Quản trị kinh doanh - Chapter 11: Monopoly and monopsony

1Monopoly and MonopsonyChapter 11Copyright (c)2014 John Wiley & Sons, Inc.2Chapter Eleven OverviewThe Monopolist’s Profit Maximization ProblemThe Profit Maximization ConditionEquilibriumThe Inverse Pricing Elasticity Rule2. Multi-plant Monopoly and Cartel ProductionThe Welfare Economics and MonopolyChapter ElevenCopyright (c)2014 John Wiley & Sons, Inc.3Chapter ElevenA MonopolyDefinition: A Monopoly Market consists of a single seller facing many buyers.The monopolist's profit maximization problem:Max (Q) = TR(Q) - TC(Q) Qwhere: TR(Q) = QP(Q) and P(Q) is the (inverse) market demand curve.The monopolist's profit maximization condition: TR(Q)/Q = TC(Q)/Q MR(Q) = MC(Q)Copyright (c)2014 John Wiley & Sons, Inc.4Chapter ElevenA Monopoly – Profit MaximizingAlong the demand curve, different revenues for different quantitiesProfit maximization problem is the optimal trade-off between volume (number of units sold) and margin (the differential between price).Monopolist’s demand Curve is downward-sloping Copyright (c)2014 John Wiley & Sons, Inc.5Chapter ElevenA Monopoly – Profit MaximizingDemand Curve:Total Revenue:Total Cost (Given):Profit-Maximization: MR = MC Copyright (c)2014 John Wiley & Sons, Inc.6Chapter ElevenA Monopoly – Profit MaximizingAs Q increases TC increases, TR increases first and then decreases.Profit Maximization is at MR = MCCopyright (c)2014 John Wiley & Sons, Inc.7Chapter ElevenA Monopoly – Profit MaximizingMR>MC, firm can increase Q and increase profitMR0Copyright (c)2014 John Wiley & Sons, Inc.13Chapter ElevenAverage RevenueSinceThe price a monopolist can charge to sell quantity Q is determined by the market demand curve the monopolists’ average revenue curve is the market demand curve.Copyright (c)2014 John Wiley & Sons, Inc.14Chapter ElevenMarginal Revenue and Average RevenueThe demand curve D and average revenue curve AR coincideThe marginal revenue curve MR lies below the demand curveCopyright (c)2014 John Wiley & Sons, Inc.15Chapter ElevenMarginal Revenue and Average RevenueWhen P decreases by $3 per ounce, (from $10 to $7), quantity increases by 3 million ounces (from 2 million to 5 million per year)Copyright (c)2014 John Wiley & Sons, Inc.16Chapter ElevenMarginal Revenue and Average RevenueConclusions if Q > 0:MR 0 When demand is inelastic ( > -1), MR 0Inelastic region (0>>-1), MR 1 ("demand is everywhere elastic") to get an interior solution. As b -> 1 (demand becomes everywhere less elastic), P* -> infinity and P - MC, the "price-cost margin" also increases to infinity.As b -> , the monopoly price approaches marginal cost.Elasticity Region of the Demand CurveCopyright (c)2014 John Wiley & Sons, Inc.33Definition: An agent has Market Power if s/he can affect, through his/her own actions, the price that prevails in the market. Sometimes this is thought of as the degree to which a firm can raise price above marginal cost.Chapter ElevenMarket PowerCopyright (c)2014 John Wiley & Sons, Inc.34Chapter ElevenThe Lerner Index of Market PowerDefinition: the Lerner Index of market power is the price-cost margin, (P*-MC)/P*. This index ranges between 0 (for the competitive firm) and 1, for a monopolist facing a unit elastic demand.Copyright (c)2014 John Wiley & Sons, Inc.35Chapter ElevenThe Lerner Index of Market PowerRestating the monopolist's profit maximization condition, we have: P*(1 + 1/) = MC(Q*) or [P* - MC(Q*)]/P* = -1/In words, the monopolist's ability to price above marginal cost depends on the elasticity of demand. Copyright (c)2014 John Wiley & Sons, Inc.36Chapter ElevenComparative Statics – Shifts in Market DemandRightward shift in the demand curve causes an increase in profit maximizing quantity.