• Construct an Edgeworth box diagram with initial endowment and X = XA + XB and Y = YA + YB.
• In general it is possible to reallocate X and Y between A and B so that at one person is made better off without making the other worse off. Such points are referred to as Pareto improvement over the initial allocation.
• Pareto efficient points correspond to the tangency of the indifference curves of A and B. At these points of tangency it is not possible to make one person better off without making the other worse off.
• Pareto efficient points are not unique. Corresponding to an initial allocation ‘L’ there are an infinite number of points of tangency of indifference curves of A and B, each of which is Pareto efficient but they differ in how much A and B gain from the reallocation of X and Y.
• If instead of the initial allocation ‘L’ we choose another arbitrary allocation, we can arrive another locus of points which are Pareto efficient.
• Extending this idea we can trace the locus of all such points of tangency of the indifference curves of A and B. The locus of all these points of tangency is called the contract curve.
• Along the contract curve the following condition holds:
(1)
This is the condition for Pareto efficiency in an exchange economy.
Reference
Joseph E. Stiglitz; Economics of the Public Sector, third edition; W.W.Norton and Company, New York, 2000
