0.171 for dairy products, 0.075 for meat products and 0.292 for other food products, in average over the estimation period.

(insert Table 1)

The discussion now focuses on conjectural elasticity parameters which measure the degree of market imperfection for the three considered commodities. For each good, computing tstatistics provide a simple test of the price-taking assumption by suggesting acceptance or rejection of price-taking ( 0;; = 0) at a specified level of significance. One easily verifies that each conjectural elasticity estimate is significantly different from zero at the five percent level of significance. The hypothesis that these distortion parameters are ail identically zero ( 0 11 = 0 22 = 0 33 = 0) is also rejected at the five percent level of significance. Correspondingly the hypothesis that a product has been characterised by monopsony-monopoly behaviour ( 0;; = 1) is rejected at the same level of significance.

For each commodity, the degree of oligopsony-oligopoly power may be measured by the Lemer-analog index which is defined as: M Q:

.-w-H.() -0;;. [L(Q~).em;•Pm-Y;;•W;] (l 4 ) L; = P, , , Tl = __ ..:.:m!.:: =.,_ I -=''----------P; -W; P;-W;

The Lemer indexes are presented in Table 2. The sample mean values of these indexes are 0.68 for dairy products, 0.56 for meat products and 0.63 for other food products. Accordingly, for dairy products and in average over the study period, 68 % of the unit margin of food retail firms is explained by the oligopsony-oligopoly power of these firms. The corresponding percentages are 56 % for meat products and 63 % for other food products. These estimates suggest that on the average of the study period, the unit margin for dairy products is 212 % higher than in the competitive case. The corresponding percentages are 127 % for meat products and 170 % for other food products.

The values of Lemer indexes are continuously and regularly declining over time for the three commodities, suggesting that market power decreases over time. The declining trend in market power of French food retail firms is a priori counter-intuitive since the increase in mergers and acquisitions, as well as the accelerated closing of small, family-operated and specialised food retailers should lead, on contrary, to an augmented market power on the belief that increased concentration implies augmented anticompetitive bchaviour. 2 At this stage, it is first interesting to note that most studies which measure market power in oligopolies and/or oligopsonies for different food industries also find a declining trend in market power while market concentration increases. As an example, [START_REF] Schroeter | Marketing margins, market power, and price uncertainty[END_REF] identify a decreasing trend in market power for the US beefpacking industry over the 1976-88 period of increasing market concentration. [START_REF] Hamilton | The Effect ofFarm Supply Shifts on Concentration and Market Power in the Food Processing Sector[END_REF] develop a theoretical framework to explain such a result. They allow for cost differences among food processors and endogenize entry and exit. Under these conditions, they show that increasing concentration (measured by the Lemer index) and decreasing market power are likely to occur simultaneously in response to a shift in farm supply. Let us consider, e.g., the case where the farm supply curve is inelastic which implies that market power in the processing industry is high, farm prices are low and numerous inefficient high-cost firms are able to produce (relative to the case of elastic supply). "When technical change causes the supply of raw products to become more elastic, the farm supply curve is able to more readily absorb increases in production without creating large, commensurate increases in the price of raw products. lncumbent firms consequently expand their use of raw products, increasing farm prices and precipitating the exist of high-cost firms in the industry." In other words, a clockwise rotation of the farm suppl y curve leads to a decrease in market power while market concentration increases due to the exit of inefficient high-cost processors.

From a more empirical point of view, one plausible explanation of the declining trend in market power in the French food retail industry may be the following. One can reasonably expect that variable distribution costs of food retail firms increase over the study period. 3 lncentives to increase capacity utilisation levels in order to achieve significant cost economies (by spreading costs over a larger volume of sales) may then offset incentives to exert market power by restricting input use and output sale. In other words, retail firms may seek maximal growth of sales by assuring the necessary flow of inputs to operate near maximal capacity rather than maximal profits. Complementary and/or alternative explanations which merit further investigation may also be proposed. For example, one may reasonably expect that in a contracting market price competition is more intense in order to sustain volume of sales. One can also reasonably suppose that fixed costs are relatively more important for small and specialised food retailers than they are for supermarkets. Accordingly small and specialised firms may behave so as to equate price and average cost. Our measure of market power is then upward biased, particularly for the first years of our sample where the number of these small and specialised firms was larger.

