In a two- person, two- good exchange economy:

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In a two-person, two-good exchange economy, the competitive equilibrium allocation is Pareto-optimal. This means that the allocation cannot be improved upon without making one of the individuals worse off. The competitive equilibrium prices may or may not be on the contract curve, which represents the set of feasible allocations based on the individuals' endowments and preferences. The competitive equilibrium allocation is not necessarily on the budget curve, which represents the set of allocations that exhaust the individuals' budgets. There is a competitive equilibrium in this economy as long as certain conditions are met, such as the individuals having convex preferences and the goods being divisible.

In a Two- Person, Two- Good Exchange Economy