5.10 Oligopoly
An oligopoly is a market with just a few firms that have significant market power, perhaps through advertising, product differentiation, or high barriers to entry. 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 \(MC = 20\)
1) Perfect Collusion
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, an organization of oil-exporting developing nations, which was able to raise the price of a gallon of gasoline in the US from $1.80 to $11.65 in the 1970s.
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.
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
Answer:
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?
Answer:
2) Bertrand Competition
In the Bertrand oligopoly model, firms compete on price and can capture the entire market by undercutting their rival slightly.
- What price will firms charge in equilibrium? (Hint: They will undercut each other until price equals marginal cost)
Answer:
- Calculate firm profits at this equilibrium.
Answer:
3) Cournot Competition
In the Cournot model, firms choose quantities simultaneously.
- Show that Firm 1’s revenue function is \(TR = (100 - Q_1 - Q_2) Q_1\).
Answer:
- 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.
Answer:
- 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 \(Q_2\).
Answer:
- Calculate the market price and each firm’s profit.
Answer:
4) Analysis
Compare the three models by filling in this table:
| Model | Price | Total Quantity | Firm Profits |
|---|---|---|---|
| Perfect Collusion | |||
| Bertrand | |||
| Cournot |