Monopoly • market with a single seller • Firm demand = market demand Monopoly • Firm demand is downward sloping • Monopolist can alter market price by adjusting its ECON 370: Microeconomic Theory own output level Summer 2004 – Rice University Stanley Gilbert Econ 370 - Monopoly 2 Causes of Monopolies Profit Maximization •Created by law ⇒ US Postal Service • We assume profit maximization • a patent ⇒ a new drug • Earlier we noted – profit maximization • sole ownership of a resource ⇒ a toll highway ⇒ – Marginal Revenue = Marginal Cost • formation of a cartel ⇒ OPEC • With monopolies, that is the relevant test • large economies of scale ⇒ local utility company (natural monopoly) Econ 370 - Monopoly 3 Econ 370 - Monopoly 4 1 Mathematically Significance dp(y) dc(y) p()y + y = π ()y = p ()y y − c ()y dy dy At profit-maximizing output y*: • Since demand is downward sloping: dp/dy < 0 – So a monopoly supplies less than a competitive market dπ ()y d dc(y) would = ()p()y y − = 0 – At a higher price dy dy dy • MR < Price because to sell the next unit of output it has to lower its price on all its product dp()y dc(y) p()y + y = – Not just on the last unit dy dy – Thus further reducing revenue Econ 370 - Monopoly 5 Econ 370 - Monopoly 6 Linear Demand Linear Demand Graph • If demand is q(p) = f – gp • Then the inverse demand function is p – p = f / g – q / g –Let a = f / g, and a –Let b = 1 / g – Then p = a – bq p(y) = a – by • Since output y = demand q, the revenue function is – p(y)·y = (a – by)y = ay – by2 y • Marginal Revenue is a / 2b a / b –MR = a –2by MR(y) = a –2by Econ 370 - Monopoly 7 Econ 370 - Monopoly 8 2 Profit-Maximization: An Example Graphically • Linear Demand: p(y) = a – by • Cost function c(y) = F + αy + βy2 p – So, MC = α +2βy a • At profit maximizing y*, MR = MC, So p(y) = a – by – a –2by = α –2βy p* a − α MC(y) = α + 2βy y* = 2(b + β ) α y* y * * a − α p()y = a − by = a − b 2(b + β ) MR(y) = a –2by Econ 370 - Monopoly 9 Econ 370 - Monopoly 10 Elasticity and Monopolistic Pricing Elasticity and Monopolistic Pricing 2 dp()y ⎡ y dp(y)⎤ MR()y = p ()y + y = p()y ⎢1+ ⎥ Since MR = MC, then dy ⎣ p()y dy ⎦ * ⎡ 1⎤ * p(y ) 1+ = MC(y ) Since Own-price elasticity of demand is ⎣⎢ ε ⎦⎥ p()y dy ε = y dp()y In particular, note that: * ⎡ 1⎤ 1 p(y ) 1+ ≥ 0 ⇒ 1+ ≥ 0 ⇒ ε ≤ −1 ⎡ 1⎤ ⎢ ε ⎥ ε Then MR()y = p ()y 1+ ⎣ ⎦ ⎣⎢ ε ⎦⎥ Econ 370 - Monopoly 11 Econ 370 - Monopoly 12 3 Markup Pricing Pure Profits Tax Levied on a Monopoly • One Interpretation of the elasticity results is • Pure profits tax levied at rate t Markup pricing – Reduces profit from π(y*) to (1 – t)π(y*) – Output price = MC + “markup” – Monopolist maximizes after-tax profit, (1 – t)π(y*) • Issues – Same as maximizing before-tax profit, π(y*) – How big is a monopolist’s markup? • Implications – How does it change with the own-price elasticity of – Profits tax has no effect on monopolist’s choices of demand? output, price or input demands – The profits tax is a neutral tax Econ 370 - Monopoly 13 Econ 370 - Monopoly 14 Quantity Tax Levied on a Monopolist Quantity Tax Graph • A quantity tax of $t per output unit – Raises the marginal cost of production by $t p – Reduces profit-maxing output – Causes market price to rise – Input demands to fall t p MC(y) + t • The quantity tax is distortionary p* MC(y) yt y* y MR(y) Econ 370 - Monopoly 15 Econ 370 - Monopoly 16 4 Tax impact on Consumers Tax impact on Consumers • Can a monopolist “shift” all of a $t quantity tax to (k + t)ε kε tε p( y t ) − p( y*) = − = consumers? 1 + ε 1 + ε 1 + ε • Suppose MC= k (constant) kε • is amount of tax shifted to buyers. • With no tax (MR=MC=k): p( y*) = 1 + ε •E.g. if ε = -2, amount of tax shifted is 2t • Tax increases MC to (k+t), changing profit- • In general, if ε < -1 (always true for monopolist) maximizing price (MR=MC=k+t) to – ε /(1 + ε) > 1, and (k + t)ε – monopolist passes on more than the tax! p( yt ) = 1 + ε • The amount of tax shifted to buyers is: p(yt) – p(y*) Econ 370 - Monopoly 17 Econ 370 - Monopoly 18 Inefficiency of Monopoly: Graph Inefficiency of Monopoly: Graph • Efficient output level ye satisfies p(y) = MC(y) • Both buyer and seller could gain from production of one more unit…so Pareto Inefficient • Total gains-from-trade are maximized p p DWL p(y) p(y) p* CS CS pe MC(y) pe PS MC(y) PS ye y y* ye y Econ 370 - Monopoly 19 Econ 370 - Monopoly 20 5 Regulating Monopolies Generally Natural Monopoly: Introduction • Licensing (patents) • Natural monopoly – Technology has very large economies-of-scale • Antitrust Remedies – Firm can supply whole market at lower average total – Conduct Remedies cost than possible with more than one firm – Structural Remedies • Regulation (especially natural monopolies) • Considerations – Firm must be allowed to earn profit ≥ 0 – A Firm will use