Economic Exchange and Social Organization: The Edgeworthian foundations of general equilibrium theory

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The advantage of this general method is that it is applicable to the particular case of imperfect competition where the conceptions of demand and supply at a price are no longer appropriate" Edgeworth p. The only way of resolving indeterminacy of contract then is to appeal to the utilitarian principle of maximizing the sum of the utilities of traders over the range of final settlements. Thus, Edgeworth introduced into economics the generalized utility function, U x, y, z, The Edgeworth Box is a way of representing various distributions of economic resources.

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It is a rectangular diagram with Subject A's Origin on one corner, and Subject B's origin on the opposite corner. The width of the box is the total amount of one commodity, and the height is the total amount of the other commodity.

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Thus, every possible division of the goods between the two people can be represented as a point in the box. If we draw among points in Edgeworth's Box, we obtain indifference curves , representing combinations of the goods that are of equal value for both Subject A and Subject B.

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Edgeworth's original two axis depiction was developed into the now familiar box diagram by Pareto in , and was popularized in a later exposition by Arthur Lyon Bowley. Imagine two people Octavio and Abby with a fixed amount of resources between the two of them — say, 10 liters of water and 20 hamburgers. If Octavio takes 5 hamburgers and 4 liters of water, then Abby is left with 15 hamburgers and 6 liters of water.

The Edgeworth box is a rectangular diagram with Octavio's origin on one corner represented by the O and Abby's origin on the opposite corner represented by the A.

The width of the box is the total amount of one good, and the height is the total amount of the other good. In theory, it is possible to draw among these points indifference curves for both Abby and Octavio representing combinations of the goods that are of equal value, respectively, to Octavio and Abby. For example, Abby might value 1 liter of water and 13 hamburgers the same as 5 liters of water and 4 hamburgers, or 3 liters and 10 hamburgers.

There is, of course, an infinity of such curves assuming water and hamburgers to be infinitely divisible that could be drawn among the combinations of goods for either consumer Octavio or Abby. Wherever one of these curves for Abby happens to just touch but not cross a curve of Octavio's, a unique combination of the two goods is identified that yields both consumers a maximum value. Such tangential contacts between the infinity of indifference-curve pairs, if plotted, will form a trace connecting Octavio's origin O to Abby's A.

The curve connecting points O and A is often called the contract curve. Edgeworth's limit theorem examines the range of possible outcomes which may result from free market exchange or barter between groups of people. It shows that while the precise location of the final settlement the ultimate division of goods between the parties is indeterminate, there is a range of potential outcomes which shrinks as the number of traders increases.

Edgeworth used a variant of what is now known as the Edgeworth box with quantities traded, rather than quantities possessed, on the relevant axes to analyze trade between groups of traders of various sizes. In general he found that "Contract without competition is indeterminate, contract with perfect competition is perfectly determinate, [and] contract with more or less perfect competition is less or more indeterminate" Edgeworth If trade in two goods, X and Y, occurs between a single pair of traders, A and B, the potential outcomes of this trade can be shown in an Edgeworth box.

This is Edgeworth's key finding—the result of trade between two people can be predicted within a certain range but the exact outcome is indeterminate. This finding was erroneously disputed by Alfred Marshall and the discussions between the two on this point is known as the "barter controversy. If there is a sufficient number of traders, the core of the market will shrink such that the point of final settlement is perfectly determinate.

This point is equal to the price-taking equilibrium at which trade is assumed to take place at in models of perfect competition. 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 and obtain the gains from trade for themselves as other traders will always have an incentive to leave the group out in the cold. 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 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. 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.

Advances in game theory , such as those developed by John F. 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 stylized, involving traders obtaining information by making, breaking, and re-making contracts with each other without cost. Usually children only learn about animals from far-off places in zoos and on TV. The new Wild Animals series makes these amazing animals accessible and provides a brilliant chance for children to learn all about the animals in their natural environments.

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