ECON 115. Industrial Organization

Transcription

1 ECON 115 Industrial Organization

2 1. Review of the First Midterm 2. Review of Price Discrimination, Product Differentiation & Bundling 3. Introduction to Oligopolies 4. Introduction to Game Theory and Cournot Duopoly

3 Review Midterm Review Final comments on the behavior of monopolies. Price Discrimination 1 st, 2 nd and 3 rd Product Differentiation Bundling & Tie-in Sales What you see in the real economy Oligopolies Introducing Oligopoly Game Theory Nash Equilibrium Cournot Model of Duopoly

4 We began this course with two goals: (1)Understand imperfect competition from (2)... an economic perspective. 4

5 Over the past three lectures we have considered one form of imperfect competition the monopoly and examined methods used to increase profits. These methods include various forms of price discrimination, horizontal and vertical product differentiation and bundling and tie-in sales. In all cases, we have used various economic theories to understand how monopolies operate. 5

6 2 nd Degree Price Discrimination 3 rd Degree Price Discrimination Product differentiation Bundling and Tie-sales Example: Quantity Discounts Example: Group Pricing Example: A new product. Example: Combo Products Consumers can t be identified; must force them to reveal their true selves. (Selfselect). Consumers can be identified by some observable characteristic. Consumers want products close to their preferences in space, time or characteristics Consumers willing to pay more in the aggregate. Rule: leave some consumer surplus on the table to induce high-demand groups to buy large quantities. Rule: charge consumers with low elasticity of demand a high price; equate MR for all groups. Rule: add a new product (n + 1) if: n(n + 1) < tn/2f N = size of market F = setup $ t = preference for a new product Rule: must examine profits on a case by case basis. 6

7 2 nd Degree Price Discrimination Industrial Organization FROM THE REAL ECONOMY 3 rd Degree Price Discrimination Horizontal Product differentiation Bundling Starbucks Latte: Tall: $2.85 (24 ) Venti: $3.95 (20 ) Oreos (Walmart) 15oz: $2.98 (20 ) 20oz: $3.50 (18 ) Theaters: Adult: $10.00 Senior: $7.00 Matinee: $6.00 Insurance: Student Discount Good Driver Fit Civic Accord Crosstour Ridgeline McDonalds Burgers & Fries Big Mac ( 68) Egg McMf ( 71) Drive Thru ( 75) Microsoft Office Word, Excel and Power Point. McDonald s Extra Value Meal. Computer Bundle: Laptop, Flash Drive, Case, Printer (Costco) 7

8 Question: in the real world, how do firms identify different groups demand functions, individuals desire for different products or consumers willingness to pay? Entrepreneurship = alertness to market opportunities. Competition is an ongoing process of discovery. Entrepreneur means acting man in regards to changes occurring in the data of the market. Ludwig von Mises The entrepreneur brings into mutual adjustment those discordant elements which resulted from prior market ignorance. Israel Kirzner I wish to consider competition... as a procedure for discovering facts. Freidrich Hayek 8

9 We now turn to a common type of market, where firms interact with a few competitors oligopoly market. Each firm has to consider its rival s actions with regards to prices, outputs, advertising, etc. This kind of strategic interaction is analyzed using game theory. To understand games, we assume players are rational distinguish between cooperative and noncooperative games distinguish between simultaneous and sequential games 9

10 With oligopoly, there is no single theory. We employ game theoretic tools that are appropriate. Outcomes depends upon available information. Definitions used in Game Theory Strategy: plan of action Strategy combination: one particular strategy choice for each player Outcome: given the strategy combination, it s the payoff earned by each player. 10

11 Need a concept of equilibrium Players (firms) choose a strategy. The strategy combination determines outcome. The outcome determines pay-offs (profits?). Equilibrium first formalized by Nash: No firm wants to change its current strategy given that no other firm changes its current strategy. 11

12 A final critical dimension of games is time. In some games, moves (choices) are made sequentially. One player (firm) moves first and then the second player (firm) follows. Examples: chess and checkers In other games, players (firms) make choices simultaneously, thereby acting without knowing what the other player will do Example: Rock-Scissors-Paper 12