private information to its own advantage – Law of unintended consequences Econ 370 - Monopoly 21 Econ 370 - Monopoly 22 Natural Monopoly: Graph Regulating a Natural Monopoly: Intro $/output unit • Problem facing regulators – Want efficient output (p = MC) ATC(y) –Want DWL = 0 – But impossible with natural monopoly • At efficient output ye, ATC(ye) > p(ye) p* Demand • Regulated monopoly has an economic loss MR(y) DWL MC(y) y y* Econ 370 - Monopoly 23 Econ 370 - Monopoly 24 6 Regulating a Natural Monopoly: Graph Regulating a Natural Monopoly $/output unit • Natural monopoly cannot use p = MC – If so, profit is < 0 ATC(y) – Monopolist will exit – Destroys both the market and any gains-to-trade • Regulatory schemes induce natural monopolist to produce the efficient output w/o exiting Demand MR(y) MC(y) ATC pe Economic Loss y ye Econ 370 - Monopoly 25 Econ 370 - Monopoly 26 Alternative Forms of Monopoly Pricing Types of Price Discrimination • Uniform pricing – single price to all customers • 1st-degree – Each output unit is sold at a different price • Price-discrimination – Prices differ across buyers – Charge different prices to different customers – Requires different markets w/ no trade • 2nd-degree – Price varies with quantity demanded by buyer – Also requires different elasticities – All customers face the same price schedule – Can only raise profits (or get same) • 3rd-degree price discrimination – Price paid by buyers in group is same for all units – Price differs across buyer groups • senior citizen discounts • student discounts • no discounts for middle-aged persons Econ 370 - Monopoly 27 Econ 370 - Monopoly 28 7 1st-degree Price Discrimination: Intro 1st-degree Price Discrimination: Graph • Each output unit is sold at a different price Sell the y’th unit for $p(y’) • Requires that monopolist can discover Sell the y’’th unit for $p(y’’) – the buyer w/ the highest valuation of its product Sell the y’’’ th unit for MC $p(y’’’) – the buyer w/ the next highest valuation $ – Etc., etc., etc. p(y′) p(y′′) MC(y) p(y′′′) p(y) y′ y′′ y′′′ y Econ 370 - Monopoly 29 Econ 370 - Monopoly 30 1st-degree Price Discrimination: Graph 1st-degree Price Discrimination: Graph • Gains to monopolist on these trades are: • The monopolist gets the maximum p(y´) – MC(y´), p(y´´) – MC(y´´), and possible gains from trade zero • First-degree price discrimination • The consumers’ gains are zero $ $ is Pareto-efficient p(y′) p(y′′) MC(y) PS MC(y) p(y′′′) p(y) p(y) y′ y′′ y′′′ y y′′′ y Econ 370 - Monopoly 31 Econ 370 - Monopoly 32 8 1st-degree Price Discrimination: Summary 2nd Degree Price Discrimination • First-degree price discrimination •2nd Degree Price discrimination includes – gives monopolist all possible gains-to-trade • 2-part tariffs – leaves buyers with zero consumer surplus – supplies efficient amount of output • Volume Discounts • Fixed Price-Quantity bundles – For example, mobile-phone service is sold this way Econ 370 - Monopoly 33 Econ 370 - Monopoly 34 Two-part tariffs Two-Part Tariffs: Entrance Fee • Two-part tariff • Two part tariff: p1 + p2x – lump-sum fee p1 plus •What p1? is maximum entrance fee = p1? – price p2 for each unit purchased •Maximum p = surplus buyer gains from entering • Thus the cost of buying x units of product is 1 the market • p + p x 1 2 • So, monopolist strategy: –Set p1 = CS – Solve for optimal p2 Econ 370 - Monopoly 35 Econ 370 - Monopoly 36 9 Two-Part Tariffs: Graph Two-Part Tariffs: Graph Should the monopolist set p2 = MC? Should the monopolist set p2 = MC? p1 = CS PS is profit from sales $/output $/output unit p(y) unit p(y) Total profit MC(y) CS p2 = p(y′′) MC(y) p = p(y′′) 2 PS y′′ y Econ 370 - Monopoly 37 Econ 370 - Monopoly y′′ y 38 Two-Part Tariffs: Maximizing Profits 3rd-degree Price Discrimination • Monopolist maximizes profit w/ two-part tariff • Price paid by buyers in a given group is the same – setting unit price p2 = marginal cost and for all units purchased – setting its lump-sum entrance fee p equal to 1 • Price may differ across buyer groups (if demand Consumers’ Surplus at output where p = MC 2 elasticities are different) • Monopolist gets all gains from trade • Monopolist manipulates price by altering quantity • Outcome is efficient supplied to each market • How many units of product will the monopolist supply to each group? Econ 370 - Monopoly 39 Econ 370 - Monopoly 40 10 3rd-degree Price Discrimination 3rd-degree Price Discrimination: Profit • Two markets, 1 and 2 • For given supply levels y1 and y2 the firm’s profit is • y1 = quantity supplied to market 1 • π(y1, y2) = p1(y1)y1 + p1(y2)y2 –c(y1 + y2) • p1(y1) = inverse demand function in market 1 • What values of y1 and y2 maximize profit? • y2 = quantity supplied to market 2 • p2(y2) = inverse demand function in market 2 Econ