Oligopoly Market Structure: What are the elements? What is implicitly assumed about conditions of entry?

Advertising game: 2-firm non-cooperative bimatrix with high (cost=$200) and low (cost=$100) levels of advertising expenditure. Non-price competition. Prisoners Dilemma structure. $10 profit margin per unit. Zero sum advertising -just redistributes fixed overall demand of 100 units at P=$15. If firm A advertises high and firm B advertises low, A sells 75 and B sells 25.

Students compute profits for each matrix….

Describe Nash equilibrium to this game…. Inefficient, rent-dissipating equilibrium (from the two firms' perspective).

Compatibility of standards game: 2-firm non-cooperative bimatrix game with manufacturers of videocassette tapes and players. Suppose that the player manufacturer's profits are higher under standard 1, while the tape manufacturer's profits are higher under standard 2. Profits are zero if they individually select different standards.

Put bimatrix on board….Describe Battle of the Sexes Nash equilibria…. Note the role of interdependency here….

Note that the bimatrix is also called the strategic form of the game….

Cournot Oligopoly:

Most simple case: Duopoly with identical products and constant marginal cost.

Example:

Inverse market demand: P = a - bQ

Market sales quantity: Q = q1 + q2

Marginal cost: C

Firm 1's profit: (P-C)*q1 = (a - bq1 - bq2 - C)*q1

Profit maximization: MR = MC a - 2bq1 - bq2 = C; q1(q2) = (a - bq2 - C)/2b

Simplification yields q1(q2) = (a-C)/2b - q2/2

Students: prove to yourself that we can similarly get:

q2(q1) = (a-C)/2b - q1/2

We have derived what are called best response functions for firms 1 and 2. For example, firm 1's profit-maximizing output level depends on firm 1's conjecture regarding firm 2's output.

The Nash equilibrium requires that each firm's conjectures be correct. In this case, firm 1's conjecture regarding q2 is correct (i.e., firm 2 behaves as firm 1 originally conjectured), and firm 2's conjecture regarding q1 is correct (i.e., firm 1 behaves as firm 2 originally conjectured). This Nash equilibrium features mutual best responses.

Algebraic Solution:

q1(q2) = (a-C)/2b - ½*[(a-C)/2b - q1/2]; simplify….

q1 = 2(a-C)/4b - (a-C)/4b + q1/4

¾*q1 = (a-C)/4b

q1* = 4(a-C)/12b = (a-C)/3b

Students: demonstrate to yourselves that

q2* = (a-C)/3b

Q* = 2(a-C)/3b

Compare Cournot to both the "competitive" (P = MC) and the cartel/monopoly solutions:

Competitive Case:

P = MC a -bQ = C; Q* = (a-C)/b

Monopoly Case:

MR = MC a - 2bQ = C; Q* = (a-C)/2b

Draw diagram on board. Compare profit under the three equilibria…. Note that under noncooperative Cournot oligopoly, the firms produce more (and their joint profits are less) than if they could collude or cooperate.

Students read on their own the von Stackelberg and Bertrand oligopoly models and equilibria….

Product Differentiation:

The quantity of good 1 demanded is less sensitive to the price of good 2 than to its own price, and vice versa.

q1 = x - yp1 + ½yp2

q2 = x - yp2 + ½yp1

As before, assume constant marginal cost C.

Firm 1's profit: q1*(p1-C) = (p1-C)(x - yp1 + ½yp2)

Firm 2's profit: q2*(p2-C) = (p2-C)(x - yp2 + ½yp1)

Suppose that firms strategize over price rather than quantity (as in Cournot). Then…

Firm 1's optimal price: x - 2yp1 + ½yp2 + yC = 0; simplify….

p1(p2) = (x + yp2/2 + yC)/2y = (x + yC)/2y + p2/4

By symmetry we can get:

p2(p1) = (x + yC)/2y + p1/4

Solve for Bertrand/Nash equilibrium (mutual best response):

p1 = (x + yC)/2y + ¼*[(x + yC)/2y + p1/4]; simplify…

(p1 - p1/16) = 5(x + yC)/8y; simplify…

p1* = 80(x + yC)/120y = 2(x + yC)/3y

For example, suppose that x = 100, y = 1, and C = 20. Then p1* = 240/3 = 80 (see book pp. 110-112)

Similarly p2* = 2(x + yC)/3y.

Note that in both cases, product differentiation allows price to exceed marginal cost, and so we do not get the perfectly competitive solution. You should be able to show that if the products are identical and price is the strategic variable, then price will be equal to marginal cost…. By the same token, the less sensitive q1 is to p2, the higher will be the equilibrium prices….

Collusion:

One relatively common method of collusion is for firms to establish quotas that in sum are equal to the monopoly output, and continue producing at the quota amount until cheating is detected (i.e., the other firm over-produces). Cheating then "triggers" the firm detecting the cheating to increase its own production output forever. The problem with this so-called trigger strategy is that it may not be credible (as is assumed in the text on pages 114-116), and if it is not credible, it will not serve as deterrent.

Methods of Collusion:

-Price leadership

-Similar price markup systems

-Basing point systems (ex: all prices based on shipment from a common point, even if shipments do not actually originate from a common point)

-Marketing associations through which all orders flow

Challenges:

-What if firms have different costs, and thus the optimal price differs across firms?

-What if products are differentiated?

-What if it is difficult for the cartel to monitor member output?

-What if entry is relatively easy, or there is substantial non-cartel production?

If there is imperfect monitoring, then one can expect periods of reversion to Cournot or competitive pricing. Example: Cartel pricing of rail rates, 1880 - 86 (p. 122 of text).

Antitrust law toward price fixing:

Distinguish per se legal doctrine from rule of reason doctrine. Per se rule applies to acts that can have no beneficial effects, and are limited to price fixing cases. From a law and economics point of view, the anticipated net benefits of a full-blown investigation of possible mitigating circumstances in a price fixing case are small.

Most all other antitrust situations are subject to rule of reason doctrine.

Discuss Williamson's diagram showing the tradeoffs involved when a merger might lower (constant) average cost, but also result in collusion (i.e., before P = AC = MC, but now P > AC as in standard monopoly). Should the merger be stopped on efficiency grounds? Trade off: decline in consumer surplus equal to the deadweight loss triangle, but increase in surplus (all of which goes to the producer!) from AC falling.

From an efficiency perspective, antitrust cases in which there are gains but no losses (i.e., AC falls but the market remains competitive) should be ok, while those that generate losses but no gains (i.e., costs don't change but the market becomes collusive) should be illegal. But what about mixed cases such as that identified by Williamson?

Per-Se Cases: Addyston Pipe (1899), Trenton Potteries (1927). What did the U.S. Supreme Court argue in these cases with regard to the "reasonableness" of price-fixing? How did opinions change on cartelization as a remedy for industrial decline in the 1930s, and what are some examples? Appalachian Coal, ag. marketing orders… How did Socony-Vacuum (Mobil) move the court back to per-se in 1940? Does per-se apply to price fixing in professions such as law, optometry, etc? See Virginia Bar Assocation case. How was the NCAA case different from other price fixing cases?

What is conscious parallelism (tacit collusion)? Case: 1946 American Tobacco. What is "parallelism plus" (plus advance knowledge of impending rival actions)…. Currently one must find explicit collusion, and so conscious parallelism is legal.