Problem 5 [Regulation of a natural monopoly] Imagine that the demand and the cost function in a market is the following: P = 10-Q C = q2 +9 A. Consider that in the market there is a monopoly regulated with the first best prices. Calculate the prices, the profit of the monopoly and the consumer surplus. B. Consider that in the market there is a monopoly regulated with the second best prices. Calculate the prices, the profit of the monopoly and the consumer surplus. C. Consider that in the market there is a monopoly regulated with the optimal non-linear prices. Calculate the prices, the profit of the monopoly and the consumer surplus. D. Assume now that the monopoly is regulated with the first best prices. Taking into account the cost structure in the market, do you expect the entry of other firms? Argue your