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3. [25] Assume a natural monopoly with total cost TC 2 500+ 2062 and facing a demand Q = 100 P. Round solutions to the second decimal. (a) [7] Find the price the monopolist would choose and the quantity it would produce. (b) [10] The regulatory authority decides to regulate this industry by means of a Loeb and Magat incentive mechanism. That is, if the monopoly sets a price 13, the regulator agrees to pay the rm an amount equal to the consumer surplus at 13. What will the new price be? How much will the regulator end up paying the monopoly? (c) [8] Many taxpayers start to complain about the money the government is paying the monopoly. As a response, the regulator changes the regulation to Ramsey pricing, ordering the rm to set the price that maximizes welfare subject to the constraint that the rm makes zero prots. Find the Ramsey price of this