Mutual interdependence occurs when the price or output of choices made by any one firm affects the profits of all.
The Fundamental Assumptions
1. Sellers are price makers.
2. Sellers behave strategically.
3. The conditions of entry may range from completely blocked to perfectly free.
4. Buyers are price takers.
The Appropriate Market Structure
1. The size and number of buyers. We are interested in markets with many buyers, no one of whom is large enough to exert any influence on price.
2. The size and number of sellers. We are interested in markets with relatively few (but more than one) firms in the industry. In this case, they are likely to recognize their mutual interdependence.
3. The degree of substitutability of different sellers’ products. This can range from perfect substitutes to goods that are highly differentiated. However, producers must be able to recognize their influence on one another.
4. The extent to which buyers are informed about prices and available alternatives. The model can encompass both well-informed and poorly informed consumers.
5. The conditions of entry. Oligopoly allows for conditions of entry ranging from blocked to completely free.
15.1 Quantity-Seeking Oligopolists
These are the assumptions for considering the model:
1. There are two firms in the industry. A market in which there are only two suppliers is referred to as a duopoly.
2. Further entry into the market is completely blocked. (We only need to worry about the behavior of the two firms.)
3. The firms produce homogeneous products.
4. The firms have identical, constant marginal costs equal to c. This implies that if the firm’s output level is x, then its total cost is c*x.
A self-enforcing agreement is one in which each firm finds that abiding by the agreement is in its self interest, given that the other firms do so too.
A tacit agreement is a situation in which firms have come to a common understanding about how they should behave in a market without actually discussing it among themselves. Usually firms use tacit agreements rather than explicit agreements, because explicit agreements are often illegal.
The best response is a decision maker’s best course of action, given what the other decision makers are doing.
A market is at a Nash equilibrium when each firm is choosing the strategy that maximizes its profit, given the strategies of the other firms in the market.
A Cournot equilibrium (or Cournot-Nash equilibrium) is a Nash equilibrium in a market in which each firm’s strategy consists of its choice of output level. For example:
1. Given that Firm B sells z units, Firm A’s profit is maximized by selling y units.
2. Given that Firm A sells y units, Firm B’s profit is maximized by selling z units.
Finding a Cournot Equilibrium
Deriving the Best-Response Functions
The residual demand curve is the firm-specific demand curve faced by the supplier, given the price or output strategies chosen by its rivals. The axes of this graph are output (x-axis) and cost (y-axis). Assuming a particular level of output for the rival(s), the firm can then determine how to maximize its own output – i.e. its best response to the other firm’s action.
The best-response curve (or reaction curve) is a schedule showing a decision maker’s best course of action for each set of choices made by other decision makers. The axes of this graph are Firm A’s output (x-axis) and Firm B’s output (y-axis). The reaction curve tells us Firm B’s profit-maximizing output choice for any given output level by firm A.
Using Reaction Curves to Find the Cournot Equilibrium
To be in equilibrium, each firm must be at a point on its reaction curve. The point where the reaction curves cross represents the conditions in which each firm is best responding to the other. The Cournot-Nash equilibrium is found at the intersection of the two reaction curves.
Comparison of Cournot, Monopoly, and Perfect Competition
Viability of the Full Cartel Agreements
Cournot duopolists collectively produce more output than would a monopolist.
Are We Back to Perfect Competition?
Under the Nash-Cournot equilibrium, the level of industry output is greater than the joint-profit maximizing level and less than the competitive level.
An Algebraic Example of Cournot Equilibrium
This section provides the derivation of the mathematical solution to this problem. (See text book)
1. A firm’s profit falls when its own cost rises.
2. A firm’s profit rises when its rival’s cost rises.
Comparison of Cournot Duopoly, Competition, and Monopoly
The monopolist produces the least output followed by the Cournot Duopoly, followed by perfect competition, which results in the greatest output.
The monopolist has the highest prices, followed by the Cournot Duopoly market, and the market in perfect competition has the lowest prices.
