1Chapter 11MonopolyKey issues1. monopoly profit maximization: MR = MC2. market power3. monopoly welfare effects: p > MC ⇒ DWL 4. cost advantages that create monopolies5. government actions that create monopolies6. government actions that reduce market power7. dominant firm and competitive fringeApplications and problems1.granting TV monopoly rights2.monopolizing by merging3.Botox: patent monopoly4.controlling key ingredient5.price of textbooks6.Chinese monopoly becomes dominant firm2Monopoly• monopoly: only supplier of a good for which there is no close substitute• monopoly's output is the market output: q = Q• monopoly's demand curve is market demand curve• its demand curve is downward sloping• it doesn't lose all its sales if its raises its price• it is a price setterProfit maximizationall firms maximize profits by choosing quantity such thatmarginal revenue = marginal cost MR(Q) = MC(Q)Marginal revenue•firm's MR curve depends on its demand curve• monopoly's MR curve• lies below its demand curve at any positive quantity• because its demand curve is downward sloping• demand curve shows price, p, it receives for selling a given quantity, Q• price = p = average revenue3Marginal revenue, MR• change in revenue from selling one more unit• MR = ∆R/∆Q (Calculus: MR = dR(Q)/dQ)• if firm sells exactly one more unit, ∆Q = 1,• its marginal revenue is MR = ∆R• ∆R = R2–R1• MR < p at any given Q for a monopoly (but not for a competitive firm)Figure 11.1a Average and Marginal RevenuePrice, p,$ per unitqq+ 1Quantity, q, Units per yearp1(a) Competitive FirmDemand curveABR1= A R2= A + B∆R = R2–R1= B = p1Figure 11.1b Average and Marginal RevenueQQ+ 1Quantity, Q, Units per yearp1p2Price, p,$ per unit(b) MonopolyDemand curveABCR1= A + CR2= A + B∆R = R2–R1= B – C = p2-C4Deriving monopoly’s MR curve• monopoly increases its output by ∆Q, • by lowering its price per unit by ∆p/∆Q (slope of demand curve)• so monopoly loses (∆p/∆Q) × Q on units originally sold at higher price: area C• but earns an additional p on extra output: area B • thus: MR = p + (∆p/∆Q) × Q= p + a negative term < pCalculus derivation• monopoly’s revenue is R(Q) = p(Q)Q• differentiating with respect to Q: • thus: MR = p + a negative term < p() ()()dR Q dp QMR p Q QdQ dQ==+Figure 11.2 Elasticity of Demand and Total, Average, and Marginal Revenuep, $ per unitDemand ( p = 24 – Q)Perfectly elasticPerfectlyinelasticElastic, ε< –1Inelastic, –1 < ε< 0ε= –1∆p = –1∆Q = 1∆Q = 1∆MR= –2Q, Units per day241201224MR = 24 – 2Q5Linear MR curve• for all linear demand curves, p = a - bQ• MR curve is a straight line, MR = a -2bQ• MR curve hits vertical (price) axis where demand curve does• slope of MR curve = 2 × slope of demand curve• MR curve hits horizontal axis at half the quantity as the demand curveIn our example• p = 24 – Q•so a = 24 and b = 1• ∆p /∆Q = -1• hence MR = p + (∆p/∆Q) × Q= (24 – Q) + (-1) × Q = 24 – 2QUsing calculusR(Q) = p(Q)Qif linear:R(Q) = [a - bQ]Q = aQ - bQ2MR = dR/dQ = a -2bQ6MR and elasticity of demand• MR at any given quantity depends on• demand curve's height (price)• demand curve's shape (elasticity)• thus, it depends on its elasticityDerive MR/elasticity formula• demand elasticity:ε= (∆Q/Q)/(∆p/p) = (∆Q/∆p)(p/Q)• MR = p + (∆p/∆Q) × Q= p + (∆p/∆Q)(Q/p)p11pε=+MR and price• MR• MR closer to p the more elastic is demand• where demand curve hits price axis (Q = 0), demand curve is perfectly elastic ⇒ MR = p• MR = 0 where demand elasticity is ε= -1• MR < 0 where demand is inelastic: 0 0ε> -111pε=+7Table 11.1 Quantity, Price, Marginal Revenue, and Elasticity for the Linear Inverse Demand Curve p=24-QFigure 11.2 Elasticity of Demand and Total, Average, and Marginal Revenuep, $ per unitDemand ( p = 24 – Q)Perfectly elasticPerfectlyinelasticElastic, ε< –1Inelastic, –1 < ε< 0ε= –1∆p = –1∆Q = 1∆Q = 1∆MR= –2Q, Units per day241201224MR = 24 – 2QChoosing price or quantity• monopoly can set p or Q to maximize its profit, π• monopoly is constrained by market demand curve• it cannot set both Q and p (cannot pick a point above demand curve)• if monopoly sets p, demand curve determines Q• if monopoly sets Q, demand curve determines p• because monopoly wants to maximize π, it chooses same profit-maximizing solution whether it sets p or Q8Profit maximizationall firms, including monopolies, use a two-step analysis1. firm determines output, Q*, at which it makes highest π, where • MR = MC• in elastic portion of demand curve2. firm decides whether to produce Q* or shut down: p 0 AVCFigure 11.3 Maximizing Profit1218248610814460601224R, π, $012624ACAVCeDemandπ= 60MCMRQ, Units per dayRevenue, RProfit, πQ, Units per dayp, $ per unit(a) Monopolized Market(b) Profit, RevenueSR cost in our example• C(Q) = Q2+ 12• MC = dC(Q)/dQ = 2Q• AVC = VC/Q = Q2/Q = Q• AC = C/Q = (Q2+ 12)/Q = Q + 12/Q9Profit is maximized where • MR = 24 – 2Q = 2Q = MC⇒ Q = 6• inverse demand: p = 24 – Q = 24 – 6 = 18• AVC = Q = 6 < p = 18 so produce• π > 0 because AC = Q + 12/Q = 8 < p = 18 Market powerability of a firm to charge a price above marginal cost profitably No check on bank market powerbanks exercise substantial market power on the rate for bounced checks• although you had no idea that a check wouldn't clear, your bank charges you an average of $4.75 to $7.50 (up to $10)• large banks charge more than small ones• bad check writer also pays an average of $15 to $19.50 (up to $30)10Bank costs • bank's handling fees for bad checks = $1.32• most checks eventually clear (check writer merely miscalculated balances)• even including losses from fraud, total MC= $2.70 (Center for the Study of Responsive Law) • thus, banks are exercising substantial market power: price > MCMarket power and shape of demand curve• market power depends on shape of demand curve (elasticity)• at profit-maximizing quantity:11MRp MCε=+=()111/pMCε=+Lerner index (price markup)1pMCpε−=−• Lerner index is (p – MC)/p• if firm profit maximizes,• Lerner index ranges from 0 to 1• p 0 MC•0/ p – MC / p•0/ (p – MC)/p / p/p = 111Causes of market powermonopoly's demand curve is relatively inelastic if• consumers are willing to pay
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