ECON6021 (Nov 2004) Oligopoly

Market Structure Monopoly – a single firm A patented drug to cure SARS A single power supplier on HK Island Oligopoly – a few major players The top 4 cereal manufacturers sell 90% of all cereals in the US HK property developing market Collusion: price fixing

Monopolistic competition – a large number of firms, selling differentiated goods, with some market power, easy entry and exit Local bakery Perfect competition – numerous firms, homogeneous product, no market power, easy entry and exit International agricultural product market

Profit Maximization Regardless of market structure, the following are assumed: Firm’s objective: to maximize economic profit Choice variable: quantity, unless otherwise stated Hence, setting Q so that MR = MC (provided that MR cuts MC from above, and the resulting profit is not lower than not producing at all)

Oligopoly Three models of oligopoly Cournot competition Bertrand competition Stackelberg competition Most complex market – strategic interaction, collusion, first mover advantage, commitment, etc.

Cournot Competition An industry is characterized as Cournot oligopoly if There are few firms in the market serving many consumers. The firms produce either differentiated or homogeneous products. Each firm believes rivals will hold their output constant if it changes its output. Barriers to entry exist.

Reaction Functions and Equilibrium further simplifications: duopoly -- 2 firms only reaction function defines the profit- maximizing level of output for a firm for given output levels of the other firm. Q ₁ =r ₁ (Q ₂ ). and Q ₂ =r ₂ (Q ₁ ).

Reaction Functions

Finding reaction functions If the (inverse) demand is P=a-b(Q ₁ +Q ₂ ). The marginal revenues of firms 1 and 2 are MR ₁ (Q ₁,Q ₂ ) = a-bQ ₂ -2bQ ₁ MR ₂ (Q ₁,Q ₂ ) = a-bQ ₁ -2bQ ₂ ∙ Assume constant marginal costs c ₁ and c ₂. Setting MR=MC, we have a-bQ ₂ -2bQ ₁ =c ₁ for firm 1. Firm 1’s reaction function: Q ₁ =r ₁ (Q ₂ )=((a-c ₁ )/(2b))-(1/2)Q ₂ Similarly, firm 2’s reaction function: Q ₂ =r ₂ (Q ₁ )=((a-c ₂ )/(2b))-(1/2)Q ₁

Isoprofit curves for firm 1

Firm 1’s Isoprofit curve

Cournot Equilibrium In case c 1 = c 2 =c, we have Q 1 c =Q 2 c =2(a-c)/3

Extensions: Changes in Marginal Cost

Collusion

Firm 2 colludes but firm 1 cheats

Stackelberg Oligopoly An industry is characterized as a Stackelberg oligopoly if: There are few firms in the market serving many consumers. The firms produce either differentiated or homogeneous products. A single firm (the leader) selects an output before all other firms choose their outputs. All other firms (the followers) take as given the output of the leader and choose outputs that maximize profits given the leader's output. Barriers to entry exist.

Model ∙ Two firms--Firm 1 is the leader with a "first- mover" advantage, and Firm 2 is the follower, who maximizes profit given the output produced by the leader. ∙ same cost functions, and demand function as in Cournot model Follower's reaction function: Q ₂ =r ₂ (Q ₁ )=((a-c ₂ )/(2b))-(1/2)Q ₁, which is simply the follower's Cournot reaction function.

Firm 1’s profit exceeds that under Cournot competition

Bertrand Oligopoly An industry is characterized as a Bertrand oligopoly if: There are few firms in the market serving many consumers. The firms produce identical products as a constant marginal cost. Firms engage in price competition and react optimally to prices charged by competitors. Consumers have perfect information and there are no transaction costs. Barriers to entry exist.

Model Consider a Bertrand duopoly, and both firms have the same marginal cost. Price war -- Both firms charge a price equal to marginal cost: P ₁ =P ₂ =MC! If fixed costs >0, both earn negative profits! Hence a so called Bertrand paradox!!

Some solutions to the Bertrand paradox ∙ Product Differentiation -- undercutting will not steal all the sale from the other firm Capacity constraint (Edgeworth) price cutting now is less profitable if you cannot satisfy the extra quantity demanded (because of your limited capacity) Kreps & Scheinkman (1983, Bell J. of Economics) -- "Quantity Precommitment & Bertrand Competition yield Cournot Outcomes" in stage 1, two firms choose capacity In stage 2, after capacities fixed and observed, the two firms choose prices Result: Cournot outcome is replicated

Application 1: Capital investment capital investment (equipment, building, etc.) as a deterrence device many such investment is sunk cost and difficult to resell, making it a credible threat to potential entrants

Application 2: Horizontal Merger Before merger three firms (each with one plant), same marginal costs, Cournot competition After merger firm 1 and firm 2 merge together to become a mega firm, with a single owner-manager making decisions for both plants, marginal cost in each plant remains unchanged, Cournot competition

Further insights: Merger and divisionalization Horizontal merger -- which allows output decision coordination among the merged firms -- is beneficial only when a sufficiently large fraction of firms are involved More generally, flexibility and ability of coordination might weaken one's position to profit [ ∴ inflexibility may improve your profitability] Oligopolists have incentives to divisionalize, franchise, and even divest [≡ set off assets] M - form firms -- e.g., General Motor, consisting of a number of almost autonomous divisions selling often same class of automobiles

Alfred P. Sloan and General Motors Alfred Sloan (1963): “According to General Motors plan of organization … the activities of any specific Operation are under the absolute control of the General Manager of that Division, subject only to very broad contact with the general officers of the Corporation.” Description of GM’s operating divisions in Moody’s Instustrial Manual (1993): “ …each of which is self- contained administrative unit with a general manager responsible for all functional activities of his division.” Other major automobile manufacturers have similar structures.

Divisionalization Divisionalization is traditionally explained by the difficulty arising from managing a large firm Baye, Crocker, and Ju (1996, AER) argue that in the absence of such consideration, divisionalization still arises from strategic interaction in oligopolistic competition a fixed number of firms in stage 1, each firm decides the number of autonomous divisions to have (divisionalization is costly) in stage 2, all divisions of all firms compete by choosing output levels In equilibrium, each firm chooses more than one division despite costs to set up a division

Commitment not to intervene Assumption in the paper: the headquarters can commit not to interfere with each autonomous division's decision. In reality. Is this assumption reasonable? Or how firms can make it to happen? compensation of each division's manager is made to depend on his sale, making the manager defiant to headquarters' incentive to coordinate, if any. franchising divestiture

Recap Three models of oligopoly have been introduced. Interdependence of choices are emphasized. A lot of interesting issues can be addressed.