# ECON6021. Market Structure. Profit Maximization. Monopoly a single firm A patented drug to cure SARS A single power supplier on HK Island

Size: px
Start display at page:

Download "ECON6021. Market Structure. Profit Maximization. Monopoly a single firm A patented drug to cure SARS A single power supplier on HK Island"

Transcription

1 Market Structure ECON6021 Oligopoly 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 Profit Maximization 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 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) 1

2 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. Choice variable -- output Barriers to entry exist. Cournot Competition Suppose that two firms duopoly--are competing by choosing quantities of goods to place on the market Both have identical, constant marginal costs Normalize these to be zero Everyone faces a linear demand curve How to Find Reaction Function (a.k.a. Best Response Function)? Reviewing Monopoly If firm 1 anticipates that firm 2 will choose to produce NO output, then firm 1 is a monopolist in this market We can find firm 1 s best response to this conjecture via the usual solution to monopoly problems 2

3 Graphical Solution Comments Price Notice that marginal revenue lies below demand curve MR Demand Discounts to attract the next customer have to be passed along to all the other existing customers Therefore, the increment to revenue is less than the willingness to pay of the marginal customer Quantity Comments Graphical Solution Part 2 Notice that marginal revenue lies below demand curve Price Discounts to attract the next customer have to be passed along to all the other existing customers Therefore, the increment to revenue is less than the willingness to pay of the marginal customer Pm MR Demand Qm Quantity 3

4 Other Conjectures Now suppose that firm 1 conjectures that firm 2 will produce 10 units. Firm 1 faces the following demand curve P Comments Notice that this just shifts the location of the y- axis in the standard diagram The best response of firm 1 is calculated the same way---solve the monopoly problem for the adjusted demand curve. 10 Q Graphical Solution Firm 2 produces 10 Graphical Solution Optimal Firm 1 Production Price Price Demand Demand P* MR1 MR1 10 Quantity 10 Q* Quantity Firm 1 s quantity 4

5 Some Math We can write the graphical situation down as an optimization problem. Firm 1 conjectures firm 2 s quantity, q 2, and chooses its own quantity, q 1, to maximize profits Suppose demand is P = 12 Q, then Choose q 1 to maximize Profit 1 = q 1 x P Profit 1 = q 1 x (12 q 1 q 2 ) More Geometric Intuition Profit 1 = q 1 x (12 q 1 q 2 ) Notice that if q 1 = 0, firm 1 earns no profits Likewise if q 1 = 12 q 2 Thus, the profit function looks like Profit Slope is flat at The top q 1 Calculus Profit 1 = q 1 x (12 q 1 q 2 ) Differentiate with respect to q 1 and find the q 1 at the top of the hill (i.e. slope = 0) This yields: d Profit 1 /dq 1 = 12 2q 1 q 2 (This is the slope of the hill) 12 2q 1 q 2 = 0 (This is the top of the hill slope = 0) q 1 = 6 -.5q 2 (This is the best response function) Equilibrium An equilibrium is a pair of mutual best responses. This means that each side conjectures the other s move correctly and best responds to it. So we need q 1 and q 2 solving q 1 = 6 -.5q 2 q 2 = 6 -.5q 1 Solving: q 1 = q 2 = 4 5

6 Sequential Competition Now let s compare this to the situation where firm 1 moves first --- and is observed --- followed by firm 2. Firm 2 s problem is just the same as it was before. Therefore, firm 1 anticipates that if it chooses q 1, firm 2 will choose q 2 = 6 -.5q 1 Knowing this, what should 1 choose? Firm 1 s Optimization Firm 1 should look forward and reason back in making its decision Recall: Profit 1 = q 1 x (12 q 1 q 2 ) But firm 1 knows (looking forward) that q 2 = 6 -.5q 1 Therefore, firm 1 will choose q 1 to maximize Profit 1 = q 1 x (12 q 1 (6 -.5q 1 )) Profit 1 = q 1 x (6.5q 1 ) Calculus Once again, firm 1 seeks to get to the top of its profit hill: Profit 1 = q 1 x (6.5q 1 ) dprofit 1 /dq 1 = 6 q 1 The slope is flat at the top 6 q 1 = 0 q 1 = 6 And, knowing q 1, q 2 = 3 Comments Going first in this game (Stackelberg competition) enables firm 1 to gain market share at firm 2 s expense Even though the market price is now lower (8 units of the good on the market when moves were simultaneous versus 9 now) Firm 1 s profits are higher How do we know this without calculating it? This game has a first-mover advantage 6

7 How did firm 1 gain an advantage? Commitment Firm 1 could commit to produce more when its production decision was observable by 2 Strategic substitutes Further, firm 1 s good is a (perfect) substitute for 2 s good. By committing to produce more, firm 2 was obliged to scale back production Thus, the two goods are strategic substitutes. More generally, back to Cournot competition If the (inverse) demand is P=a-b(Q₁+Q₂). The marginal revenues of firms 1 and 2 are MR₁(Q₁,Q₂) = a-bq₂-2bq₁ MR₂(Q₁,Q₂) = a-bq₁-2bq₂ Assume constant marginal costs c₁ and c₂. Setting MR=MC, we have a-bq₂-2bq₁=c₁for firm 1. Firm 1 s reaction function: Q₁=r₁(Q₂)=(a-c₁)/(2b)-(1/2)Q₂ Similarly, firm 2 s reaction function: Q₂=r₂(Q₁)=(a-c₂)/(2b)-(1/2)Q₁ Reaction Functions Isoprofit curves for firm 1 7

8 Firm 1 s Isoprofit curve Cournot Equilibrium In case c 1 = c 2 =c, we have Q 1c =Q 2c =(a-c)/3 Extensions: Changes in Marginal Cost Collusion 8

9 Firm 2 colludes but firm 1 cheats Firm 1 s profit exceeds that under Cournot competition Bertrand Oligopoly Model 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. Consider a Bertrand duopoly, and both firms have the same marginal cost. Price war -- Both firms charge a price equal to marginal cost: P₁=P₂=MC! If fixed costs >0, both earn negative profits! Hence a so called Bertrand paradox!! 9

10 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 10

11 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 selfcontained 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. 11