(a) MC is increases as Q increases(b) MC decreases as Q increasesCopyright (c)2014 John Wiley & Sons, Inc.37Chapter ElevenComparative Statics – Monopoly Midpoint RuleFor a constant MC, profit maximizing price is found using the monopoly midpoint rule – The optimal price P* is halfway between the vertical intercept of the demand curve a (choke price) and vertical intercept of the MC curve c.Copyright (c)2014 John Wiley & Sons, Inc.38Chapter ElevenComparative Statics – Monopoly Midpoint RuleGiven P and MC what is the profit maximizing P and Q?Copyright (c)2014 John Wiley & Sons, Inc.39Chapter ElevenComparative Statics – Shifts in Marginal CostWhen MC shifts up, Q falls and P increases.Copyright (c)2014 John Wiley & Sons, Inc.40Chapter ElevenComparative Statics – Revenue and MC shiftsUpward shift of MC decreases the profit maximizing monopolist’s total revenue.Downward shift of MC increases the profit maximizing monopolist’s total revenue.Copyright (c)2014 John Wiley & Sons, Inc.41Chapter ElevenMulti-Plant MonopolyRecall: In the perfectly competitive model, we could derive firm outputs that varied depending on the cost characteristics of the firms. The analogous problem here is to derive how a monopolist would allocate production across the plants under its management.Assume: The monopolist has two plants: one plant has marginal cost MC1(Q) and the other has marginal cost MC2(Q). Copyright (c)2014 John Wiley & Sons, Inc.42Chapter ElevenWhenever the marginal costs of the two plants are not equal, the firm can increase profits by reallocating production towards the lower marginal cost plant and away from the higher marginal cost plant.Example:Suppose the monopolist wishes to produce 6 units3 units per plant with MC1 = $6 MC2 = $3Reducing plant 1's units and increasing plant 2's units raises profitsMulti-Plant Monopoly – Production AllocationCopyright (c)2014 John Wiley & Sons, Inc.43QuantityPriceMC1MCT3 6 9•36Chapter ElevenMulti-Plant Monopoly – Production AllocationExample: Multi-Plant MonopolistThis is analogous to exit by higher cost firms and an increase in entry by low-cost firms in the perfectly competitive model.Copyright (c)2014 John Wiley & Sons, Inc.44MC2••36Chapter ElevenQuantityPriceMC1MCT3 6 9Multi-Plant Monopoly – Production AllocationExample: Multi-Plant MonopolistThis is analogous to exit by higher cost firms and an increase in entry by low-cost firms in the perfectly competitive model.Copyright (c)2014 John Wiley & Sons, Inc.45Question: How much should the monopolist produce in total? Definition: The Multi-Plant Marginal Cost Curve traces out the set of points generated when the marginal cost curves of the individual plants are horizontally summed (i.e. this curve shows the total output that can be produced at every level of marginal cost.)Example:For MC1 = $6, Q1 = 3MC2 = $6, Q2 = 6Therefore, for MCT = $6, QT = Q1 + Q2 = 9Chapter ElevenMulti-Plant Marginal Costs CurveCopyright (c)2014 John Wiley & Sons, Inc.46Chapter ElevenMulti-Plant Marginal Costs CurveThe profit maximization condition that determines optimal total output is now: MR = MCTThe marginal cost of a change in output for the monopolist is the change after all optimal adjustment has occurred in the distribution of production across plants. Copyright (c)2014 John Wiley & Sons, Inc.47QuantityPriceMCTMRP*MC1Chapter ElevenMulti-Plant Monopolistic MaximizationMC2Copyright (c)2014 John Wiley & Sons, Inc.48QuantityMCTDemandQ*1 Q*2 Q*TChapter ElevenPriceMRP*MC1MC2Multi-Plant Monopolistic MaximizationCopyright (c)2014 John Wiley & Sons, Inc.49Chapter ElevenMulti-Plant Monopolistic MaximizationExample:P = 120 - 3Q demandMC1 = 10 + 20Q1 plant 1MC2 = 60 + 5Q2 plant 2What are the monopolist's optimal total quantity and price?Step 1: Derive MCT as the horizontal sum of MC1 and MC2. Inverting marginal cost (to get Q as a function of MC), we have:Q1 = -1/2 + (1/20)MCTQ2 = -12 + (1/5)MCTACopyright (c)2014 John Wiley & Sons, Inc.50Chapter ElevenLet MCT equal the common marginal cost level in the two