Blue curve of Pareto efficient points, at points of tangency of indifference curves in an Edgeworth box. If the initial allocations of the two goods are at a point not on this locus, then the two people can trade to a point on the efficient locus within the lens formed by the indifference curves that they were originally on. The set of all these efficient points that could be traded to is the contract curve. In the graph below, the initial endowments of the two people are at point X, on Kelvin's indifference curve K1 and Jane's indifference curve J1. From there they could agree to a mutually beneficial trade to anywhere in the lens formed by these indifference curves. But the only points from which no mutually beneficial trade exists are the points of tangency between the two people's indifference curves, such as point E. The contract curve is the set of these indifference curve tangencies within the lens—it is a curve that slopes upward to the right and goes through point E.
In microeconomics, the contract curve or Pareto set[1] is the set of points representing final allocations of two goods between two people that could occur as a result of mutually beneficial trading between those people given their initial allocations of the goods. All the points on this locus are Pareto efficient allocations, meaning that from any one of these points there is no reallocation that could make one of the people more satisfied with his or her allocation without making the other person less satisfied. The contract curve is the subset of the Pareto efficient points that could be reached by trading from the people's initial holdings of the two goods. It is drawn in the Edgeworth box diagram shown here, in which each person's allocation is measured vertically for one good and horizontally for the other good from that person's origin (point of zero allocation of both goods); one person's origin is the lower left corner of the Edgeworth box, and the other person's origin is the upper right corner of the box. The people's initial endowments (starting allocations of the two goods) are represented by a point in the diagram; the two people will trade goods with each other until no further mutually beneficial trades are possible. The set of points that it is conceptually possible for them to stop at are the points on the contract curve.
However, most authors[2][3][4][5][6][7][8][9] identify the contract curve as the entire Pareto efficient locus from one origin to the other.
Any Walrasian equilibrium lies on the contract curve. As with all points that are Pareto efficient, each point on the contract curve is a point of tangency between an indifference curve of one person and an indifference curve of the other person. Thus, on the contract curve the marginal rate of substitution is the same for both people.
^Varian, Hal R. (2010). Intermediate microeconomics : a modern approach (8 ed.). New York: W.W. Norton & Co. ISBN 978-0-393-93424-3. OCLC 317920200.
^Varian, Hal R. Microeconomic analysis, third edition, 1992, page 324.
^Nicholson, Walter. Snyder, Christopher. "Intermediate Microeconomics and Its Application", eleventh edition, 2010, page 362.
^Pindyke, Robert S. Rubinfeld, Daniel L. "Microeconomics", ninth edition, 2018, page 620.
^Jehle, Geoffrey L. Reny, Philip J. "Advanced Microeconomic Theory", third edition, 2011, page 197.
^Perloff Jeffrey M. "Microeconomics, Theory and Applications with Calculus", fifth edition, page 338.
^Browning,Edgar K. Zupan, Mark, A. "Microeconomics, Theory and Applications", twelfth edition, 2015, page 148.
^Kreps, David M. "A Course in Microeconomic Theory", 1990, page 156.
^Serrano, Roberto. Feldman, Alan M. "A Short Course in Intermediate Microeconomics with Calculus", 2013, page 271.
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