13 Some strategies are never chosen no matter what rivals do. These are called dominated strategies. Since they are never employed, they can be eliminated. One strategy might always be chosen, no matter what the rivals do. This is called a dominant strategy. 13

14 Here s an example using two airlines, Delta and American. Assumptions of the game: Prices are set; airlines compete solely along the dimension of departure times; 70% of consumers prefer evening departure, while 30% prefer morning departure; If the airlines choose the same departure times they split the market equally; In this game, the pay-off = market share. 14

15 The Pay-Off Matrix American Morning Evening Delta Morning Evening (15, 15) (30, 70) (70, 30) (35, 35) KEEP15

16 If American If American The Pay-Off Matrix chooses an evening chooses a morning departure, Delta departure, Delta will also choose will choose American evening evening Morning Evening Morning (15, 15) (30, 70) Delta Evening (70, 30) (35, 35) KEEP16

17 The morning departure The Pay-Off Matrix is a dominated The morning departure strategy for Delta Both airlines American is also a dominated choose an strategy for American evening Morning Evening departure Delta Morning Evening (15, 15) (30, 70) (70, 30) (35, (35, 35) 35) KEEP17

18 Now let s change the assumptions. Assume Delta has a frequent flier program. Due to the frequent flyer program, more travelers prefer Delta. Therefore, when both airlines choose the same departure times, Delta gets 60% of the travelers. This changes the pay-off matrix. 18

19 The Pay-Off Matrix American Morning Evening Delta Morning Evening (18, 12) (30, 70) (70, 30) (42, 28) KEEP19

20 If Delta chooses a morning departure, American will choose evening American The Pay-Off Matrix But if Delta chooses an evening departure, American will choose morning Morning Evening Delta Morning Evening (18, 12) (30, 70) (70, 30) (42, 28) KEEP20

21 American knows this and so chooses a morning departure Morning Industrial Organization American has no dominated strategy The Pay-Off Matrix Morning However, a morning departure is still a dominated American strategy for Delta Evening (18, 12) (30, 70) Delta Evening (70, (70, 30) 30) (42, 28) KEEP21

22 What if there are no dominated or dominant strategies? We need to use the Nash equilibrium concept. 22

23 To illustrate, turn the airline game into a pricing game: 60 passengers with a reservation price = $500; 120 passengers with a reservation price = $220; Price discrimination is not possible (perhaps for regulatory reasons or because the airlines can t identify the passenger types). Cost = $200 per passenger; Airlines must choose between $500 or $220 price; If equal prices are charged the passengers are split; The low-price airline gets all the passengers. The pay-off matrix is transformed. 23

24 The Pay-off Matrix American P H = $500 P L = $220 Delta P H = $500 P L = $220 ($9000,$9000) ($0, $3600) ($3600, $0) ($1800, $1800) KEEP24

25 If both price high then both get 30 passengers. Profit per passenger is $300 If Delta prices high If both price low and American low they each get 90 then American gets passengers. all 180 passengers. The Pay-off Matrix Profit per passenger Profit per passenger is $20 is $20 American Industrial Organization If Delta prices low and American high then Delta gets P H = $500 all 180 passengers. Profit per Delta passenger is $20 P L = $220 P H = $500 P L = $220 ($9000,$9000) ($0, $3600) ($3600, $0) ($1800, $1800) KEEP25

26 (P H, P H ) is a Nash equilibrium. If both are pricing igh then neither wants to change (P H, P L ) cannot be (P L, P L ) is a Nash The If American Pay-Off prices Matrix equilibrium. low then Delta should If both are pricing also price low low then neither wants American to change Industrial a Nash equilibrium. Organization P H = $500 P L = $220 (P L, P H ) cannot Pbe H = $500 a Nash equilibrium. If American Deltaprices high then Delta should P L = $220 also price high ($9000,$900 $9000) ($0, $3600) 0) ($3600, $0) ($1800, ($1800, $1800) $0) $1800) KEEP26

