A water supply company provides water to city of Richmond. The demand for water in city of Richmond is p(q) = 10-g, and this company's costs are c(g) = 1 + 2q. (a) Depict the following in a figure: the demand curve p(q), the associated marginal revenue MR(q), the marginal cost of production MC(q) and the average cost of production AC(q). Discuss why this situation illustrates a "natural monopoly". (b) Find the amount of water that this firm will produce if it is unregulated as a monopolist. Determine the corresponding prices and profits for the firm. (c) Determine the amount of water that this firm will produce if a regulatory agency in city of Richmond forces the firm to price according to marginal cost (i.c., to produce an amount of output q* that solves p(q) = MC(q)). Find the corresponding prices and profits for the firm when it is regulated. (d) Consider now that the regulatory agency allows the monopoly to charge two different prices: a high price p for the first units, and a low price p(q) for the remaining (q-91) (i.c., the units from 9 up to the output level you found in part (c), q*). In addition, the regulatory agency also imposes the condition that the firm cannot make any profits, = 0, when charging these two prices. Find the value of q and the associated price p(91). Depict these two prices and quantities in a figure and shade the areas of benefits and losses for the firm.