Lecture 11: Oligopoly and Strategic Behavior

Transcription

1 Lecture 11: Oligopoly and Strategic Behavior Few Firms in the Market: Each aware of others actions Each firm in the industry has market power Entry is Feasible, although incumbent(s) may try to deter it. Examples: Airlines, Telecommunications, Search Engines, Automobiles, Microprocessors Measuring market concentration: concentration indices C i = combined market share of i largest firms, eg, C 4. H = Herfindahl index, aka HHI. H = s i 2 both of these vary between 0 (many, many firms) and 1 (monopoly). Example: 4 firms in the market: S 1 =.50, S 2 =.25, S 3 =.15, S 4 =.10 C 3 =.90, HHI= =.345 Market structure and performance Nature of comp. Value of H Intensity of price comp. perfect below.2 fierce oligopoly.2 to.6 varies* monopoly.6 or above light * Firms must understand the nature of markets in which they compete. There are reasons why, for example, even firms in an industry such as pharmaceuticals have, by economywide standards, impressive profitability, while top firms in the airline industry seem to achieve low rates of profitability even in the best of times. (BDS, p.7)

2 In an oligopoly, degree of market power depends on: Demand Elasticity Market Concentration Collusive Behavior The five forces framework (Michael Porter, Competitive Strategy, NY, Free Press, 1980) Degree of market power depends primarily on rivalry within the industry, but also takes into account, vertical structure, the threat of entry, and threat of substitute products. Quantity (Cournot) Competition Assume Homogeneous Products: MC=10 for both firms Demand: P=70-Q= 70- (q 1 +q 2 ), since Q= q 1 +q 2, where Q=total quantity. π 1 = Pq 1 TC 1 = (70-q 1 -q 2 ) q 1-10q 1 π 1 =60q 1 q 12 q 2 q 1 dπ 1 /dq 1 =60-2q 1 -q 2 =0 or q 1 =(60-q 2 )/2 (Reaction function of firm 1) Similarly, π 2 =60q 2 q 22 q 1 q 2 q 2 =(60-q 1 )/2 (Reaction function of firm 2) q 2 Reaction function of firm 1 Reaction function of firm 2 Solve for the Nash Equilibrium Quantities Reaction functions intersect at q 1 = q 2 =20. Nash equilibrium is (q 1 *=20, q 2 *=20). P=30 q 1

3 Computing Profits: π 1 = π 2 = (P-MC)q= (30-10)20=400. What would a monopoly do? MR=MC implies that 70-2Q=10, or Q=30. P=40 and total profits are 900. If each firm produced q=15, each firm would earn 450. Prices are higher and total quantity is lower under monopoly. Suppose that there were three firms. Total quantity would exceed 40 and the price and the profits would fall. As the number of firms gets very large, Cournot model approaches perfect competition Cartel Application: Let firm 1=SA, firm 2=Rest of the Cartel RC. Product is oil Suppose that the strategies of both SA and RC are limited to either producing 20 million barrels or 15 million barrels. If one firm produces 20 million barrels and the other firm produces 15 million barrels, P=35 and the firm producing 20 million barrels earns 500, while the firm producing 15 million barrels earns 375. A one shot game Rest of Cartel s Output Saudi Arabia s Output Unique Nash equilibrium of one shot game is (20,20)

4 Leader-Follower (Stackelberg) Model One firm has a first mover advantage Suppose that there are two firms and that firm 1 has the first mover advantage. Firm 1 knows that firm 2 will react according to its reaction function and takes this into account. Example: Consider the previous example: π 1 =60q 1 q 12 q 2 *q 1 q 2 *=(60-q 1 )/2 (Reaction function of firm 2) To solve: Plug q 2 * into profit equation and solve for q 1. Repeated Games Suppose that each firm adopts the following Tit for Tat trigger strategy: I will produce at the cooperative level as long as my competitor did so if the previous period. If, however, my competitor deviates from that level, I will produce 20 million barrels forever. (Punishment threats must be credible to be effective.) Each player must determine whether it is worthwhile to deviate from the cooperative output level. Such a deviation results in a short term gain. But there are long term losses. Hence there is a tradeoff which depends, in part, on the discount rate. Cooperation yields the following payoff: /(1+r) + 450/(1+r) 2 +. = 450(r +1)/r Deviation yields the following payoff /(1+r) + 400/(1+r) 2 +.= /r Cooperation can be sustained if: r<( )/( )=1, that is if the discount rate is less than 100%. In general cooperation can be sustained if r<(cartel profit one shot eq. Profit)/(deviation profit - cartel profit).

5 Without repetition of play, players are less likely to cooperate Repetition can create much stronger incentives to cooperate Trading off the gains from being non-cooperative today with the last future cooperation Tradeoff of SR gains vs. LR losses means that the discount rate matters