Monopolistic Markets. Regulation

Transcription

1 Monopolistic Markets Regulation

2 Comparison of monopolistic and competitive equilibrium output The profits of a monopolist are maximized when MC(Q M ) = P(Q M ) + Q P (Q M ) negative In a competitive market: MC(Q C ) = P Thus: MC(Q M ) < MC(Q C ) Competitive supply = MC with positive slope Thus: Q M < Q C

3 Comparison of monopolistic and competitive equilibrium output P A monopolist produces an output Q M which is smaller then the competitive output Q C MC P M AC P C D Q M MR Q C Q

4 Welfare loss caused by monopol P Consumers loose A+B Producer gains A - C > 0 Welfare loss: B + C P M P C A B C D MC MR Q M Q C Q

5 Regulation of a monopol Inefficiency of monopol: Output falls short of the competitive output. Regulation: Fix price P = P C Problema: Monopolist might make negative profits when the price is regulated. If the regulator fixes P = P C the monopolist then prefers to close down (natural monopol)

6 Price regulation P P M AC (Q M ) AC (Q C ) P C Monopolistic profits In the case of a natural monopol the firm makes losses if P=P C Losses when P = P C AC MC MR D Q M Q C Q

7 Solution 1: Price regulation based on average cost P Fix price P=P R equal to average cost. Advantage: the firm covers costs (π = 0) Disadvantage: output larger than Q M but smaller than the efficient Q C (still welfare loss) P M P R AC P C MC MR D π = 0 Q M < Q R < Q C Q M Q R Q C Q

8 Solution 2: Nationalization Fix P = P C and subsidise the firm such that it keeps operating. Advantage: efficient output Disadvantage: in order to pay the subsidy the state has to impose taxes (welfare loss) Subsidy = Q C (AC(Q C ) - P C ) AC P C MC Q M MR Q C D Q

9 Monopolistic Markets Price Discrimination

10 Price discrimination So far we have assumed that the monopolist charges the same price for every unit sold and that this price is the same for each customer (P M ). We will now relax this restriction. We will see that the monopolist can increase his profits by charging different prices for different units and customers.

11 Extracting consumer surplus P Part of the consumer surplus can be extracted by charging prices higher than P M to consumers with willingness to pay higher than P M. P M P C MC Profits can also be obtained from the consumers who do not buy when the price is P M by charging lower prices. MR D Q M Q C Q

12 Three degrees of price discrimination First degree: Each client is charged a price equal to his willingness to pay (perfect discrimination) Second degree: Charge different unit prices for different quantities of the same good. Third degree: Devide the consumers into groups of differing demands and charge a different price for each group.

13 First degree price discrimination P Variable profits when the price is P M. Additional profits generated by first degree price discrimination. P M P C MC MR D Q M Q C Q

14 First degree price discrimination Normally it is not practically feasible to charge a different price to each consumer. Moreover the monopolist does not know the consumers willingness to pay. In reality first degree price discrimination is imperfect, charging a number of different prices to groups of customers based on estimates of the groups` willingness to pay.

15 Second degree price discrimination Normally the willingness to pay per unit diminishes with the total number of units purchased. Implementation 1: Charge P 1 for the first Q 1 units sold, charge P 2 < P 1 for the next Q 2 units sold, charge P 3 < P 2 for... (e.g. electricity) Implementation 2: Quantity discounts

16 Third degree price discrimination Suppose that two groups of consumers demand a good: 1 and 2 Each group has its own demand curve P 1 (Q 1 ) y P 2 (Q 2 ) The monopolist can charge two different prices. Example: Cinema tickets for students and non-students

17 Third degree price discrimination Group 1 (Students) P 1 P 2 Group 2 (Non-Students) D 1 MR 1 D 2 MR Q 2 1 Q 2 The demand of Group 1 is more elastic, E d1 > E d2.

18 The monopolist`s decision Which price to charge to each group? Profits = Total revenue Total cost Total revenue = R(Q 1,Q 2 ) = R 1 (Q 1 ) + R 2 (Q 2 ) = P 1 (Q 1 )Q 1 + P 2 (Q 2 )Q 2 Total cost = C(Q 1,Q 2 ) = C(Q 1 +Q 2 ) The firm chooses Q 1 y Q 2 to maximize profits. Max P 1 (Q 1 )Q 1 + P 2 (Q 2 )Q 2 - C(Q 1 +Q 2 )

19 First order conditions Max R 1 (Q 1 ) + R 2 (Q 2 ) - C(Q 1 +Q 2 ) dπ dq dπ dq 2 = dr dq 1 = dr dq 2 dc dq dc dq 2 = 0 = 0 MR 1 (Q 1 ) = MC(Q 1 +Q 2 ) = MR 2 (Q 2 )

20 Third degree price discrimination with constant MC P P 2 MR 1 ( Q 1 ) =MR 2 ( Q 2 ) = MC P 1 D 1 MC MR 1 MR 2 D 2 Q 2 Q 1 Q

21 Third degree price discrimination with increasing MC P P 2 MR 1 ( Q 1 ) =MR 2 ( Q 2 ) = MC (Q T ) P 1 Donde Q T = Q 1 +Q 2 MC D 1 MR 1 MR 2 D 2 Q 2 Q 1 Q T Q

22 Determination of the price ratio MR 1 = MC implies: MR 2 = MC implies: Thus when MR 1 = MR 2 =MC: The higher price is charged to the group whose demand is less elastic (Grupo 2 = Non-Students).

23 Example A monopolist faces two markets with the following demand curves Q 1 =100-P 1 ; Q 2 =100-2P 2 The marginal cost of the monopolist is constant MC=20. Calculate equilibrium quantity and price in each market when the monopolist can discriminate in price. Calculate the Lerner index for each market. Which would be the monopolist`s decision if he

24 Example P 1 = 100-Q 1 ; P 2 = 50 -Q 2 /2; D 1 less elastic than D 2 R 1 = (100-Q 1 )Q 1 ; MR 1 = 100-2Q 1 R 2 = (50-Q 2 /2)Q 2 ; MR 2 = 50 - Q 2 MR 1 (Q 1 *) = MC Q 1 * = 40; P 1 * = 60 MR 2 (Q 2 *) = MC Q 2 * = 30; P 2 * = 35 < P 1 * L 1 =(P 1 *-MC) / P 1 * = 2/3 = 1/E d1 = -(Q 1 */P 1 *)(dp 1 /dq 1 ) L 2 =(P 2 *-MC) / P 2 * = 3/7= 1/E d2 = -(Q 2 */P 2 *)(dp 2 /dq 2 ) The monopoly power is larger in market 1 Q = Q1+Q2 = 200-3P; P = (200-Q)/3; MR = (200-2Q)/3 MR(Q*) = MC Q* = 70; P* = 130/3 =