If I have two consumers in an Edgeworth box, and one of them, say A, as perfect substitutes as preferences, and the other, B, has perfect complements, then the contract curve goes starts from B's endpoint and goes through all of the "kinks" in his indifferencecurves. But where does it end? At the point where it hits the edge of the edgeworth box, or does it continue somehow along the frame?
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. Indifference curves (derived from each consumer's utility function) can be drawn in the box for both A and B. The points on, for example, one of B's indifference curves represent equally liked combinations of quantities of the two goods. Hence A is indifferent between one combination of goods and another on any one of her indifference curves, and the same is true for B. There are an infinite number of such curves that could be drawn among the combinations of goods for each consumer. With B's origin (the point representing zero of each good) at the lower left corner of the Edgeworth box and with A's origin at the upper right corner, typically B's indifference curves would be convex to his origin and A's would be convex to his origin. When an indifference curve for A crosses one of the indifference curves for B at more than one point (so the two curves are not tangent to each other), a space in the shape of a lens is created by the crossing of the two curves; any point in the interior of this lens represents an allocation of the two goods between the two people such that both people would be better off, since the point is on an indifference curve farther from both of their respective origins.