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Natural Monopoly and Inducing the Right Behavior: The demand for a product is Q = 100P. The product is produced by a regulated monopoly. The

Natural Monopoly and Inducing the Right Behavior: The demand for a product is Q = 100P. The product is produced by a regulated monopoly. The marginal cost of production is MC = 10. The marginal cost is known to the monopolist, but not to the regulator.

(a) What is the formula for the consumer surplus CS(P) at price P?

(b) What price maximizes the total surplus?

(c) If the monopolist chooses price P, in addition to its profits it gets a subsidy from the government equal to CS(P). What price will the monopolist choose to maximize its payoffs?

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