plants. Then: QT = Q1 + Q2 = -12.5 + .25MCTAnd, writing this as MCT as a function of QT: MCT = 50 + 4QTUsing the monopolist's profit maximization condition: MR = MCT => 120 - 6QT = 50 + 4QT QT* = 7 P* = 120 - 3(7) = 99Multi-Plant Monopolistic MaximizationCopyright (c)2014 John Wiley & Sons, Inc.51Chapter ElevenExample:P = 120 - 3Q demandMC1 = 10 + 20Q1 plant 1MC2 = 60 + 5Q2 plant 2What is the optimal division of output across the monopolist's plants?MCT* = 50 + 4(7) = 78Therefore,Q1* = -1/2 + (1/20)(78) = 3.4Q2* = -12 + (1/5)(78) = 3.6Multi-Plant Monopolistic MaximizationBCopyright (c)2014 John Wiley & Sons, Inc.52Chapter ElevenCartelDefinition: A cartel is a group of firms that collusively determine the price and output in a market. In other words, a cartel acts as a single monopoly firm that maximizes total industry profit.Copyright (c)2014 John Wiley & Sons, Inc.53Chapter ElevenThe problem of optimally allocating output across cartel members is identical to the monopolist's problem of allocating output across individual plants.Therefore, a cartel does not necessarily divide up market shares equally among members: higher marginal cost firms produce less.This gives us a benchmark against which we can compare actual industry and firm output to see how far the industry is from the collusive equilibriumCartelCopyright (c)2014 John Wiley & Sons, Inc.54Chapter ElevenThe Welfare Economies of MonopolySince the monopoly equilibrium output does not, in general, correspond to the perfectly competitive equilibrium it entails a dead-weight loss.Suppose that we compare a monopolist to a competitive market, where the supply curve of the competitors is equal to the marginal cost curve of the monopolistCopyright (c)2014 John Wiley & Sons, Inc.55MCDemandMRQMPMPCQCCS with competition: A+B+C ; CS with monopoly: A PS with competition: D+E ; PS with monopoly: B+DABCDEDWL = C+EChapter ElevenThe Welfare Economies of MonopolyCopyright (c)2014 John Wiley & Sons, Inc.56Chapter ElevenNatural MonopoliesDefinition: A market is a natural monopoly if the total cost incurred by a single firm producing output is less than the combined total cost of two or more firms producing this same level of output among them. Benchmark: Produce where P = ACCopyright (c)2014 John Wiley & Sons, Inc.57ACNatural Monopoly falling average costsChapter ElevenQuantityPriceDemandNatural MonopoliesCopyright (c)2014 John Wiley & Sons, Inc.58Chapter ElevenBarriers to EntryDefinition: Factors that allow an incumbent firm to earn positive economic profits while making it unprofitable for newcomers to enter the industry.Structural Barriers to Entry – occur when incumbent firms have cost or demand advantages that would make it unattractive for a new firm to enter the industryLegal Barriers to Entry – exist when an incumbent firm is legally protected against competitionStrategic Barriers to Entry – result when an incumbent firm takes explicit steps to deter entryCopyright (c)2014 John Wiley & Sons, Inc.59Chapter ElevenA MonopsonyDefinition: A Monopsony Market consists of a single buyer facing many sellers.The monopsonist's profit maximization problem:Max  = TR – TC = P*f(L) – w*Lwhere: Pf(L) is the total revenue for the monopsonist and w*L is the total cost.The monopsonist's profit maximization condition: MRPL = P*MPL = P (Q/L) = TC/L = w + L (w/L) = MEL Copyright (c)2014 John Wiley & Sons, Inc.60Chapter ElevenMonopsony - ExampleQ = 5LP = $10 per unitw = 2 + 2LMEL = w + L (w/L) = 2 + 4L MRPL = P*(Q/L) = 10*5 = 50 MEL = MRPL2 + 4L = 50 (or) L = 12W = 2 + 2L = $26Copyright (c)2014 John Wiley & Sons, Inc.61Chapter ElevenInverse Elasticity Pricing RuleMonopsony equilibrium condition results in:where:  is the price elasticity of labor supply, (w/L)(L/w)Copyright (c)2014 John Wiley & Sons, Inc.62Chapter ElevenThe Welfare Economies of MonopsonyCopyright (c)2014 John Wiley & Sons, Inc.