i> 0(4)ηrepresents the elasticity of the price function. Until now I assumed ηalways being 0,5.However, 0,5 is an estimated average value (Dolan, 1987) and in practice ηmay vary. Forvalues of ηbetween -1 and 1 the following function applies (see also Figure 2):110FFRFFR(5)Working Paper981
UNFAIRALLOCATIONOFGAINSUNDEREQUALPRICEINCOOPERATIVEPURCHASINGFigure 2: Dependency of FFR to η(for all ηthe maximum added value is reached by q=100%)With an elasticity of 1,0 and a corresponding FFR of 0%, all organisations increasing theirvolume through the consortium will receive fewer gains. The smallest organisation willalways receive the largest part of the gains. The largest organisation will always receive thesmallest part of the gains. The 25% ruleThe 38% rule applies to organisations increasing or decreasing their cooperative volume. NowI consider the situation where the total volume of a consortium is fixed. Figure 3 illustratesthis scenario for different quantities of organisation 2.Figure 3: Type of gains for organisation 2 with different quantities of q2while N is constant14thAnnual IPSERA 2005 Conference, Archamps, France982equalpriceiequalpricei + ni= Mi
SCHOTANUSF.At the point whereq2becomes 50% of the total volume, the added value of this organisationreaches its maximum value. At the point where q2becomes 25% of the total volume, the EP-outcome for organisation 2already reaches its maximum. With theorem and proof 3 I provethat this is always the case in the model. Again, this percentage is independent of po, c1and c2in the price structure, the number of organisations, and the division of the volumes of theseorganisations. To conclude, when using EP and assuming a continuous price function, organisationspurchasing 25% of the total volume will receive the maximum allocation of gains. Larger orsmaller members will receive a smaller amount of gains. I define 25% as the Second FairnessRatio (SFR) of EP with an average price function.Theorem 3While using the EP concept and given the price function (2), consortium members purchasing 25% of the total volume will receive the maximum allocation of gains. Proof 0202· (() - ())= ·- iiiiiequalpricevqprice qprice NpcqpcqNHere, Nfixedand,0202'- 0211- 02425%iiiiipcpcequalpricevqNqNNqif qSFR N then SFROnce more, the dependent variable in this proof is η. If η = -1, SFR = 50%. This is a fairsituation as SFR equals the point where the added value reaches its maximum (50%). When η> -1, SFR < 50%, this could lead to an unfair situation as SFR reaches its maximum before theadded value does. For SFRthe following function applies (see also Figure 4):11SFRFFR(6)Working Paper983
UNFAIRALLOCATIONOFGAINSUNDEREQUALPRICEINCOOPERATIVEPURCHASINGFigure 4: Dependency of SFR to η(for all ηthe maximum added value is reached by q=50%)Limitations and further research