15.2 Price-Setting Oligopolists
A Bertrand equilibrium (or Bertrand-Nash equilibrium) is a Nash equilibrium in a market in which each firm’s strategy consists of its choice of the price at which to sell its output. For example:
1. Given that Firm B charges pB per ticket, Firm A’s profit is maximized by charging pA per ticket, and
2. Given that Firm A charges pA per ticket, Firm B’s profit is maximized by charging pB per ticket.
Finding the Bertrand Equilibrium
The market curves for each firm depend on the other:
1. If Firm A charges a higher price than Firm B, then all customers buy from firm B.
2. If Firm A charges a lower price than Firm B, then all customers buy from firm A.
3. If Firm A and Firm B chare the same price, then customers buy half of the amount demanded from A and the other half from B.
When all firms have marginal costs that are equal at c, the Bertrand equilibrium entails all firms setting their prices equal to c.
Cournot or Bertrand?
Why Are Bertrand and Cournot Duopolies So Different?
When dealing with the Cournot equilibrium, cheating on the number of units sold causes the price to fall for both firms. The fact that Firm A’s price falls in response to B’s cheating means that B does not get the whole market just by lowering its price a little.
In the Bertrand firms, if Firm B decides to cheat by lowering its price slightly, Firm A does not change its price to match (it’s prices are stuck), and Beta could get the whole market at almost the same price. The incentive to cheat under these conditions is much larger than under Cournot.
Which Model Should We Use?
We want to focus on the choices to which the firm has to stick. In most markets, prices can be adjusted more quickly than quantities (it’s just a matter of changing price lists), while changing quantities means the firm actually has to change its production operations. Therefore, the quantity-setting Cournot model is often more appropriate.
In a Cournot market, both firms would set quantity at a level that was difficult to change. If one firm cheats (and produces more), the other firm can quickly change its price, but it can’t change its output level.
In a Bertrand market, both firms would set prices that would be difficult to change (mail order catalogues, or bids on a project). If Firm A cheated and set a lower price, Firm B would not be able to adjust their price quick enough, and Firm A would take the entire market.
15.3 Cooperation and Punishment
A more realistic model must take into account that firms make choices repeatedly. In this case, firms can make decisions based on actions that have taken place in the past. If one firm cheats on the deal today, the other firm may punish it in the future.
A Model of Repeated Interaction
If Firm B takes T days to detect Firm A’s cheating, then cheating allows firm A to earn an extra profit. (The extra profit is equal to its profit per day if it cheats minus the profit per day if it sticks to the agreement.) Once Firm A has been caught cheating, it suffers a net punishment per day. (This is the profit if it had stuck to the agreement minus the profit it will earn if it is being punished.) This punishment takes place from the T+1st day.
1. The longer it takes to catch a cheater, the greater the incentive to cheat.
2. The less likely it is that a cheater will be caught, the greater the incentive to cheat.
3. The harsher the punishment that a cheater faces, the lower the incentive to cheat on an agreement. However, a threat or promise by a firm is credible only if it would be in the firm’s self-interest to carry out the threat or promise if called upon to do so.
4. The more complex the collusive agreement has to be, the less likely it is to succeed.
Market Structure and Collusion
1. The more that the firms’ costs differ, the less likely is cooperation, all else equal.
2. The more that demand varies from period to period, the less likely is cooperation, all else equal. This is because changing demand makes the collusive argument more complex.
3. The easier it is for firms to monitor their rival’s output levels, the more likely is cooperation, all else equal. This is because it is easier to catch the cheater.
4. Product differentiation may increase or decrease the likelihood of cooperation, all else equal. Since not all customers will choose based on price, the gains to cheating are lower. However, punishment is more difficult because changing output may not affect the other firm – you are not a strong credible threat.
5. When prices are negotiated with each customer separately, collusion is less likely to be successful, all else equal.
6. When individual orders are large relative to the overall market, collusion is less likely to be successful, all else equal. When the stakes of one order are high, firms may ignore the future.
7. The more firms in a market, the less likely is cooperation, all else equal. More firms make collusion more complicated and cheating harder to detect.