Understanding Monopoly Dynamics and Market Failures in
School
Northumbria University**We aren't endorsed by this school
Course
ECN AF5041
Subject
Economics
Date
Dec 11, 2024
Pages
3
Uploaded by DoctorPorcupinePerson1200
Seminar Market Failures Week 2 AF5041 Intermediate Micro PROBLEM SET 2 Monopoly 1.A monopolist faces a demand curve, ?π·= 120 β 2π, and costs,πΆ(?) = 20? + 100. a)Write the monopolist's profits in terms of the price it charges. π = π? β πΆ(?) = π(120 β 2π) β [20(120 β 2π) + 100]β π = 120π β 2π2β 2400 + 40π β 100 = 160π β 2π2β 2500b)Use the derivative (wrtprice) to determine the monopolist's profit-maximizing price. ππππ= 160 β 4π = 0 βΉ ππ= 40c)Now, derive the monopolist's inverse demand based on the demand equation above. Write out the monopolist's profits in terms of quantity. π = 60 β 0.5?π·π = π? β ππΆ = (60 β 0.5?)? β (20? + 100) = 60? β?22β 20? β 100d)Use the derivative wrtQ to determine the monopolist's optimal quantity. What price does the monopoly charge? πππ?= 60 β ? β 20 = 0 βΉ ?π= 40ππ= 60 β 0.5?π= 402.Consider a town with a single movie theatre, and that movie theatre faces a downward sloping demand curve for its tickets. The movie theatre has a fixed number of seats available for each show but the marginal cost of filling a seat is zero. Why might it be in the movie theatreβsinterest to not to sell out every show even though the marginal cost of selling additional seats is virtually zero? (Hint: Use a graph and figure out how the fixed number of seats affects output decision i.e., compare MR and MC and based on capacity whether to leave seats empty or sell out all seats)
Seminar Market Failures Week 2 AF5041 Intermediate Micro The firm may or may not choose to sell out the theater depending on the demand (and marginal revenue). The firm will sell up until the marginal revenue is zero. If this occurs at a quantity less than the theater capacity, then it's optimal to leave empty seats. If the marginal revenue is zero beyond the capacity, then the firm will sell out all of its seats.Deadweight Loss 3.Suppose that market demand for a good is ? = 480 β 2π. The marginal cost is ?πΆ = 2?. Calculate the deadweight loss resulting from a monopoly in this market. First, solve for the competitive equilibrium by substituting MC for p in the demand equation and solve for Q. Q = 480 - 2(2Q) = 480 - 4Q. Rearranging yields 5Q = 480, or Q = 96. Since price equals marginal cost, p = 2(96) = 192. Second, solve the monopoly output by setting marginal revenue equal to marginal cost. Rewrite the demand curve as p = 240 - 1/2Q so that MR = 240 - Q. Setting MR = MC yields 240 - Q = 2Q or Q = 80. For this quantity, a monopoly can charge a price of 200 and the marginal cost at that output level is 160. The deadweight loss is [(200 - 160) β(96 - 80)]/2 = 320. Natural Monopoly 4.The average cost for a typical electric-power-production firm is π΄πΆ = 100 β 10? + ?2where Q is measured in billion kilowatt hours per day. At the current regulated price, consumers demand 4 billion kilowatt hours per day. Is this market a natural monopoly? If demand increases to 10 billion kilowatt hours, is this market a natural monopoly? Explain. The firm enjoys economies of scale up to 5 billion kilowatt hours (kwhr) per day (Minimum AC). At 4 billion kwhr per day, the firm is a natural monopoly. At 10 billion kwhr per day, this firm is no longer a natural monopoly. Monopsony 5.Show with a graph that an increase in the minimum wage can increase the level of employment in a monopsony market
Seminar Market Failures Week 2 AF5041 Intermediate Micro 6.Demand for labour in a given market is ?π·= 100 β 2π€and supply is ?π= 2π€. Compare the competitive and monopsony equilibrium levels of employment and wage For the competitive market solution, set ?π= ?π·βΉ 100 β 2π€ = 2π€ βΉ π€π= 25For the monopsony solution, calculate ?πΈπΏand set it equal to demand for the employment level; then plug L*into the supply curve to get the equilibrium wage. ?πΈπΏ= π€(?π) + ?ππ€π?= 0.5? + ? β 0.5 = ?π€(?π·) = 50 β 0.5?Set ?πΈπΏ= π€(?π·) βΉ ? = 50 β 0.5? βΉ ?β= 33.3 πππ π€β= 16.677.Suppose a monopoly producer is also a monopsonist in the labour market. Demand for the output is π = 100 β ?. The production function is ? = ?, and the labour supply curve is π€ = 10 +?. How much labour does the firm hire? What wage is paid? The firm's marginal revenue product of labor is ??? = 100 β 2?. Marginal expenditure is 10 + 2?. Setting them equal yields 10 + 2? = 100 β 2?or ? = 90/4 = 22.5units of labor, for which the firm will pay a wage of (10 + ?) = 32.5.