Edgeworth Box

The Edgeworth box is a graphical tool used to analyze the distribution and exchange of two goods between two economic agents, as well as the conditions for equilibrium in a pure exchange economy. It was first introduced by British economist Francis Ysidro Edgeworth and later refined by A.L. Bowley. The Edgeworth box can be used to examine the exchange of two goods (X and Y) between two agents in a pure exchange economy (the Edgeworth exchange box), or to analyze the allocation of production factors (K and L) between two firms. In the first case, indifference curves between the two goods are used, while in the second, isoquant curves are employed to represent the relationship between the production factors.

Edgeworth exchange box

Given two economic agents (A and B) with endowments of goods (X and Y) and no production activity, the Edgeworth box helps determine how much of each good will be exchanged between the two agents, based on their initial endowments and personal preferences.

In the first Cartesian diagram (Diagram A), we show the indifference curves for agent A. Agent A starts with an initial endowment of X_A units of good X and Y_A units of good Y. In the second diagram (Diagram B), we show the indifference curves for agent B. Agent B’s initial endowment consists of X_B units of good X and Y_B units of good Y.

Edgeworth box construction

To construct the Edgeworth box, we rotate agent B's Cartesian diagram (Diagram B) 180° and overlay it onto Diagram A. The result is a rectangular graph with two origins. From the lower-left origin O_A, we can measure agent A’s endowments and exchanges. From the upper-right origin O_B, we can do the same for agent B. The Edgeworth box is visually represented as follows:

The Edgeworth box is composed of two overlapping Cartesian diagrams. Both diagrams measure the quantities of goods A and B along their axes. The lengths of the X and Y axes in the Edgeworth box are determined by the total endowments of goods owned by both agents. For example, the length of the X-axis is given by the sum X_A + X_B, representing the total quantity of good X owned by both agents A and B. Similarly, the Y-axis is defined by the sum Y_A + Y_B, representing the total quantity of good Y. The indifference curves remain convex toward their respective origins.

For instance, agent B's indifference curves I_B are convex toward the origin O_B, and agent B always prefers the outer indifference curve I''_B over the inner one I'_B. This particular feature of the Edgeworth box allows us to observe how the endowments of the two agents change during the process of exchange. The Edgeworth box is a key graphical tool in political economy and microeconomics.

Edgeworth production box

In the Edgeworth production box, the Cartesian axes represent the quantities of the production factors K and L. Isoquants on the Cartesian plane show the combinations of these factors required to produce goods A and B. The sum K_A + K_B represents the total amount of capital (K) available in the market, while the sum L_A + L_B represents the total amount of labor (L). Based on the production technology used by the firms (represented by isoquants), the points where the isoquant curves touch (tangency points) indicate the optimal allocation of capital (K) and labor (L).

Edgeworth box equilibrium. The equilibrium in the Edgeworth box occurs at points where the indifference curves of both consumers are tangent (the contract point). At these points, the marginal rate of substitution between the goods is equal for both consumers. This equilibrium represents a Pareto optimal situation, meaning that neither consumer can improve their utility without reducing the other’s. The set of all tangency points between the indifference curves is known as the contract curve. Similarly, the set of tangency points between isoquant curves is also referred to as the contract curve.