# Microeconomics II. ELTE Faculty of Social Sciences, Department of Economics. week 9 MARKET THEORY AND MARKETING, PART 3

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1 MICROECONOMICS II.

2

3

4 ELTE Faculty of Social Sciences, Department of Economics Microeconomics II. MARKET THEORY AND MARKETING, PART 3 Author: Supervised by February 2011

5 Prepared by:, using Jack Hirshleifer, Amihai Glazer és David Hirshleifer (2009) Mikroökonómia. Budapest: Osiris Kiadó, ELTECON-könyvek (henceforth: HGH), and Kertesi Gábor (ed.) (2004) Mikroökonómia el adásvázlatok. kertesi/kertesimikro/ (henceforth: KG).

6 Oligopolies Denition We call a form of market structure oligopoly where a small number of rms exist (having market power only together); product is homogenous; number of rms is xed (dicult to enter the market).

7 Oligopolies (cont.) Denition If rms simultaneously decide of the output level and have the same market power, then we talk about Cournot-oligopoly, in case of two companies: Cournot-duopoly. Productions of the two companies: q 1, q 2 Cost functions of the two companies: C 1 (q 1 ), C 2 (q 2 ) Demand function: Q = D(P), inverse demand function: P = D 1 (Q) = D 1 (q 1 + q 2 ) Prot functions: Π 1 = Pq 1 C 1 (q 1 ) = D 1 (q 1 + q 2 )q 1 C 1 (q 1 ) Π 2 = Pq 2 C 2 (q 2 ) = D 1 (q 1 + q 2 )q 2 C 2 (q 2 )

8 Oligopolies (cont.) First order conditions of prot-maximizing: Π 1 (q = D q 2 ) (1+ q 2 )q 1 +D 1 (q 1 +q 2 ) MC 1 (q 1 ) = 0 q 1 q 1 q 1 Π 2 (q = D q 2 ) (1+ q 1 )q 2 +D 1 (q 1 +q 2 ) MC 2 (q 2 ) = 0 q 2 q 2 q 2 Reaction curve (optimal output "reaction" of a company given its beliefs about the other rm's choice): q 1 = RC 1 (q e 2) q 2 = RC 2 (q e 1) Cournot-equilibrium: Beliefs about output levels correspond to actual output levels: q 1 = RC 1 (q 2) q 2 = RC 2 (q 1)

9 Oligopolies (cont.) Reaction curves RC 1 curve determines rm 1's optimal choice of output as a function of its beliefs about rm 2's output choice, and RC 2 curve shows rm 2's optimal choice of output as a function of its beliefs about rm 1's output choice.

10 Oligopolies (cont.) Exercise P = 100 (q 1 + q 2 ) MC 1 = 20 + q 1, and MC 2 = 20 + q 2 Determine the reaction curves and the Cournot-equilibrium! Solution: MR 1 = MC q 1 q 2 = 20 + q 1 RC 1 = q 1 = 80 q 2 3 Similarly: RC 2 = q 2 = 80 q1. Solving the two functions: 3 q 1 = q 2 = 20, Q = 40, P = 60, Π 1 = Π 2 = 600

11 Oligopolies (cont.)

12 Oligopolies (cont.) Cournot oligopoly (n alike rms) Π i = (a (q q i q n ))q i C i (q i ) Π i n = a q j 2q i MC i (q i ) = 0 q i j=1,j i a (n + 1)q MC = 0 q = a MC n + 1 Monopoly: q m = a MC 2 Competition: p = a nq = a (a MC) n MC(n ) n+1 Denition If rm 1 (leader) decides rst about output and rm 2 (follower) decides after observing his competitor's decision, we talk about Stackelberg-duopoly.

13 Oligopolies (cont.) Exercise P = 100 (q 1 + q 2 ) MC 1 = 20 + q 1, and MC 2 = 20 + q 2 Let's determine the Stackelberg-equilibrium! Solution: The follower maximizes his prot in case of every value of q 1, hence his reaction curve can be easily determined: Π 2 = D 1 (q 1 + q 2 )q 2 C 2 (q 2 ) max RC 2 (q 1 ) = q 2 (q 1 ) Π 1 = D 1 (q 1 + q 2 (q 1 ))q 1 C 1 (q 1 ) max Π 1 (q = D q 2 (q 1 )) (1 + q 2(q 1 ) )q 1 + q 1 q 1 q 1 +D 1 (q 1 + q 2 (q 1 )) MC 1 (q 1 ) = 0 RC 1 (q 2 ) = q 1 (q 2 )

14 Oligopolies (cont.) Applied to the exercise: Π 2 = (100 (q 1 + q 2 ))q 2 C(q 2 ) 100 q 1 2q 2 q 2 20 = 0 q 2 = 80 q 1 3 Π 1 = (100 (q q 1 )q 1 C(q 1 ) q q q 1 = 0 q 1 = 160 7, q 2 = Stackelberg: Π 1 610, Π 2 544, Q 42, P 58 Cournot: Π 1 = Π 2 = 600, Q = 40, P = 60

15 Oligopolies (cont.) Consequence It is clear that in case of Stackelberg-duopoly the leader is in a favourable situation: produces more and realizes higher prot; while in case of Cournot-duopoly the two companies are symmetric.

