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According two the first two fundamental theorems of welfare economics, if there exist a series of economic agents each with a set of initial resource allocations who are able to buy/sell and satisfy the weak axiom of revealed preference (WARP), then their optimal allocation is also Pareto efficient; and, if a Walrasian equilibrium solution to this market exists, it must also be Pareto efficient. Therefore, any market satisfying these mathematical properties possesses a price vector that will ensure Pareto efficiency.

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Q: How does a free market ensure an effcient allocation of resources?
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