Finally, it is important to underline that our empirical mode) constrains the conjectural elasticity parameters to be constant. This is clearly a weak point of our analysis which may have an impact on our empirical results and may also explain, at least partially, the estimated declining trend in market power. From ( 14), one verifies that high (in absolute value) demand and supply price elasticities tend to yield low Lemer-analog indexes, other things equal and in particular for constant conjectural elasticity estimates. The degree of market imperfection and market power is negatively associated with factors that intensify price competition in input and output markets. As an example, [START_REF] Schroeter | Measuring market power in multi-product oligopolies: The US meat industry[END_REF] assume that the conjectural elasticity parameter is a negative fonction of capacity utilisation level where the latter is used as an indicator for firms to intensify competition. Using a similar argument, Murray assumes that the conjectural elasticity parameter is a positive fonction of transport costs per unit distance. Because of the Jack of statistical information, it was not possible in our case to estimate a mode! where the three conjectural elasticity parameters were specified as a function of proxies which reflect an intensified or conversely a decreased competition. Furthennore it is important to note that it is very difficult to give a sound economic content to such fonctions which remain very ad-hoc.

(insert Table 2)

Concluding remarks

This paper develops and estimates an empirical mode! of pricing behaviour for retail finns in both a quantity-setting oligopoly engaged in the joint production of demand-related final goods and a quantity-setting oligopsony for supply-unrelated wholesale goods. The procedure consists of simultaneously estimating a system of demand functions for final goods, supply functions for wholesale goods and the retail industry first-order profit-maximisation conditions, from which an estimate of the degree of imperfect competition and of oligopolyoligopsony power for the different commodities can be retrieved. The procedure adopted draws thus on a method of identifying and measuring market power that has been developed by Gollop and Roberts, and Appelbaum, and that has extensively been applied to various industries in the manufacturing sector, as well as to export markets. To our knowledge, it is the first time that the methods ofNEIO are applied to the retail industry. The mode) is applied to the French food retail industry. Three commodities are distinguished, i.e., dairy products, meat products and other food products. Since a summary and a discussion of empirical results has already been provided in the previous section, here we simply note that i) we strongly reject the hypothesis that French food retail firms behave competitively and ii) more than 50 per cent of the wholesale-to-retail price margins for the three goods are attributable to oligopoly-oligopsony distor:tions. The empirical model incorporates certain simplifying assumptions, such as the specification of supply functions for wholesale goods and marginal cost functions for retail firms, that limits its practical relevance. Market conduct parameter estimates are subject to important caveats stemming mainly from the imposition of these strong assumptions. Further research is clearly necessary using more refined and more detailed data sets to verify the robustness of our empirical results. (1) D84 is a dummy variable that takes into account the milk quota regime introduced in 1984. lt takes a value of zero over the 1977-1983 period and one over the 1984-1993 period.

(2) The hypothesis of no serial correlation was tested against the alternative of first-order serial correlation. lt was rejected in two supply functions (i.e., for dairy products and other food products) and in the final demand sub-system. When the supply function for other food products was corrected for serial correlation, we were not able to obtain convergence. In the same way, when the dependant variable was specified as a linear function of time in this equation, the estimate of b; was negative. Accordingly only the supply fonction for dairy products and the final demand sub-system were corrected for first-order serial correlation in Table 1, and the estimated supply fonction for other food products does not depend on time. 1 If the jth firm does not produce the kth good, Q{ = 0 and àn 1 (Q 1 *) / ôQ/ ~ 0. In order to encompass both the interior solution and the corner regimes where the considered retail firm specialises in the distribution of some goods only, equation (Sb) may be written as: We allow for some quantities to be equal zero at the firm level, but the equilibrium industry quantity of each good is strictly positive.

2 A concentration index encompasses two aspects, i.e., the number of firms and the size distribution of competitors. lt must decline with the number of firms and it must increase with the level of inequality among firms. lt is now well recognised that market power increases when the number of firms declines, but the assumed positive link between market power and firm size inequality for a given number of firms is less obvious. On this point, see [START_REF] Barla | Finn Size lnequality and Market Power[END_REF] who finds that there exits a non-linear U-shaped relationship between market power and firm size inequality in the case of the US airline industry.

3 Retail firms provide consumers with a large variety of distribution services: accessibility of location, assortment, assurance of product delivery in the desired form and at the desired time, information and ambience. Higher levels of these services cost the firms more and reduce the costs for consumers [START_REF] Betancourt | The outputs of retail activities: French evidence[END_REF].

  I ôQ/).Q/* = -I:~:>m/•0{;.pm.Q~• + L Y mm•0~;• Wm.Q~• i = 1, ... , M m=I l=I m=I

Table 1 .

