Monopoly. Monopoly. Causes of Monopolies. Profit Maximization. ECON 370: Microeconomic Theory. Summer 2004 Rice University Stanley Gilbert

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1 Monool market with a single seller Monool ECON 370: Microeconomic Theor Firm demand = market demand Firm demand is downward sloing Monoolist can alter market rice b adjusting its own outut level Summer 2004 Rice Universit Stanle Gilbert Econ Monool 2 Causes of Monoolies Created b law US Postal Service a atent a new drug sole ownershi of a resource a toll highwa formation of a cartel OPEC large economies of scale local utilit coman (natural monool Profit Maximization We assume rofit maximization Earlier we noted rofit maximization Marginal Revenue = Marginal Cost With monoolies, that is the relevant test Econ Monool 3 Econ Monool 4 1

2 π Mathematicall ( = ( c( At rofit-maximizing outut *: dπ d ( = d d ( ( ( dc d ( dc( d ( + = d d = 0 Significance ( dc( d ( + = d d Since demand is downward sloing: d/d < 0 So a monool sulies less than a cometitive market would At a higher rice MR < Price because to sell the next unit of outut it has to lower its rice on all its roduct Not just on the last unit Thus further reducing revenue Econ Monool 5 Econ Monool 6 Linear Demand Linear Demand Grah If demand is q( = f g Then the inverse demand function is = f / g q / g Let a = f / g, and Let b = 1 / g Then = a bq Since outut = demand q, the revenue function is ( = (a b = a b 2 Marginal Revenue is MR = a 2b a a / 2b ( = a b a / b MR( = a 2b Econ Monool 7 Econ Monool 8 2

3 Profit-Maximization: An Examle Linear Demand: ( = a b Cost function c( = F + α + β 2 So, MC = α +2β At rofit maximizing *, MR = MC, So a 2b = α 2β * a α = 2( b + β * * a ( = a b = a b α 2( b + β a * α Grahicall ( = a b * MC( = α + 2β MR( = a 2b Econ Monool 9 Econ Monool 10 Elasticit and Monoolistic Pricing ( d MR ( = ( + d Since Own-rice elasticit of demand is ( d ε = d 1 = 1 + ε Then MR( ( ( ( ( d = ( 1 + d Elasticit and Monoolistic Pricing 2 Since MR = MC, then * 1 * ( 1 MC( + = ε In articular, note that: * 1 ( ε 1 ε ε Econ Monool 11 Econ Monool 12 3

4 Marku Pricing One Interretation of the elasticit results is Marku ricing Outut rice = MC + marku Issues How big is a monoolist s marku? How does it change with the own-rice elasticit of demand? Pure Profits Tax Levied on a Monool Pure rofits tax levied at rate t Reduces rofit from π(* to (1 tπ(* Monoolist maximizes after-tax rofit, (1 tπ(* Same as maximizing before-tax rofit, π(* Imlications Profits tax has no effect on monoolist s choices of outut, rice or inut demands The rofits tax is a neutral tax Econ Monool 13 Econ Monool 14 Quantit Tax Levied on a Monoolist Quantit Tax Grah A quantit tax of $t er outut unit Raises the marginal cost of roduction b $t Reduces rofit-maxing outut Causes market rice to rise Inut demands to fall The quantit tax is distortionar t * MC( + t MC( t * MR( Econ Monool 15 Econ Monool 16 4

5 Tax imact on Consumers Can a monoolist shift all of a $t quantit tax to consumers? Suose MC= k (constant With no tax (MR=MC=k: kε ( * = 1 + ε Tax increases MC to (k+t, changing rofitmaximizing rice (MR=MC=k+t to t ( k + t ε ( = 1 + ε The amount of tax shifted to buers is: ( t ( * Econ Monool 17 t ( Tax imact on Consumers ( k + t ε kε tε ( * = = 1 + ε 1 + ε 1 + ε is amount of tax shifted to buers. E.g. if ε = -2, amount of tax shifted is 2t In general, if ε < -1 (alwas true for monoolist ε /(1 + ε > 1, and monoolist asses on more than the tax! Econ Monool 18 Inefficienc of Monool: Grah Efficient outut level e satisfies ( = MC( Total gains-from-trade are maximized Inefficienc of Monool: Grah Both buer and seller could gain from roduction of one more unit so Pareto Inefficient e CS PS ( MC( * e ( CS PS DWL MC( e * e Econ Monool 19 Econ Monool 20 5