27 There are two Nash equilibria to this Industrial version Organization of the game The Pay-Off There Matrixis no simple way to choose between these equilibria American Custom and familiarity might lead both to P H = $500 P L = $220 price high P H = $500 Regret Deltamight cause both to price low P L = $220 ($9000,$900 $9000) 0) ($3600, $0) $0) ($0, $3600) ($1800, ($1800, $1800) $1800) KEEP27

28 We now move to oligopoly models. There are three dominant oligopoly models Cournot Bertrand Stackelberg They are distinguished by: The decision variable that firms choose The timing of the underlying game Concentrate on the Cournot model in this section 28

29 The Cournot model begins with a duopoly. Two firms making an identical product (NOTE: Cournot supposed this was spring water); Demand for this product is: P = A - BQ = A - B(q 1 + q 2 ) where q 1 is output of firm 1 and q 2 is output of firm 2 Marginal cost for each firm is constant at c per unit To get the demand curve for one of the firms we treat the output of the other firm as constant So for firm 2, demand is P = (A - Bq 1 ) - Bq 2 29

30 P = (A - Bq 1 ) - Bq 2 $ The profit-maximizing choice of output by A - Bq 1 firm 2 depends upon the output of firm 1. A - Bq 1 Marginal revenue for firm 2 is: Solve this c MR 2 = (A - Bq 1 ) - 2Bq for output 2 MR 2 MR 2 = MC A - Bq 1-2Bq 2 = c q 2 q* 2 q* 2 = (A - c)/2b - q 1 /2 If the output of firm 1 is increased the demand curve for firm 2 moves to the left Demand MC Quantity 30

31 q* 2 = (A - c)/2b - q 1 /2 This is the reaction function for firm 2. It gives firm 2 s profit-maximizing choice of output for any choice of output by firm 1. There is also a reaction function for firm 1. By exactly the same argument it can be written:: q* 1 = (A - c)/2b - q 2 /2 Cournot-Nash equilibrium requires that both firms be on their reaction functions. 31

32 (A-c)/B q 2 Industrial Organization The reaction function for firm 1 is q* 1 = (A-c)/2B - q 2 /2 (A-c)/2B q C 2 Firm 1 s reaction function C The reaction function for firm 2 is q* 2 = (A-c)/2B - q 1 /2 q C 1 (A-c)/2B Firm 2 s reaction function (A-c)/B q 1 KEEP32

33 (A-c)/B (A-c)/2B q C 2 q 2 If firm 2 produces (A-c)/B then firm 1 will choose to produce no output Industrial Organization Firm 1 s reaction function C The Cournot-Nash equilibrium is at the intersection of the reaction functions If firm 2 produces nothing then firm 1 will produce the monopoly output (A-c)/2B q C 1 (A-c)/2B Firm 2 s reaction function (A-c)/B q 1 KEEP33

34 (A-c)/B q 2 q* 1 = (A - c)/2b - q* 2 /2 q* 2 = (A - c)/2b - q* 1 /2 Firm 1 s reaction function q* 2 = (A - c)/2b - (A - c)/4b + q* 2 /4 3q* 2 /4 = (A - c)/4b (A-c)/2B (A-c)/3B C Firm 2 s reaction function (A-c)/2B (A-c)/B (A-c)/3B q* 2 = (A - c)/3b q 1 q* 1 = (A - c)/3b 34

35 In equilibrium each firm produces q * 1 = q * 2 = (A - c)/3b Total output is, therefore, Q* = 2(A - c)/3b Recall that demand is P = A - BQ So the equilibrium price is P* = A - 2(A - c)/3 = (A + 2c)/3 Profit of firm 1 is (P* - c)q * 1 = (A - c) 2 /9 Profit of firm 2 is the same. A monopolist would produce Q M = (A - c)/2b Competition between the firms causes them to produce more product. Price is lower than the monopoly price. But output is less than the competitive output (A - c)/b where price equals marginal cost. 35

36 What if there are more than two firms? Much the same approach. Say that there are N identical firms producing identical products This denotes output Total output Q = q 1 + q 2 + of + every q N firm other than firm 1 Demand is P = A - BQ = A - B(q 1 + q q N ) Consider firm 1. It s demand curve can be written: P = A - B(q q N ) - Bq 1 Use a simplifying notation: Q -1 = q 2 + q q N So demand for firm 1 is P = (A - BQ -1 ) - Bq 1 36

