Editing Edgeworth's limit theorem (section)

===Trade with less than perfect competition===
[[Image:Edgeworthprocess2.svg|thumb|Figure 2 - Trade between two pairs of people.<ref name=creedy/>]]
[[Image:Edgeworthprocess3.svg|thumb|Figure 3 - The new limits of the contract curve.<ref name=creedy/>]]
Suppose a single extra pair of identical traders is added to this initial pair. As these new traders are identical to the first pair, the same Edgeworth box can be used to analyse the exchange. To examine the new outer limits of the trade, Edgeworth considered the situation where trade occurs at the limit of trade between two people (point C or C' in ''Figure 2''). If trade were to occur at point C one of the B's (say B(1)) would receive all the gains from trade. The one A who trades with B(1) (say A(1)) now has a mix of goods X and Y which he is able to trade with A(2). As the two A's are identical, they will agree to split their post-trade endowments equally between them, placing them at point P in ''Figure 2'' which gives them a higher utility than they would otherwise receive (indifference curve U'(a) instead of U(a)). B(2) now has an opportunity and strong incentive to offer the A's a better price for their goods and trade with them at this price, leaving B(1) out in the cold. This process of B's competing against one another to offer the A's a better price will continue until the A's are indifferent between trading at P and trading on the contract curve (''Figure 3''). The same reasoning can be applied to the case where A(1) initially receives all the gains from trade, and it can be shown that the outermost limit given by U(b) will also move inwards. This is called the shrinking core of the market - as an extra pair of traders is added, the feasible range of trades shrinks.

[[Image:Edgeworthprocess4.svg|thumb|Figure 4 - Final settlement of trade with multiple pairs of traders.<ref name=creedy/>]]
If a third pair of traders is added, the core of the market shrinks further. If trade occurs at the limit where B(1) gets all the gains from trade, the point P is now two thirds of the way along the line EC. This improves the bargaining power of the A's who are able to get onto a higher indifference curve as B's compete to trade with them. The outer limit of final settlement where there are multiple pairs of traders can be generalised (''Figure 4'') where K = (n-1)/n.