# Edgeworth box

In

economics , an**Edgeworth box**, named afterFrancis Ysidro Edgeworth , is a way of representing various distributions of resources. Edgeworth made his presentation in his famous book, "Mathematical Psychics: An essay on the application of mathematics to the moral sciences", 1881. Edgeworth's original two axis depiction was developed into the now familiar box diagram by Pareto in 1906 and was popularized in a later exposition by Bowley. The modern version of the diagram is commonly referred to as the Edgeworth-Bowley box.The Edgeworth box is used frequently in

general equilibrium theory , and can aid in finding thecompetitive equilibrium of a simple system.**Example**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. Thus, every possible division of the goods between the two people can be represented as a point in the box.

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). The indifference curve is often derived from each consumer'sutility function .**Pareto set**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 (which consumer realizes the greater value cannot be known, even to the consumers). 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 thePareto set , since each point on the curve isPareto optimal . The utilities which can be achieved by a given point on the Pareto set constitute what is sometimes called theutility possibility frontier . It is important to note that while it is often described as a curve, the Pareto set may be all points within some shape, or even the whole box.The vocabulary used to describe different objects which are part of the Edgeworth box diverges. The entire Pareto set is sometimes called the contract curve, while Mas-Colell, Winston, and Green, in their famous Microeconomics text, "Microeconomic Theory" (1995), restrict the definition of the contract curve to only those points on the Pareto set which make both Abby and Octavio at least as well off as they are at their initial endowment. Other authors who have a more game theoretical bent, such as

Martin Osborne andAriel Rubinstein in their "A Course in Game Theory" (1994), uses the term core for the section of the Pareto set which is at least as good for each consumer as the initial endowment.In order to calculate the Pareto set, the slope of the indifference curves for both consumers must be calculated. That slope is the negative of the

marginal rate of substitution , so since the Pareto set is the set of points where both indifference curves intersect tangentially, it is also the set of points where each consumer's marginal rate of substitution is equal.**ee also***

Welfare Economics

*List of economics topics

*Utility **External links*** [

*http://www.sscnet.ucla.edu/ssc/labs/cameron/e1f98/imapedge.html java applet UCLA*]**References*** Mas-Colell, Andreu; Whinston, Michael D.; and Jerry R. Green. Microeconomic Theory. Oxford University Press, US: 1995, ISBN 0-19-507340-1

* Osborne, Martin J. and Ariel Rubinstein: A Course in Game Theory, MIT Press, 1994, ISBN 0-262-65040-1

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### Look at other dictionaries:

**Edgeworth-Box**— Indifferenzkurven für zwei Güter x und y. Edgeworth Box mi … Deutsch Wikipedia**Edgeworth-Box**— analytisches Hilfsmittel zur Ermittlung der in der Wohlfahrtsökonomik verwendeten ⇡ Kontraktkurve. Sie entsteht durch die Kombination der Indifferenzkurvensysteme zweier Tauschpartner (vgl. Abbildung „Edgeworth Box – Entstehung“). Dazu müssen die … Lexikon der Economics**Edgeworth's limit theorem**— is an economic theorem created by Francis Ysidro Edgeworth that examines a 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… … Wikipedia**Edgeworth**— steht für: Orte in den Vereinigten Staaten: Edgeworth (Massachusetts) Edgeworth (Pennsylvania) Edgeworth (Texas) Personen: Francis Ysidro Edgeworth (1845–1926), englischer Ökonom Kenneth Essex Edgeworth (1880–1972), irischer Astronom Richard… … Deutsch Wikipedia**Edgeworth**— [ edʒwəːθ], 1) Francis Ysidro, britischer Volkswirtschaftler und Statistiker, * Edgeworthstown (Irland) 8. 2. 1845, ✝ Oxford 13. 2. 1926; war 1890 1922 Professor in Oxford, 1891 1926 Herausgeber des »Economic Journal« (London). Edgeworth… … Universal-Lexikon**Edgeworth paradox**— In economics, the Edgeworth paradox describes a situation in which two players cannot reach a state of equilibrium with pure strategies, i.e. each charging a stable price.Suppose two companies, A and B, sell an identical commodity product, and… … Wikipedia**Edgeworth**— Francis Ysidro, 1845–1926, aus Irland stammender Nationalökonom, der zunächst in London und von 1891 bis 1922 in Oxford lehrte. Wie sein Zeitgenosse ⇡ Marshall in Cambridge kam er von der Ethik zur Wirtschaftstheorie. E. hat im Gegensatz zu… … Lexikon der Economics**Francis Edgeworth**— Francis Ysidro Edgeworth Francis Ysidro Edgeworth (* 8. Februar 1845 in Edgeworthstown, County Longford, Irland; † 13. Februar 1926 in Oxford, Oxfordshire, England) war ein irischer Ökonom. Edgeworth vertrat die Idee der Progressivsteuer, die er… … Deutsch Wikipedia**Francis Y. Edgeworth**— Francis Ysidro Edgeworth Francis Ysidro Edgeworth (* 8. Februar 1845 in Edgeworthstown, County Longford, Irland; † 13. Februar 1926 in Oxford, Oxfordshire, England) war ein irischer Ökonom. Edgeworth vertrat die Idee der Progressivsteuer, die er… … Deutsch Wikipedia**Francis Ysidro Edgeworth**— (8 February 1845 ndash; 13 February 1926) made significant contributions to the methods of statistics during the 1880s. From 1891 onward he was the editor of a leading academic journal in economics and his own writings in economics were… … Wikipedia