Edgeworth box

In economics, an Edgeworth box, named after Francis Ysidro Edgeworth, is a way of representing various distributions of resources. Edgeworth made his presentation in his 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 his book "Manual of Political Economy",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. It can aid in representing the competitive equilibrium of a simple system or a range of such outcomes that satisfy economic efficiency. It can also show the difficulty of moving to an efficient outcome in the presence of bilateral monopoly. In the latter case, it serves as a precursor to the bargaining problem of game theory that allows a unique numerical solution.

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 Abby takes 4 liters of water and 5 hamburgers, then Octavio is left with 6 liters of water and 15 hamburgers. 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.

Indifference curves (derived from each consumer's utility function) can be drawn in the box for both Abby and Octavio. The points on, for example, one of Octavio's indifference curves represent equally liked combinations of quantities of the two goods. Hence Abby is indifferent between one combination of goods and another on any one of her indifference curves, and the same is true for Octavio. 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 are an infinite number of such curves that could be drawn among the combinations of goods for each consumer (Octavio or Abby).

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