Monopoly Problems M1). Why for a monopoly, marginal revenue is less than price? M2). If the inverse demand function for a monopoly's product is p = 100 - 6Q, what is the firm's marginal revenue function ? M3). If the inverse demand curve a monopoly faces is p = 30 - 2Q, and MC is constant at 2, then what quantity is profit maximizing for the monopoly? M4). A monopoly incurs a marginal cost of $1 for each unit produced. If the price elasticity of demand at the monopoly optimum equals 1.5, what price should monopoly charge to maximize its profits? M5). A monopoly sets a price of $25 per unit for an item that has a marginal cost of $10. Assuming profit maximization, what is the demand elasticity? M6). If the inverse demand curve a monopoly faces is p = 30 - 2Q, and MC is constant at 2, then what is the deadweight loss from monopoly? M7). Why does this cost function suggests a natural monopoly? TC = 500 + 5Q M8) What is the justification for patents giving an inventor a monopoly for a product? (M9) John Gardner is the city planner in a medium sized city. The city is considering a proposal to award an exclusive contract to Clear Vision, Inc., a cable television carrier. Mr. Gardner has discovered that an the demand in the city and C,, and total cost of Clear Vision are equal to: P= 28- 0.0008Q and TC= 120,000 + 0.0006Q2 where Q the number of cable subscribers and P the price of basic monthly cable service. Mr. Gardner knows relatively little economics and has hired you to answer the questions listed below. a. What price and quantity would be expected if the firm is allowed to operate completely unregulated? b. Mr. Gardner has asked you to recommend a price and quantity that would be socially efficient. Recommend a price and quantity to Mr. Gardner using economic theory to justify your answer. Compare the economic efficiency implications of (a) and (b) above. Your answer need not include numerical calculations, but should include relevant diagrams to demonstrate deadweight loss.(from questions 6 to 9)