If two people have identical homothetic preferences and if their indifference curves have a diminishing marginal rate of substitution, then in an Edgeworth box, the locus of Pareto optimal allocations between them is a diagonal straight line.

Homothetic Preferences

Preferences where if a consumer prefers a bundle of goods A to B, they will also prefer a scaled-up version of A to the same scale-up of B, maintaining the same proportions.

Marginal Rate of Substitution

How quickly a consumer agrees to trade one good for another, aiming to keep their level of pleasure steady.

Edgeworth Box

A diagram used in economics to show the distribution of resources, illustrating how different mixes of goods can lead to an optimal allocation.