MECZQO: Microeconomics Homework Assignment 6 Problem 1. The Lerner index, formalized in 1934 by economist Abba Lerner, is a way to measure a rm's market power. It is dened by: _PMgC _ P where P is the price and M90 is the marginal cost. L : (1.1) Explain why L can be interpreted as measuring market power. (1.2) Using the markup pricing formula we saw in class, write an expression for L in terms of the price elasticity of demand 5. (1.3) If a rm with market power faces a price elasticity of demand 5 = 3, what is its Lerner index? Problem 2. A friend of yours is considering developing a new app. Developing this app would cost 500. After it is developed, the app can be made available to any number of customers at zero additional cost. The inverse demand function for this app is P[Q) = 100 Q. (2.1) What is the xed cost of this app? What is the variable cost? (2.2) Find the price that your friend should charge for the app and the prot your friend would make. (2.3) Suppose that, after your friend develops the app, the market becomes per~ fectly competitive. Calculate the short-run supply function of your friend's company. (2.4) Would you recommend that your friend develops this app if you expect the market to become perfectly competitive immediately after it is developed? Justify. Problem 3. The inverse demand function in the market for industrial thermo- static valves is given by P(Q) = 100 Q2. The monopolist in this market has a total cost function C(Q) = IUQQ. (3.1) Calculate the price elasticity of demand when the price is P = 25. (3.2) Find the prot-maximizing quantity when the rm can perfectly price dis- criminate. (3.3) Find the prot-maximizing quantity when the firm cannot price discriminate. Problem 4. A high-end lamp monopolist operates in the Midwest where the demand for lamps is given by Q1031) = 200 P1. Producing lamps costs 10 per unit. (4.1) Derive the prot maximizing price and the prots at this price. (4.2) What is the demand elasticity at this price? The monopolist has the opportunity to expand to the East Coast. This would entail launching an advertising campaign at a cost of 1000, a onetime expense. The demand on the East Coast is given by Q2(Pg) = 160 3P2. The per-unit cost of selling lamps on the East Coast is identical to the cost of selling them in the Midwest. Suppose the monopolist must charge the same price in both markets. [4.3) What is the total demand when the monopolist charges a price P? (4.4) Derive the prot maximizing price and the prots at this price in the case where the monopolist must charge the same price in both markets. Would you recommend the monopolist to expand to this market? Now suppose that the monopolist will sell through a network of distributors, and can charge different prices on the East Coast and in the Midwest. [4.5) What price would the monopolist charge in the Midwest? What price would the monopolist charge in the East? What are the total prots? Would you recommend the monopolist to expand in this case? Problem 5. Sal's satellite company provides ultrafast internet to subscribers in LA and NY. The demand functions are QM = 50 (l/3)PNy and QM = 80 (2/3)PLA where Q is in thousands of subscriptions per year and P is the subscription price per year. The cost of pr0viding Q units of service is given by TC : 1000 + 30Q Where Q : QJ'VY + QLA' [5.1) What are the profit-maximizing prices and quantities for the NY and LA markets? (5.2) As a consequence of a new technology that the Pentagon developed, sub- scribers in LA are now able to get the NY broadcast and vice versa so Sal can charge only a single price. What price should Sal charge? [5.3) In which situation is Sal better off? In terms of consumers\" surplus which situation do people in LA prefer and which do people in NY prefer? Why