Disproving Pareto’s Contract Curve Mathematically

Pareto’s contract curve is a geometric concept; consequently, many textbooks supplement it with mathematical justification. This booklet disproves such mathematics. It argues that treating two antagonistic firms as a single entity is flawed, and that maximizing an ever-increasing objective can never yield a solution. Furthermore, this paper clarifies that output is a third-dimensional measure; therefore, all attempts to find a solution using a two-dimensional Edgeworth box are either incorrect or misleading.