37 P = (A - BQ -1 ) - Bq 1 $ The profit-maximizing A - BQ choice of output by firm -1 1 depends upon the output of the other firms. A - BQ -1 Marginal revenue for firm 1 is: MR 1 = (A - BQ -1 ) - 2Bq 1 MR 1 = MC A - BQ -1-2Bq 1 = c Solve this c for output q 1 q* 1 q* 1 = (A - c)/2b - Q -1 /2 If the output of the other firms is increased the demand curve for firm 1 moves to the left Demand MC MR 1 Quantity 37

38 q* 1 = (A - c)/2b - Q -1 /2 Q* -1 = (N - 1)q* 1 q* 1 = (A - c)/2b - (N - 1)q* 1 /2 How do we solve this for q* 1? (1 + (N - 1)/2)q* 1 = (A - c)/2b q* 1 (N + 1)/2 = (A - c)/2b q* 1 = (A - c)/(n + 1)B Q* = N(A - c)/(n + 1)B P* = A - BQ* = (A + Nc)/(N + 1) Profit of firm 1 is P* 1 = (P* - c)q* 1 The firms are identical. So in equilibrium they will have identical outputs = (A - c) 2 /(N + 1) 2 B KEEP38

39 q* 1 = (A - c)/2b - Q -1 /2 Q* -1 = (N - 1)q* 1 q* 1 = (A - c)/2b - (N - 1)q* 1 /2 (1 + (N - 1)/2)q* 1 = (A - c)/2b q* 1 (N + 1)/2 = (A - c)/2b q* 1 = (A - c)/(n + 1)B As the number of firms increases output of each firm falls KEEP39

40 q* 1 = (A - c)/2b - Q -1 /2 Q* -1 = (N - 1)q* 1 q* 1 = (A - c)/2b - (N - 1)q* 1 /2 (1 + (N - 1)/2)q* 1 = (A - c)/2b q* 1 (N + 1)/2 = (A - c)/2b q* 1 = (A - c)/(n + 1)B Q* = N(A - c)/(n + 1)B As the number of firms increases aggregate output increases KEEP40

41 q* 1 = (A - c)/2b - Q -1 /2 Q* -1 = (N - 1)q* 1 q* 1 = (A - c)/2b - (N - 1)q* 1 /2 (1 + (N - 1)/2)q* 1 = (A - c)/2b q* 1 (N + 1)/2 = (A - c)/2b q* 1 = (A - c)/(n + 1)B Q* = N(A - c)/(n + 1)B P* = A - BQ* = (A + Nc)/(N + 1) As the number of firms increases price tends to marginal cost KEEP41

42 q* 1 = (A - c)/2b - Q -1 /2 Q* -1 = (N - 1)q* 1 q* 1 = (A - c)/2b - (N - 1)q* 1 /2 (1 + (N - 1)/2)q* 1 = (A - c)/2b q* 1 (N + 1)/2 = (A - c)/2b q* 1 = (A - c)/(n + 1)B Q* = N(A - c)/(n + 1)B P* = A - BQ* = (A + Nc)/(N + 1) Profit of firm 1 is P* 1 = (P* - c)q* 1 As As the the number number of of firms firms increases profit price tends of each to marginal firm falls cost = (A - c) 2 /(N + 1) 2 B KEEP42

43 What if the firms do not have identical costs? Much the same analysis can be used. Marginal costs of firm 1 are c 1 and of firm 2 are c 2. Demand is P = A - BQ = A - B(q 1 + q 2 ). We have marginal revenue for firm 1 as before. MR 1 = (A - Bq 2 ) - 2Bq 1 Equate to marginal cost: (A - Bq 2 ) - 2Bq 1 = c 1 Solve this for output q 1 q* 1 = (A - c 1 )/2B - q 2 /2 q* 2 = (A - c 2 )/2B - q 1 /2 A symmetric result holds for output of firm 2 43

