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2 Exchange economies The ability of price-mediated trade to achieve efficient outcomes is often described as "the magic of markets". Demonstrate this magic via an example with three agents and three goods. Instructions: . Write down a three-agent, three-good exchange economy with fully specified preferences and endowments, in which the endowments are not Pareto-efficient. . Demonstrate failure of Pareto-efficiency at the endowments by finding an alternative allocation of goods which is a Pareto-improvement. 2 . Calculate a competitive equilibrium of the exchange economy, and show that the equi- librium allocation is Pareto-efficient by finding a corresponding set of Pareto weights