Edgeworth Box

Edgeworth Box - a graphic design used in microeconomics , consisting of two diagrams with indifference curves . First described by the British economist and philosopher Francis Edgeworth in 1881, further developed in the works of Wilfredo Pareto and Arthur Bowley . The Edgeworth Box is one of the tools in the theory of general equilibrium and is sometimes called the “box of exchange of wealth”. It is well suited for analyzing the distribution of two goods between two economic subjects in an exchange economy in consumer theory or for analyzing the distribution of two productive resources in production theory .

Fig. 1. Edgeworth box with two indifference curves and initial distribution${\displaystyle {\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">E</span></span>}}_{\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">one</span></span>}}}$ {\ displaystyle E_ {1}}

Fig. 2. Improving the situation of both subjects due to the exchange leading to the distribution${\displaystyle {\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">E</span></span>}}_{\mathrm{<span\; class="mwe-math-element"><span\; class="mwe-math-mathml-inline\; mwe-math-mathml-a11y"\; style="display:\; none;">2</span></span>}}}$ {\ displaystyle E_ {2}}

A box is created by connecting two coordinate systems , each of which corresponds to an economic subject. The points of reference of coordinate systems located opposite each other depict states in which one of the subjects has all the units of both goods, and the other does not have any. The space bounded by the four axes of the two coordinate systems graphically represents all the theoretically possible distributions of both goods. The length of each axis measures the amount of the good displayed.

Indifference curves expressing combinations of goods that are of equal value to an economic subject are the preferences of both economic subjects. The farther is the indifference curve from the individual point of reference, the greater the level of utility achieved by the economic entity in the possession of a combination of both goods.

For any initial distribution of benefits between economic subjects, there are two indifference curves passing through a point in the Edgeworth box corresponding to the distribution, and reflecting the specific level of utility on which each of the subjects is located. If these curves do not touch each other at a given point, both economic actors can improve their position through exchange. In this case, the indifference curves form a "lens" in the space of Edgeworth's drawer (Fig. 1), any point within which takes each of the participants to a higher level of utility. This new situation is a Pareto-improvement in relation to the initial distribution of benefits.

If the indifference curves relate to each other at a given point, then any other resource allocation will be worse for at least one of the participants, that is, in this case there is no mutually beneficial exchange. These points are called Pareto efficient , and the set of all such points is a contractual curve .

If the initial allocation of resources is inefficient (that is, the corresponding point does not lie on the contract curve), then, with the rationality of both economic entities, voluntary exchange of benefits will be conducted until the distribution obtained becomes Pareto-efficient (Fig. 2). This point, from which it is not profitable for any of the subjects to deviate, is called an equilibrium in the economy of exchange. The set of equilibria forms the core of the economy and is a subset of the contractual curve.