6 Regulating Monoolies Generall Licensing (atents Antitrust Remedies Conduct Remedies Structural Remedies Regulation (eseciall natural monoolies Considerations Firm must be allowed to earn rofit 0 A Firm will use rivate information to its own advantage Law of unintended consequences Natural Monool: Introduction Natural monool Technolog has ver large economies-of-scale Firm can sul whole market at lower average total cost than ossible with more than one firm Econ Monool 21 Econ Monool 22 Natural Monool: Grah Regulating a Natural Monool: Intro $/outut unit ATC( Problem facing regulators Want efficient outut ( = MC Want DWL = 0 But imossible with natural monool * MR( Demand DWL At efficient outut e, ATC( e > ( e Regulated monool has an economic loss MC( * Econ Monool 23 Econ Monool 24 6

7 Regulating a Natural Monool: Grah Regulating a Natural Monool $/outut unit ATC( Natural monool cannot use = MC If so, rofit is < 0 Monoolist will exit Destros both the market and an gains-to-trade Demand Regulator schemes induce natural monoolist to roduce the efficient outut w/o exiting MR( ATC e MC( Economic Loss e Econ Monool 25 Econ Monool 26 Alternative Forms of Monool Pricing Uniform ricing single rice to all customers Price-discrimination Charge different rices to different customers Requires different markets w/ no trade Also requires different elasticities Can onl raise rofits (or get same Tes of Price Discrimination 1st-degree Each outut unit is sold at a different rice Prices differ across buers 2nd-degree Price varies with quantit demanded b buer All customers face the same rice schedule 3rd-degree rice discrimination Price aid b buers in grou is same for all units Price differs across buer grous senior citizen discounts student discounts no discounts for middle-aged ersons Econ Monool 27 Econ Monool 28 7

8 1 st -degree Price Discrimination: Intro 1 st -degree Price Discrimination: Grah Each outut unit is sold at a different rice Requires that monoolist can discover the buer w/ the highest valuation of its roduct the buer w/ the next highest valuation Etc., etc., etc. $ ( ( ( Sell the th unit for $( Sell the th unit for $( Sell the th unit for MC $( MC( ( Econ Monool 29 Econ Monool 30 1 st -degree Price Discrimination: Grah 1 st -degree Price Discrimination: Grah $ Gains to monoolist on these trades are: ( MC(, ( MC(, and zero The consumers gains are zero $ The monoolist gets the maximum ossible gains from trade First-degree rice discrimination is Pareto-efficient ( ( ( MC( PS MC( ( ( Econ Monool 31 Econ Monool 32 8

9 1 st -degree Price Discrimination: Summar First-degree rice discrimination gives monoolist all ossible gains-to-trade leaves buers with zero consumer surlus sulies efficient amount of outut 2 nd Degree Price Discrimination 2 nd Degree Price discrimination includes 2-art tariffs Volume Discounts Fixed Price-Quantit bundles For examle, mobile-hone service is sold this wa Econ Monool 33 Econ Monool 34 Two-art tariffs Two-art tariff lum-sum fee 1 lus rice 2 for each unit urchased Thus the cost of buing x units of roduct is x Two-Part Tariffs: Entrance Fee Two art tariff: x What 1? is maximum entrance fee = 1? Maximum 1 = surlus buer gains from entering the market So, monoolist strateg: Set 1 = CS Solve for otimal 2 Econ Monool 35 Econ Monool 36 9

10 Two-Part Tariffs: Grah Should the monoolist set 2 = MC? Two-Part Tariffs: Grah Should the monoolist set 2 = MC? 1 = CS PS is rofit from sales $/outut unit ( $/outut unit ( 2 = ( MC( CS 2 = ( PS Total rofit MC( Econ Monool 37 Econ Monool 38 Two-Part Tariffs: Maximizing Profits Monoolist maximizes rofit w/ two-art tariff setting unit rice 2 = marginal cost and setting its lum-sum entrance fee 1 equal to Consumers Surlus at outut where 2 = MC Monoolist gets all gains from trade Outcome is efficient 3 rd -degree Price Discrimination Price aid b buers in a given grou is the same for all units urchased Price ma differ across buer grous (if demand elasticities are different Monoolist maniulates rice b altering quantit sulied to each market How man units of roduct will the monoolist sul to each grou? Econ Monool 39 Econ Monool 40 10

