equal to the price-taking equilibrium at which trade is assumed to take place at in models of perfect competition. Generalisation This analysis can be modified to accommodate traders who are not identical or who have motivations which aren't purely selfish as well as the situation where one group of traders is larger than the other. If the traders are heterogeneous the point P will not reflect a "split the difference" trade between the group of traders and the outer limit of trade determined by this point will be modified accordingly. If the utility of one trader(s) influences the utility of another (i.e. the latter is not selfish) then the associated limit of the contract curve will shrink inwards, ruling out the most inequitable trades. If the groups of traders are differently sized, the outer limits of the contract curve will not shrink an equal amount. Implications There are two main implications of the limit theorem. The first is that the end result of trade between small groups of people is indeterminate and is determined by what were to Edgeworth non-economic factors. The second is that the equivalent of a price-taking equilibrium can arise from competition between very large groups of traders through the recontracting process. This equilibrium point cannot be moved by groups of traders acting in collusion to try to obtain the gains from trade for themselves as other traders will always have an incentive to leave the group out in the cold. This provides a justification for assuming price-taking behaviour in certain situations, even though explanations of how a price-taking situation can arise (such as tatonnement) are clearly implausible. Criticisms To a large degree the indeterminacy result relies on the assumption that the results of bargaining are indeterminate or, at the very least, outside the realm of economic speculation. Modern advances in game theory, such as those developed by John Nash, challenge this assumption and derive stable equilibria (such as the Nash equilibrium ) in complicated bargaining situations. Further, Edgeworth's proposed recontracting process is highly stylised, involving traders obtaining information by costlessly making, breaking and re-making contracts with each other. Marshall strongly criticised Edgeworth on this point. If the recontracting process does not explain real world behaviour then the result that the price-taking equilibrium point will be reached by competitive traders will not necessarily be true. See also Cooperative bargaining References Market (economics) Economics theorems