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# Int Microeconomic Analys ECN 328

Marshall

GPA 3.87

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This 0 page Class Notes was uploaded by Forrest Crist on Sunday November 1, 2015. The Class Notes belongs to ECN 328 at Marshall University taught by Staff in Fall. Since its upload, it has received 26 views. For similar materials see /class/233281/ecn-328-marshall-university in Economcs at Marshall University.

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Date Created: 11/01/15

Topic 81 Topic 81 1 Conditions of a Monopoly 11 Mathematical Representation of a Monopolist III Expressing W in Terms of Elasticity of Demand IV The Welfare Effects of Monopoly V Price Discrimination Page 1 Topic 81 Monopoly Recall Monopolist is the only seller in the industry Substantial barriers to entry 1 Large start up costs 2 Government regulations Two aspects Control prices Control entry and eXit 3 Patents 4 Unique product Page 2 Topic 81 Monopolist has a downward sloping demand curve PRICE SEARCHER I Table and Graph of Monopolist Review Marginal Revenue of Monopoly Price Y TR P x Y MC ATIVA Y ATCA Y 1050 0 0 1000 1 1000 1000 400 950 2 1900 900 375 900 3 2700 800 350 850 4 3400 700 325 800 5 4000 600 300 750 6 4500 500 340 700 7 4900 400 400 650 8 5200 300 480 600 9 5400 200 580 Page 3 Topic 81 Note Monopolist MR is l ing as Y Ts Recall MR was constant for rms in pure competition At what output does pro t maximization occur Y7 Because a monopolist has a downward sloping demand curve she has no incentive to produce a lot Page 4 Topic 81 Why is P gt MR at every Y In particular P MR for 1st unit Then every item thereafter P gt MR Also since a monopolist has a downward sloping demand curve when price changes MR has two components Ex Two components of MR from a P decrease l Gain in revenue for selling an additional unit 8 2 Loss in revenue because the rm sells product at new lower price loss of 2 on each of 4 units Therefore after 1st unit MR lt P Page 5 Topic 81 Evaluating pro t and loss Monopolist Recall Y W MC and TC is maximized P gt MR Pro t 1 Find Y 2 Find TR 3 Find TC 4 Pro t TR TC Page 6 Topic 81 Loss 1 Find Y 2 Find TR 3 Find TC 4 Pro t TR TC Page 7 Topic 81 Pro t O 1 Find Y 2 Find TR 3 Find TC 4 Pro t TR TC Page 8 Topic 81 Mathematical Representation of a Monopolist For a monopolist price and quantity are simultaneously chosen ie Each price is associated with a different quantity In functional form this suggests that price is a function of output gt PY Then TR P Y 39 Y Proflt TR TC Max P Y 39 Y CY gt utilize product rule on 1St term Y FOC d7t PYYdP dCO dY dY dY PYYdP dC dY dY MR MC FOC necessary condition for pro t max Note MR has the 2 components that we talked about earlier Page 9 Topic 81 Expressing MR in terms of elasticity of demand lRPYdP dY If we multiply 2Ild term by pp MRPXdPP PdY lRplde de Recall elasticity of demand a dy p Measures how quantity demanded responds to dp Y price changes Then W p l 18 But recall elasticity is negative number so we can say MR131 1 This suggests that a monopolist s MR added revenue of selling an additional unit is ultimately dependent on consumers elasticity of demand Page 10 Topic 81 The welfare effects of monopoly Ex Market inverse demand P 24 Q Short run cost function C Q Q2 12 If the market operated by monopolist then 7r max QMR MC TRPQQ TR24QQ TR24Q Q2 MR24 2Q MC2Q MRMC 24 2Q2Q 244Q 6Qm Pm24 Qm24618 Page 11 Topic 81 If the market operated competitively then 7r max 9 P MC We can nd total output for the industry Recall MC of each rm is its supply curve Then 2 of MC for all rms in a competitive industry is the supply curve for the industry Then market equilibrium Market equilibrium occurs where demand intersects supply P MC 24Q 2Q 24 3Q QC 8 Then Pc Pc 24 Qc 248 16 Page 12 Topic 81 Price Discrimination Charging customers different prices where the difference in price does not re ect differences in production and transportation costs Require no resale The more elastic the demand curve for a consumer or group of consumers the lower their price Types of Price Discrimination 1 1st degree Monopolist charges each individual what they are willing to pay extracts all of consumer surplus Graph This is idealistic for monopolist until producers learn to read minds to nd out exactly how much each customer willing to pay Page 13 Topic 81 2 2nd degree Monopolist gives consumers discounts for buying large quantities 3 3rd degree Monopolist sells to different groups at different prices depending on the elasticity of demand for each group Explains why Citizen discount on travel and restaurants 351 continued Say monopolist has 2 groups of consumers Groupl has inverse demand P1 Y1 D1 Group 2 has inverse demand P2 Y2 D2 Cost function C Y1 Y2 Cost of producing each unit of Y1 and Y2 are the same MaX P1Y1Y1 P2Y2Y2 C Y1 Y2 1L P1Q12iY1C13Y1Y20 le le MR1MC1 di P2QpY2 C2 Y1Y20 de dYZ MR2 MC2 Page 14 Topic 81 Ex Q1 P1 100 P1 Q2P21002P2 Monopolist has constant MC 20 with no xed costs If monopolist price discriminates nd Q1 Q2 P1 P2 We have demand we need inverse demand to put into TR we need p as a function of q Q1100 P1 Q2 100 2132 Q1100 P1 Q2 100 2P2 P1 100 Q1 P2 50 Q22 So TRl P1Q1 TRZ PZQ2 TR1 100Q1Q1 TRz 50Q22Q2 TR1 100Q1 Q12 TRZ 50Q2 szZ 1R1100 2Q1 MR250 Q2 Then MR1MC MR2 MC 100 2Q1 20 50 Q220 2Q1 80 Q2 30 Q1 40 2 30 Page 15 Topic 81 Find P1 and P2 P1 100Q1 P2 P1lOO 4O P250 3O2 P1 60 P2 35 If monopolist doesn t price discriminate find Q1 Q2 P1 7 P21 Recall We can horizontally Z demand curves market demand But we can add quantities but not prices add demand curves but not inverse demand curves Q1 Q2 Q 2 Z DiD Q1Q2 Q 100 P1 100 2P2 i1 But P1 P2 if no price discrimination Q2003P Find inverse demand to calculate TR Q 200 3P 2003 Q3 P Then TR P Q TR 2003 Q3 Q TR 200Q3 Q23 Then MR 2003 2Q3 Page 16 Topic 81 So 71 maX MRMC 2003 2Q3 20 20 2003 2Q3 1403 Q 1403 X 32 Q 70 Then P 2003 Q3 P 2003 703 1303 H with discrimination 11 2P1 Q1 P2 Q2 39 CQ1 22 60 X 40 35 X 30 204030 2400 1050 1400 2050 H Without discrimination 11 P Q CQ 0 1303 X 70 2070 30333 1400 163333 Monopolist made more H by discriminating Page 17

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