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.

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Quizplus · Accepted Answer

This is a known result in microeconomics. When individuals have identical homothetic preferences and diminishing marginal rate of substitution, the Pareto optimal allocations lie along a 45-degree line (diagonal) in an Edgeworth box. This is due to the fact that the slope of the indifference curves for both individuals is the same, therefore the only way to improve one individual's utility is to decrease the other's. The Pareto optimal allocation is the point where both individuals' MRS are equal, which is on the diagonal line.

If Two People Have Identical Homothetic Preferences and If Their