The Early History of the Box Diagram

E conomists hail it as “a powerful tool,” “a work of genius,” and “one of the most ingenious geometrical constructions ever devised in economics.” It graces the pages of countless textbooks on price theory, welfare economics, and international trade. It is associated with some of the greatest advances ever made in economic theory. It elegantly depicts the two fundamental welfare theorems that are absolutely central to modern economics. In short, it ranks with the preeminent schematic devices of economics since it illuminates the most important ideas economists have to offer. It is none other than the celebrated box diagram used to illustrate efficiency in exchange and resource allocation in hypothetical two-agent, two-good, two-factor models of general economic equilibrium. The box comes in two variants. The exchange version has dimensions determined by total available stocks of the two goods (see Figure 1). It incorporates traders’ indifference maps, one with origin sited in the southwest corner and the other in the northeast corner. The box depicts opportunities for mutually beneficial trade. Thus a movement from initial endowment point E to point Z on the contract curve—a movement accomplished through a trade of ER units of the second good for RZ units of the first—benefits both traders simultaneously by putting them on higher indifference curves. In general, so long as the straight trading line EZ, whose slope measures the price of the first good in terms of the second, cuts the indifference curves of both parties at point E, it pays each to move along that line to the contract curve. Once on the contract curve, however, the potential for further mutually advantageous trades is at an end. Since the contract curve is the locus of indifference-curve tangency points, it follows that movements along the contract curve improve the welfare of one trader only by reducing that of the other.