If the initial endowment is on the contract curve, then there must always be a competitive equilibrium in which no trade takes place.

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Quizplus · Accepted Answer

If the initial endowment is on the contract curve, it represents an allocation that is Pareto efficient and all agents prefer it over any other feasible allocation. In a competitive equilibrium, prices adjust to ensure that demand equals supply in every market. Since the initial endowment already satisfies the market clearing condition and is Pareto efficient, there is no incentive for agents to trade further. Therefore, there exists a competitive equilibrium in which no trade takes place.

If the Initial Endowment Is on the Contract Curve, Then