Monopoly: Through its patented welding and riveting process, Iron-head, Inc. is a monopoly manufacturer and distributor of metal head plates worn in the skull region by unfortunates who have sustained severe head trauma. The annual market demand for head plates is P = 500 - ½Q. Total cost for Iron-head is C = 100 - 2Q + 0.5Q2.
a) Graph the demand curve, marginal revenue curve, average cost curve, and marginal cost curve for Iron-head.
b) Using calculus, derive the profit maximizing quantity of head plates released on to the market by Iron-head, the monopolistic price in equilibrium, total revenues, total costs, and profit for Iron-head under its monopoly power.
c) Suppose now that Iron-head's patent expires after 20 years of economic profit-making activity. Entry costs are small, and the market becomes perfectly competitive. (Assume that marginal costs for Iron-head are the same as the competitive market supply curve.) What is the new equilibrium quantity under perfect competition? Equilibrium price?
d) Calculate the social welfare loss that was suffered under the Iron-head monopoly during each year under the patent. How might this loss be socially justified?