44 (A-c 1 )/B (A-c 2 )/2B The equilibrium Industrial Organization output of firm 2 increases and of q 2 q* 1 = (A - c 1 )/2B - q* 2 /2 firm 1 falls If the marginal q* 2 = (A - c 2 )/2B - q* 1 /2 R 1 cost of firm 2 q* 2 = (A - c 2 )/2B - (A - c 1 )/4B falls its reaction + q* 2 /4 curve shifts to 3q* 2 /4 = (A - 2c 2 + c 1 )/4B the right R 2 C q* 2 = (A - 2c 2 + c 1 )/3B q* 1 = (A - 2c 1 + c 2 )/3B (A-c 1 )/2B (A-c 2 )/B q 1 What happens to this equilibrium when costs change? 44

45 In equilibrium, the firms produce: q * 1 = (A - 2c 1 + c 2 )/3B; q * 2 = (A - 2c 2 + c 1 )/3B Total output is, therefore, Q* = (2A - c 1 - c 2 )/3B Recall that demand is P = A - B.Q So price is P* = A - (2A - c 1 - c 2 )/3 = (A + c 1 +c 2 )/3 Profit of firm 1 is (P* - c 1 )q * 1 = (A - 2c 1 + c 2 ) 2 /9 Profit of firm 2 is (P* - c 2 )q * 2 = (A - 2c 2 + c 1 ) 2 /9 Equilibrium output is less than the competitive level Output is produced inefficiently: the low-cost firm should produce all the output. 45

46 Assume there are N firms with different marginal costs We can use the N-firm analysis with a simple change Recall that demand for firm 1 is P = (A - BQ -1 ) - Bq 1 But then demand for firm i is P = (A - BQ -i ) - Bq i Equate this to marginal cost c i A - BQ -i - 2Bq i = c i This can be reorganized to give the equilibrium condition: A - B(Q* -i + q* i ) - Bq* i - c i = 0 P* - Bq* i - c i = 0 P* - c i = Bq* i But Q* -i + q* i = Q* and A - BQ* = P* 46

47 The price-cost margin P* - c i = Bq* i for each firm is Divide by P* and multiply the right-hand side determined by Q*/Q* by its P* - c i P* = BQ* market share and q* i demand elasticity P* Q* But BQ*/P* = 1/ and q* i /Q* = s i P* - c so: i = s i P* Extending this we have: P* - c P* = H Average price-cost margin is determined by industry concentration 47

48 Now let s find the Cournot Equilibrium: Assume two identical firms (1 and 2). Both set quantity assuming the other firm s quantity is independent of their own choice of output. Equilibrium occurs when each firm does not want to change its output having observed what output the other firm has set. (Nash Equilibrium) 48

49 To illustrate Cournot, we will use a very simple linear demand function. Consider the following: Demand: P = 25 Q MC = AC = 5 Competitive Outcome: P = MC = 5 Q = 20 CS = 200, PS = 0 Monopoly outcome: MR = 25-2Q = MC= 5 Q = 10. P = 15 CS = 50, PS = 100, DWL = 50

50 P =25 - (q 1 +q 2 ) P = 25 q 1 q 2 Treat (25 q 1 ) as a constant. Total revenue for Firm 2 is: Pq 2 = (25 q 1 )q 2 q 2 2 MR = (25 q 1 ) 2q 2 MR = MC; (25 q 1 ) 2q 2 = 5 2q 2 = q 1 This gives the reaction function for Firm 2: q 2 =(20-q 1 )/2 Repeat the procedure for Firm 2. 50

51 q 1 =(20-q 2 )/2 and q 2 =(20-q 1 )/2 Plug q 2 into the q 1 equation and solve for q 1 : q 1 = 20/3. Through symmetry, q 2 =20/3 P=35/3 p 1 = p 2 = 400/9; PS=800/9 CS=800/9 CS+PS=1600/9= DWL =

52 Perfect Competition Monopoly Cournot Oligopoly (2 firms) PRICE /3 (35/3) QUANTITY /3 (40/3) SURPLUS CS = 200; PS = 0 CS = 50; PS = 100 CS = 89; PS = 89 DEADWEIGHT LOSS

53 Read Chapters 9 and 10 in the text.