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Consider 5 farmers located close to a lake. The lake is used by 5 recreational users for swimming. The farmers use fertilizer with marginal benefits

Consider 5 farmers located close to a lake. The lake is used by 5 recreational users for swimming. The farmers use fertilizer with marginal benefits MB = 12 - 2x where x is the amount of fertilizer applied. The cost per unit of fertilizer is 4. The fertilizer runoff into the lake reduces the water quality. The marginal damage from fertilizer use through reduced water quality is MD = 0.08 X for each of the recreational users. X is the total amount of fertilizer that all farms combined apply. How high is the Pigovian tax that would implement the efficient solution?

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