16 Price competition If rm 2 sets p 2 price, then the best answer of rm 1 is p 1 = p 2 ε. If rm 1 sets p 1 price, then the best answer of rm 2 is p 2 = p 1 ε. So it is worth for both companies to set their prices below their competitor's price because the lower price satises total demand. Marginal cost (competition price) can be considered as the lower limit because it is not worth to neither companies going below of it. In BertrandNash-equilibrium: p 1 = p 2 = MC (if marginal cost of the two companies are the same).

17 Price competition (cont.) The Prisoners' dilemma: oligopoly prots Firm 2 price high low Firm 1 high 100,100 10,140 price low 140,10 70,70 The Most-Favored Customer clause Firm 2 price high low Firm 1 high 100,100 10,90 price low 90,10 70,70

18 Price competition (cont.) Consequence When duopolists produce identical, the possible outcomes depend upon the nature of the payos (as determined by the market demand curve and the rms' cost functions) and the protocol of play, together with the assumed behavior of the decision-makers. If quantity is the decision variable and the simultaneous-move protocol applies, at one extreme the rms may behave as a joint monopolist (the collusive outcome) and at the other extreme as price-taking competitors (the competitive outcome).

19 Price competition (cont.) Two directions of extension: Bertrand-model under capacity-constraints Bertrand-model under product dierentiation (spatial Bertrad-model)

20 Price competition (cont.) Spatial Bertrand-model: V : reservation price of consumers (assumpt.: every consumer buys 1 item, everyone has the same reservation price) c: marginal cost (constant, same in both companies) t: marginal loss of acquisition The two are situated at the two ends of the product-scale. Consumers (N) are distributed atly along the product-scale (the lenght of the product-scale is normalized to one unit). The marginal consumer is the one who is neutral about the place of the shop: V p 1 tx m = V p 2 t(1 x m ). Location of the marginal consumer: x m (p 1, p 2 ) = p 2 p 1 + t 2t

21 Price competition (cont.) Demand for the goods of rm 1: D 1 (p 1, p 2 ) = Nx m (p 1, p 2 ) = N p 2 p 1 + t 2t Demand for the goods of rm 2: D 2 (p 1, p 2 ) = N(1 x m (p 1, p 2 )) = N p 1 p 2 + t 2t Prot functions: Π 1 (p 1, p 2 ) = (p 1 c)n p 2 p 1 + t 2t Π 2 (p 1, p 2 ) = (p 2 c)n p 2 p 2 + t 2t max p 1 max p 2

22 Price competition (cont.) First order conditions: Π 1 p 1 Π 2 p 2 = N p 2 p 1 + t 2t = N p 1 p 2 + t 2t N p 1 2t (p 1 c) = 0 N p 2 2t (p 2 c) = 0 Best answer functions (reaction curves): p 1 = p 2 + c + t 2 p 2 = p 1 + c + t 2 Nash-equilibrium: p 1 = p 2 = c + t

23 Price competition (cont.) Consequence The Nash solution is the intermediate Cournot equilibrium: each rm chooses optimally, given the other rm's production quantity. When price is the decision variable instead, the Nash solution is called the Bertrand equilibrium: each rm chooses a prot-maximizing price, given the other's price. Price competition is more severe than quantity competition, and so leads to worse outcomes for the rms (but better outcomes for the consumers). For the sequential-move protocol, the Stackelberg leader (the rst mover) is at an advantage under quantity competition but at a disadvantage under price competition.

24 Quantity Competition Reaction curves The are no longer identical, and the demand curves are P 1 = 100 q 1 sq 2 and P 2 = 100 sq 1 q 2 where s (the coecient of similarity) is 1/2. As s 0, the reaction curves swing toward the respective dashed horizontal and vertical lines, showing the optimal outputs if each rm were an independent monopolist.

25 Price competition Linear reaction curves The reaction curves now have positive slopes: each rm rationally raises price if the competitor does and similarly follows a price reduction but by less than 1:1 in either case. As s 0, the reaction curves swing toward the respective and vertical dashed lines, indicating the optimal prices if each rm were an independent monopolist.

26 Price competition (cont.) Consequence When duopolists produce, the Cournot and Bertrand solutions will be a function of s, the index of similarity between the two. At one extreme (s = 1) the rms produce identical. At the other extreme (s = 0) the two rms are independent monopolists. For intermediate values of s, when quantity is the decision variable the reaction curves slope downward. When price is the decision variable the reaction curves slope upward. So for as for identical, price competition is more severe than quantity competition; the outcomes are less favorable to the rms and more favorable for the consumers.

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