2) Natural gas for residences is best provided by a monopoly due to economies of scale. Assume it costs the monopoly $4 per MMBtu for the gas and that monthly demand in MMBtus is given by D(P) = 12 - 0.2P for a typical household. This implies that the inverse demand is P(Q) = 60 - 50 and that the marginal revenue is MR = 60 - 100. a. Extra: Using algebra, verify the formula for the inverse demand. b. Extra: Using calculus, verify the formula for the marginal revenue. c. Calculate the unregulated monopoly price, quantity, monopoly profit, consumer surplus, and deadweight loss. d. Illustrate your answers on a graph.