Edgeworth Box Equilibrium

The equilibrium in the Edgeworth box is reached at the point where the indifference curves of the two economic agents are tangent. An Edgeworth box illustrates the preferences of two consumers using their respective indifference curves. Consumer A’s curves are convex toward origin O_A, while those of consumer B are convex toward origin O_B. At the point of tangency, both consumers face the same marginal rate of substitution, marking a stable and mutually beneficial equilibrium. For instance, assume consumer A is initially endowed with X_A units of good X and Y_A of good Y, while consumer B holds X_B and Y_B. These endowments are represented by point E in the Edgeworth box, lying on the indifference curves I_A and I_B for each consumer.

Point E is not a stable equilibrium because both consumers can increase their utility through trade. Consumer A benefits by trading away some of their Y_A to obtain more X_A, while consumer B gains by exchanging part of their X_B for additional Y_B. This exchange process continues until they reach point E* - the contract point - where each consumer moves to a higher, more preferred indifference curve: I′_A and I′_B. At this point, the curves are tangent, indicating that the marginal rate of substitution between the two goods is equal for both agents.

MRS_A = MRS_B

The equilibrium point E* reflects a new post-trade allocation - (X*_A, Y*_A) for A and (X*_B, Y*_B) for B - where both consumers are better off, having reached more advantageous indifference curves. Moreover, E* represents a Pareto-optimal allocation: from this point onward, it is impossible to make one consumer better off without making the other worse off. Any alternative allocation starting from E* would necessarily involve a trade-off in utility between the two.

Efficient Production Equilibrium

In the Edgeworth production box, an efficient allocation of input resources between the production of goods A and B is found at the point where their respective isoquant curves are tangent.

When firms operate on more outward (and thus more productive) isoquants, they achieve higher levels of output (Y′_A > Y_A; Y′_B > Y_B). Tangency between the isoquants indicates that the marginal rate of technical substitution of inputs is equal across both production processes.

MRTS_A = MRTS_B

The set of all tangency points between the two families of indifference curves forms a continuous path from origin O_A to O_B, known as the “contract curve”. Each point along this curve represents a Pareto-efficient allocation. In the production version of the Edgeworth box, the corresponding set of isoquant tangency points identifies all Pareto-efficient input allocations.

Core of the Economy. The set of all efficient exchanges that can arise from a given initial endowment E is referred to as the core of the economy. It is defined by the intersection of the initial indifference curves with the contract curve.