24  Oligopoly

For more information on these topics, see Varian Chapter 27: Oligopoly.

An oligopoly is a market with just a few firms that have significant market power. Consider a market with the following characteristics for all the questions in this classwork:

• Market demand: \(P = 100 - Q\)
• Two identical firms with marginal cost \(MC = 20\) and zero fixed costs

CW 1) Perfect Collusion and Cartels

Perfect collusion occurs when firms coordinate their decisions to maximize joint profits, effectively acting as one entity. This often happens through cartels - usually illegal formal agreements between firms to set prices and divide market share. One famous example is OPEC (oil).

If the cartel acts as one entity and maximizes joint profits, they make the same \((P, Q)\) decision as a monopolist would. Just as a monopolist restricts output to drive up prices, a cartel restricts each member’s output to achieve the same goal.

1. Suppose the two firms form a cartel and act like a monopolist. Calculate:

   • The profit-maximizing quantity and price
   • Each firm’s profit if they split the market equally

2. Despite high profits, cartels are inherently unstable. Let’s see why:

   • Suppose one firm “cheats” by producing 5 more units than they are supposed to according to the cartel agreement you found in part a. Find the new market quantity, find the new market price, and calculate profits for the cheating firm and the firm who stays true to the agreement. In this cartel, do firms have an incentive to cheat by producing more than their quota?

CW 2) Bertrand Competition

In a Bertrand model, firms compete on price and can capture the entire market by undercutting their rival slightly.

1. What price will firms charge in equilibrium? (Hint: They will undercut each other until price equals marginal cost)
2. Calculate firm profits at this equilibrium

CW 3) Cournot Competition

In the Cournot model, firms choose quantities simultaneously.

1. Show that Firm 1’s revenue function is \(TR = (100 - Q_1 - Q_2) Q_1\).

2. Firm 1’s reaction function is their profit maximizing \(Q_1\) given the quantity firm 2 chooses to produce. To derive this, set firm 1’s marginal revenue equal to their marginal cost (MR is found with \(\frac{\partial TR}{\partial Q_1}\)). Solve for \(Q_1\) to get the reaction function.

3. Firm 2 is symmetrical in every way to firm 1, so \(Q_2 = Q_1\). Use the equation from part b along with this equation to solve for the two unkowns, \(Q_1\) and \(Q_2\).

4. Calculate the market price and each firm’s profit.

CW 4) Analysis

Compare the three models by filling in this table:

Model             | Price | Total Quantity | Firm Profits
------------------|-------|----------------|-------------
Perfect Collusion |       |                |
Bertrand          |       |                |
Cournot           |       |                |

Which model best explains:

• Why cartels are rare despite being profitable?
• Why prices tend to fall as more firms enter a market?
• Why oligopolies often maintain prices above competitive levels without explicit collusion?

24.1 Practice Questions

Question 1: Which of the following best explains why cartels tend to be unstable?

Government regulations make them difficult to maintain
Members have a strong incentive to cheat by producing more than their quota
Consumer boycotts often break them apart
Economic recessions make coordination impossible

Question 2: In a Bertrand competition model, firms compete on price. What typically happens in equilibrium?

Firms charge the monopoly price by tacitly colluding
Firms set prices above average cost but below monopoly price
Firms undercut each other until price equals marginal cost
Firms randomly vary their prices to prevent undercutting

Question 3: What distinguishes Cournot competition from other oligopoly models?

Firms compete by setting prices rather than quantities
Firms make output decisions simultaneously while considering competitors’ likely choices
Firms take turns being the market leader
Firms explicitly coordinate their production decisions

Question 4: Perfect collusion in an oligopoly results in:

Maximum consumer surplus and minimum producer surplus
Prices and quantities similar to perfect competition
Prices and quantities identical to what a monopolist would choose
Higher quantities and lower prices than Cournot competition

Question 5: When comparing different oligopoly models, which typically produces the most competitive outcome for consumers?

Perfect collusion through cartels
Bertrand price competition
Cournot quantity competition
Sequential leader-follower competition