 1 Parameter estimates (t-ratios in parentheses), R 2 and Durbin-Watson statistics (2)

			Commodity group
	Parameter	Dairy products	Meat products	Other food products
		37999.7 (28.25)	91288.6 (47.71)	163213.0 (26.09)
		8108.3 ( 4.68)	7696.23 (2.93)	70895.5 (11.26)
		730.3 (8.60)	801.6 (7.77)	-(2)
		37214.9 (8.70)	90362.4 (20.77)	156201.0 (7.67)
		0.1547 (11.69)	0.1499 (10.05)	0.6954 (35.26)
		-0.01705 (-0.46)	-0.03877 (-0.72)	-0.01631 (-0.42)
	g;	0.01409 (2.77)	0.02580 (7.44)	0.02373 (8.31)
	J; .D84 (])	0.0676 (2. 75)
	g;.D84 (])	-0. 7028E-02 (-2.4 7) -
	0;;	0.54778E-02 (2.41) 0.44350E-02 (2.62)	0.02732 ( 4.87)
			Statistics
	Equation		DW
	Supply
	dairy products	0.9945	1.52
	meat products	0.9670	1.30
	ot. food products	0.8596	0.29
	LES
	dairy products	0.9993	1.49
	meat products	0.9996	2.19
	Optimality cond.
	Dairy products	0.9997	1.60
	meat products	0.9981	1.88
	ot. food products	0.9992	1.33

Table 2 .

 2 Estimated degrees of market power (Lemer-analog indexes)

	Year	Dairy products	Meat products	Other food products
	1978	0.9123	0.9148	0.8584
	1979	0.8326	0.7905	0.7893
	1980	0.7769	0.7068	0.7360
	1981	0.7395	0.6527	0.7038
	1982	0.7136	0.6188	0.6778
	1983	0.6885	0.5834	0.6535
	1984	0.6423	0.5560	0.6369
	1985	0.6383	0.5283	0.6143
	1986	0.6342	0.5037	0.5947
	1987	0.6268	0.4832	0.5776
	1988	0.6210	0.4662	0.5626
	1989	0.6196	0.4580	0.5502
	1990	0.6152	0.4464	0.5394
	1991	0.6073	0.4318	0.5320
	1992	0.5988	0.4188	0.5134
	1993	0.5914	0.4030	0.5034
	Mean	0.6786	0.5601	0.6277
	End notes

The authors would like to thank C. Le Moue! and Y. Surry for many helpful suggestions and comments on an earlier draft of this paper while absolving them of ail blame for any errors or shortcomings that remain.


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Regulation of cyclin D1 expression in ES cells : the role of the Ras/MAPK pathway

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Cold Spring Harbor Meetings : Mouse Molecular Genetics New-York, 2000 Poster Abstract :

Regulation of cylin D1 expression in ES cells :

the role of the Ras/MAPK pathway. The cellular machinery that is organized to collect extracellular signals and transduce them via tyrosine kinase receptors and the SOS-RAS-MEKK-MAPK pathay seems to be dedicated largely to driving RB phosphorylation. Cyclin D1 is likely to play a key role in this process as : (i) cyclin D1 expression is regulated by MAPK-dependent transcription factors (jun, fos, ets) and (ii) cyclin D1/CDK4 complexes are involved in RB phosphorylation during G1 phase of the cell cycle. The circuitry appears to be operative in virtually all cell types and its revelance is illustrated by its disruption in many types of human tumors. Using ES cells which express the neo r gene driven off the oct4 promoter (IOUD2 cells) so as to kill all spontaneously differentiating cells, we show that ES cells express low, although constant, evel of cyclin D1. This results from low activity of the cyl1 promoter. Promoter deletion analysis shows that this background activity originates from a proximal region of the promoter, and taht distal regions known to be involved in cyclin D1 expression in response to serum stimulation are not required. Treatment of IOUD2 cells with wortmannin (an inhibitor of RAS activation) or PD98059 an inhibitor of MEK) does not inhibit cyclin D1 expression. None of these inhibitors induce growth retardation. Induction of differntiation with retinoic acid (RA) up-regulates cyclin D1 expression, and distal -serum-responsiveelements of the cyl1 promoter are involved. Differentiating cells become sensitive to inhibitors of the Ras à ERK cascade. Both wortmannin and PD98059 inhibit cell growth and down-regulate expression of cyclin D1. Hence, cyclin D1 expression seems not to be regulated by the RAS à MERK à ERK phosphorylation in ES cells. This regulation is likely to be restored upon differntiation.