20 Price Leadership
For more information on these topics, see Allen, Doherty, Weigelt, and Mansfield Chapter 11: Oligopoly.
20.1 Classwork 20: Understanding Oligopoly: Cooperation, Breakdown, and Leadership
An oligopoly is a market structure with just a few firms that have significant market power. When there are only a few firms in a market, they often recognize their interdependence and may try to cooperate to increase profits. This can happen in three main ways:
- Formal Cartels: An open agreement to set prices and divide the market (like OPEC)
- Tacit Collusion: Informal coordination without explicit agreements
- Price Leadership: One dominant firm sets prices that others follow
If firms can avoid competing aggressively, they can maintain higher prices and profits. It’s like a group of restaurants on the same street agreeing not to start a price war that would hurt everyone’s margins. Of course, customers suffer as a result and total surplus declines.
- Cartel Price Setting
Suppose a market is dominated by just two firms with identical costs: \(TC = 20q\). They face a market demand curve \(P = 100 - Q\). If they form a cartel, they can maximize joint profits by acting the way a monopolist would.
Show that jointly, the two firms will supply 40 units and sell them at a price of $60 per unit.
What is the total cartel profit?
If the firms split output equally, what is each firm’s profit?
- The Temptation to Cheat
While cooperation seems attractive, it’s inherently unstable. Each firm has an incentive to “cheat” by slightly undercutting the agreed price or producing more than their quota. This is known as the prisoner’s dilemma in game theory. Continuing our previous example, suppose the cartel’s price is $60.
If one firm slightly undercuts to $59, they might start to attract many more customers: suppose they sell 30 units instead of their allotted 20 units. Calculate their profit: does it increase by undercutting the cartel?
Do firms have an incentive to undercut the cartel? If there’s a price war, what’s the price that the two firms will settle on (the lowest while producer surplus is non-negative)? What is firm profit then?
The fundamental problem is that while cooperation maximizes joint profits, each individual firm can do better by cheating—as long as others maintain the agreement. But since all firms face this incentive, agreements tend to break down.
- A Larger Cartel
Consider a three-firm cartel:
Market demand: \(P = 120 - Q\)
Each firm’s total cost: \(TC = 30Q\)
Cartel output: 45 units (15 each)
Cartel price: $75
- Calculate each firm’s cartel profit.
- Calculate the profit for the cheater if one firm increases output by 5 units while others maintain quotas (note that the market price will decrease). Does the cheater increase their profits by cheating?
- Calculate the industry profits if all firms increase output by 5 units. If all firms in the cartel cheat, what happens to each firm’s profit (compared to if all firms in the cartel follow the cartel rules)?
- Price Leadership
When explicit cooperation is illegal or not possible, markets often evolve toward price leadership, where one dominant firm effectively sets prices for the industry. Here’s how it works:
The dominant firm faces a demand curve and a fringe small firm supply curve. The dominant firm chooses a price to maximize its profit, knowing that the small firms can supply however much they want at that price and the dominant firm will supply the leftover amount that the consumers want to buy. Let’s do an example.
Let market demand be given by \(Q = 100 - 4P\) and let the small firms’ supply curve be \(Q_S = P\). That is, the small firms will take the dominant firm’s price and supply \(P\) units. Suppose also that the dominant firm has a total cost of \(TC_D = 10Q_D\).
We know that the total market quantity is equal to the dominant firm’s supply plus the small firm’s supply: \(Q = Q_D + Q_S\). Plug in for \(Q\) and \(Q_S\) to show that \(Q_D = 100 - 5P\).
Next, we want to use the \(MR_D = MC_D\) rule to find the profit maximizing quantity for the dominant firm. First, show that \(TR_D = 20 Q_D - \frac{1}{5} Q_D^2\).
Now use \(MR_D = MC_D\) to show that \(Q^*_D = 25\).
Show the corresponding price is \(P = 15\).
Calculate \(Q_S\), \(Q\), and show that \(\pi_D = 125\).
This framework helps to explain why oligopolistic industries often maintain prices above competitive levels even without explicit collusion, while still experiencing periodic price wars and competitive episodes.
20.2 Practice Questions