11 3 rd -degree Price Discrimination Two markets, 1 and 2 1 = quantit sulied to market 1 1 ( 1 = inverse demand function in market 1 2 = quantit sulied to market 2 2 ( 2 = inverse demand function in market 2 3 rd -degree Price Discrimination: Profit For given sul levels 1 and 2 the firm s rofit is π( 1, 2 = 1 ( ( 2 2 c( What values of 1 and 2 maximize rofit? Econ Monool 41 Econ Monool 42 Profit Maximization π ( 1, 2 = 1( ( 2 2 c( The rofit-maximization condition is π = i i c( + ( + 2 ( i ( ( = 0 i i i MR i ( i = MC( Imlications Imlies that MR 1 = MR 2 = MC If marginal MR 1 > MR 2, then a unit of outut should be moved from market 2 to market 1 (wh? ( = MC( MR i i Econ Monool 43 Econ Monool 44 11

12 1 ( 1 * 3rd-degree Price Discrimination: Grah MR 1 ( 1 * = MR 2 ( 2 * = MC Market 1 1 ( 1 MC 2 ( 2 * Market 2 2 ( 2 MC Theor of Monoolistic Cometition Monoolistic Cometition Elements of monool Elements of erfect cometition Monool Elements Each firm faces downward sloing demand (Less than erfect substitutes Product differentiation Trademarks Advertising 1 * 1 2 * MR 1 ( 1 MR 2 ( 2 2 Econ Monool 45 Econ Monool 46 Theor of Monoolistic Cometition Cometitive element Free entr Zero rofit in long run Firms comete in rice and quantit, roduct features (roduct differentiation Behavioral Assumtion Profit maximization, given downward sloing demand curve Theor of Monoolistic Cometition Equilibrium Each firm on its own demand curve Free entr imlies zero long run rofits Characteristics Firms roduce to left of LRAC minimum oint Firms have excess caacit Firms send mone on roduct differentiation (actual and secious But consumers get more roduct diversit Econ Monool 47 Econ Monool 48 12

13 Analsis of Factor Markets Cometitive firms factor demands Monoolist factor demands Assume: Outut rice Production Function = F(x 1, x 2 Prices 1, 2 for inuts x 1, x 2 resectivel We will analze the firm s demand curve for x 1 as rice 1 varies Holding other rices constant Inut Demands Cometitive firm is rice-taker in its outut and inut markets Since Profit = Revenue Cost i.e., π = R C Profit Maximization imlies: π R C R C = = 0 = x1 x1 x1 x1 x 1 dr/dx 1 is the Marginal Revenue Product (MRP 1 Which we rewrite as: MRP 1 = dr/dx 1 = (dr/d(d/dx 1 = MR MP 1 Econ Monool 49 Econ Monool 50 Cometitive Firm s Inut Demands C For all firms: MRPi = MR MPi = x 1 For the cometitive firm the marginal revenue of a unit of inut i is And it treats inut rices as given, so Cost C = 1 x x 2 Therefore C = 1 x1 Monoolist s Inut Demands If the firm is monoolist in outut market, but rice-taker in its inut markets Then MRP i = MR( MP i = 1 Since, MR( < for all Then in general, a monool will demand less inut than a similarl situated cometitive firm And MRP i = MP i = 1 Econ Monool 51 Econ Monool 52 13

14 Monoolist s Demands for Inuts: Grah $/inut unit i * m x i * c x i MP i (x i MR( MP i (x i Econ Monool 53 x i Monosonist s Inut Demands Assume the firm has no ricing ower in outut market, but is the sole buer in its inut markets Assume the seller s side of the market is erfectl cometitive dc d Then: MRPi = MPi = = [ ( x1 x1 + 2x2] dx1 dx1 d( x1 d( x ( 1 x1 MPi = x1 + x1 = 1 x1 dx + 1 dx1 ( x1 1 MPi = + 1 ( x1 η ( Econ Monool 54 Monool v. Monoson Monool v. Monoson (cont Monool Monoson Monool Monoson MR = MC Decision Basis Marginal Benefit (MB = MC (Where MB = MRP = MC i = MRPi ε 1 +η A B C q m MR MC A = Consumer Surlus B = Producer Surlus C = DWL Demand A B C q m ME Sul MB A = Consumer Surlus B = Producer Surlus C = DWL Econ Monool 55 Econ Monool 56 14