Oligopoly Notes

Oligopoly: A market with a small group of firms and substantial barriers to entry. Examples include Nintendo, Microsoft, and Sony.
Cartel: A group of firms that explicitly agree to coordinate their activities (e.g., OPEC).
Monopolistic competition: Firms have market power, but no additional firm can enter and earn positive profits (e.g., restaurants).

Markets differ based on:
- Number of firms.
- Ease of entry and exit.
- Ability to differentiate products.

Oligopolistic firms have an incentive to form cartels to collude on prices or quantities to increase profits.
Examples include: OPEC and Canadian Federation of Quebec Maple Syrup Producers.
Cartels form if members believe coordination will increase profits.

The diagrams illustrate the differences in price and quantity outcomes between competitive and cartelized markets, showing how cartels restrict output to raise prices.

Cartels fail if noncartel members can supply consumers with large quantities of goods.
Each member has an incentive to cheat on the cartel agreement.

Sherman Antitrust Act (1890) and Federal Trade Commission Act (1914) prohibit firms from explicitly agreeing to reduce competition.
Cartels persist because:
- International cartels and cartels in some countries operate legally.
- Some illegal cartels believe they can avoid detection or penalties are insignificant.
- Some firms coordinate activity without explicit collusion.

Cartels must be able to:
- Detect cheating and punish violators.
- Keep illegal behavior hidden from customers and government agencies.

Google, Apple, Intel, and Adobe settled an anti-poaching class action, resolving claims they agreed not to hire each other’s employees, violating U.S. antitrust laws.

Duopoly: An oligopoly with two firms.
Models:
- Cournot: Firms simultaneously choose quantities without colluding.
- Stackelberg: A leader firm chooses its quantity, and followers independently choose theirs.
- Bertrand: Firms simultaneously and independently choose prices.

Firms are identical with the same cost functions and produce undifferentiated products.
Duopoly (two firms) example.
The market lasts for only one period; firms choose quantity or price once.

A set of actions is a Nash equilibrium if no firm can obtain a higher profit by choosing a different action, holding other firms' actions constant.

Cournot equilibrium: Quantities sold by firms such that no firm can obtain a higher profit by choosing a different quantity, holding other firms' quantities constant.

Market demand: $Q = 339 - p$ (p = price, Q = total quantity).
Each airline has a constant marginal cost (MC) and average cost (AC) of $147 per passenger.
Residual demand American faces: $p = 339 - qA - qU$
Marginal revenue function: $MRA = 339 - 2qA - q_U$
American Airlines’ best response: $339 - 2qA - qU = 147 \Rightarrow qA = 96 - \frac{1}{2}qU$
United’s best-response function: $qU = 96 - \frac{1}{2}qA$
In equilibrium: $qA = 64, qU = 64, Q = 128$ , Price = $211.

Profit-maximizing condition: $\frac{p - MC}{p} = -\frac{1}{n\epsilon}$
- $n$ = number of firms
- $\epsilon$ = market elasticity of demand
If $n = 1$ , the firm is a monopoly.
As $n$ grows large, the residual demand elasticity approaches negative infinity, and $p = MC$ , which is the profit-maximizing condition of a price-taking competitive firm.
Lerner Index: $\frac{p - MC}{p} = - \frac{1}{n\epsilon}$

Table shows how firm output, market output, price, market elasticity, residual demand elasticity, and Lerner Index change with the number of firms.
As the number of firms increases:
- Firm output decreases.
- Market output increases.
- Price decreases.
- Elasticities become more elastic (more negative).
- Lerner Index decreases.