Finding Pareto-Efficient Allocations by Maximizing One Agent's Utility
A standard method for identifying Pareto-efficient allocations involves solving a constrained optimization problem. This is achieved by maximizing one agent's payoff while keeping the payoffs of all other agents constant, and any allocation found through this method is guaranteed to be Pareto efficient. [2, 3] Crucially, this process is symmetrical; the same set of Pareto-efficient allocations is identified regardless of which agent's payoff is maximized. For instance, one could maximize a fisherman's utility given a fixed payoff for a plantation owner, or vice versa, and arrive at the same conclusions. In the Angela-Bruno model, this involves maximizing Angela's utility for a given amount of rent paid to Bruno; repeating this process for all possible rent levels reveals the entire set of Pareto-efficient allocations. [1]
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