"Monopoly" "Monopoly" Chapter 5. January 30, 2015

Transcription

1 "Monopoly" Chapter 5. January 30, 2015

2 Single Seller Can determine either price or quantity supplied The monopoly has to familiarize itself with all the demand properties The monopoly s pro t-maximization problem is: max π(q) = TR(Q) TC (Q) A necessary condition for Q M > 0 is 0 = TR(QM ) Q dtc (Q M ) Q = MR(Q M ) MC (Q M ) Hence, we obtain Q M in the point where: MR(Q M ) = MC (Q M ), and the P M can be found substituting Q M into the demand function.

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4 Demand: P(Q) = a bq and TC (Q) = F + cq 2 MR(Q) = a Q m = π (Q m ) = 2bQ and MC (Q) = 2cQ a 2(b+c) and pm = a(b+2c) 2(b+c) a2 4(b+c) F Altogether, the monopoly s pro t-maximizing output is given by ( Q m a = 2(b+c) if F a2 4(b+c) 0 otherwise.

5 Monopoly and Social Welfare The conventional argument against a monopoly

6 The Social Cost of a Monopoly Firms wishing to maintaining a monopoly position must allocate resources for that goal. Resources that should not be considered as reducing welfare include: R&D leading to a patent monopoly right Bribes to politicians Resources that may count as social waste include: Persuasive advertising Excessive production or investment in capital Excessive R&D Lobbying costs

7 Discriminating Monopoly Di erent prices to consumers with di erent characteristics How rms avoid arbitrage? Di erent prices at di erent locations Age (Senior citizen versus younger consumers) Students

8 Discriminating Monopoly The monopoly chooses the output level in each market that solve: maxπ(q 1, q 2 ) = TR(q 1 ) + TR(q 2 ) TC (q 1 + q 2 ) q 1,q 2 MR 1 (q M 1 ) = MR 2 (q M 2 ) = MC (q M 1 + q M 2 ) Proposition 5.1. A discriminating monopoly selling a strictly positive amount in each market will charge a higher price at the market with less elastic demand.

9 The Cartel Multiplant Monopoly. The cartel organizes N plants by directing each plant to produce a certain amount The aggregate output is Q = N q i and TC i (q i ) F + c (q i ) 2 i=1 max π(q 1, q 2,.., q N ) = N π i (q i ) q 1,q 2,..,q N i=1 = a b N N q i q i i=1 i=1 N TC i (q i ) i=1 Hence 0 = π q j = a 2b N q i MC j (q j ) = MR(Q) MC j (q j ), j = 1, 2,.., i=1

10 Assume a = 20, b = 0.5, c = 5 The Cartel Na Hence: Q C = Nq = 2(bN +c) and p = a what would happen if N increases? a(bn +2c) bq = 2(bN +c) qi Price Profit

11 Durable-Goods Monopolies ow goods: bananas, apples, etc durable goods:car, houses and land Role of the demand Suppose there is a continuum of consumers having di erent valuations for annual services of a car Consumers live for two periods t = 1, 2 Demand function in period t =1 is p = 100 Let us compare two types of commercial transactions: selling and renting Q

12 A Renting Monopoly Assume that each period the monopoly rents a durable product for one period only. Assume that in each period the monopoly faces the demand p = 100 Q Assuming zero production cost Q R t = 50 and p R t = 50, π R t = 2, 500 for t = 1, 2 and π R = 5, 000

13 A Seller Monopoly The seller knows that those consumers who buy the durable good in t = 1 will not buy in t = 2. In t = 2 the monopoly will face a demand which is lower than the period 1 demand. Two-Period Game The payo is TR 1 + TR 2 The strategies of the seller are p 1 and p 2 ( q 1 ) The strategies of the buyers are: to buy or not to buy SPE!

14 The Second Period The residual demand p 2 = 100 q 1 q 2 Since production was assumed to be costless then: MR 2 (q 2 ) = 100 q 1 2q 2 = 0 q Solving for q 2, q 2 = Second period price and pro ts are: p 2 = 50 q π 2 = ( ) 2 q 1 2 and

15 The First Period The First Period Price should include the second period price: q p 1 = 100 q 1 + p 2 = 100 q 1 + ( q 2 ) = The monopolist chooses a rst-period output level q 1 max q 1 π(π 1 + π 2 ) = (150 3 q 1 2 )q 1 + (50 q 1 2 )2 q 1 = 40, q 2 = 30, p 1 = 90 and p 2 = 30. Hence π(π 1 + π 2 ) = = 4, 500 < π R = 5, 000 Proposition 5.3. A monopoly selling a durable good earns a lower pro t than a renting monopoly.

16 The Legal Approach to Monopoly Section 2 of the Sherman Act of 1890 states that Every person who shall monopolize, or attempt to monopolize, or combine and conspire with any other person or persons, to monopolize any party of the trade or commerce among several States, or with foreign nations, shall be deemed guilty of a felony.