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

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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)

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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

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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

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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 a − α y p()y* = a − by* = a − b 2(b + β ) MR(y) = a –2by

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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 ⎥ Then MR()y = p y ()⎡1+ ⎤ ⎣ ⎦ ε ⎣⎢ ε ⎦⎥

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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

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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)

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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*)

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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

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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

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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*

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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

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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

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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

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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

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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

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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

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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

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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?

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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

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Profit Maximization Implications

•MR(y ) = MC(y + y ) π ( y1, y2 ) = p1( y1) y1 + p2 ( y2 ) y2 − c( y1 + y2 ) i i 1 2 • Implies that –MR = MR = MC The profit-maximization condition is 1 2 – If marginal MR1 > MR2, then a unit of output should be moved from market 2 to market 1 ∂π ∂ ∂c( y1 + y2) ∂( y1 + y2) = ()pi ()yi yi − × = 0 –(why?) ∂yi ∂yi ∂( y1 + y2 ) ∂yi

⇒ MRi ()yi = MC y (1 + y2 )

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11 3rd-degree Price Discrimination: Graph Theory of Monopolistic Competition

MR1(y1*) = MR2(y2*) = MC • Monopolistic Competition – Elements of monopoly Market 1 Market 2 – Elements of perfect competition • Monopoly Elements p1(y1)

) – Each firm faces downward sloping demand * p (y )

1 2 2 ) y * – (Less than perfect substitutes) ( 2 1 y ( p

2 – Product differentiation p MC MC • Trademarks • Advertising y * y * 1 y1 2 y2

MR1(y1) MR2(y2)

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Theory of Monopolistic Competition Theory of Monopolistic Competition

• Competitive element • Equilibrium – Free entry – Each firm on its own demand curve – Zero profit in long run – Free entry implies zero long run profits – Firms compete in price and quantity, product features • Characteristics (product differentiation) – Firms produce to left of LRAC minimum point • Behavioral Assumption – Firms have “excess capacity” – Profit maximization, given downward sloping demand – Firms spend money on product differentiation (actual curve and specious) – But consumers get more product diversity

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12 Analysis of Factor Markets Input Demands

• Competitive firms factor demands • Competitive firm is price-taker in its output and input markets • Monopolist factor demands • Since Profit = Revenue – Cost • Assume: – i.e., π = R – C – Output price py

– Production Function y = F(x1, x2) • Profit Maximization implies:

– Prices p1, p2 for inputs x1, x2 respectively ∂π ∂R ∂C ∂R ∂C = − = 0 ⇒ = ∂x ∂x ∂x ∂x ∂x • We will analyze the firm’s demand curve for x1 1 1 1 1 1

– as price p1 varies • dR/dx1 is the Marginal Revenue Product (MRP1) – Holding other prices constant – Which we rewrite as:

– MRP1 = dR/dx1 = (dR/dy)(dy/dx1) = MR × MP1

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Competitive Firm’s Input Demands Monopolist’s Input Demands ∂C • For all firms: MRPi = MR × MPi = • If the firm is monopolist in output market, but ∂x1 price-taker in its input markets • For the competitive firm the marginal revenue of a • Then MRPi = MR(y) ×MPi = p1 unit of input i is py •Since, MR(y) < p for all y • And it treats input prices as given, y – Then in general, a monopoly will demand less input – so Cost C = p1x1 + p2x2 than a similarly situated competitive firm ∂C • Therefore = p1 ∂x1

• And MRPi = pyMPi = p1

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13 Monopolist’s Demands for Inputs: Graph Monopsonist’s Input Demands

• Assume the firm has no pricing power in output market, $/input unit – but is the sole buyer in its input markets • Assume the seller’s side of the market is perfectly py × MPi(xi) competitive

MR(y) × MPi(xi) dC d • Then: MRPi = pyMPi = = []p()x1 x1 + p2x2 dx1 dx1 p dp(x1) ⎡dp(x1) x1 ⎤ i pyMPi = x1 + p()x1 = ⎢ +1⎥ p()x1 dx1 ⎣ dx1 p()x1 ⎦ x*m x*c x ⎡1 ⎤ i i i pyMPi = ⎢ +1⎥ p()x1 ⎣η ⎦

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Monopoly v. Monopsony Monopoly v. Monopsony (cont)

Monopoly Monopsony Monopoly Monopsony

ME Decision Basis MC Supply p A MR = MC Marginal Benefit (MB) = MC y A (Where MB = MRP) B C C p y B 1 ⎡ 1⎤ p ⎡1+ ⎤ = MC p 1+ = MRP MR Demand MB y i ⎢ ⎥ i m m ⎣⎢ ε ⎦⎥ ⎣ η⎦ q q A = Consumer Surplus A = Consumer Surplus B = Producer Surplus B = Producer Surplus C = DWL C = DWL

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