🔹 Non-Collusive Models

These models assume that firms do not cooperate or collude but act independently in their own interest.

1. Cournot Model (1838)

Developed by: Augustin Cournot
Type: Quantity competition

Assumptions:

• Few firms (n) produce a homogeneous product.

• Firms choose output simultaneously and independently.

• Each firm aims to maximize its own profit.

• Market price depends on total market output.

• No collusion among firms.

How the Cournot Model Works:

1. Each firm chooses an output level, assuming the rival’s quantity is fixed.
2. The market price is determined by the total quantity supplied (from both firms) based on the demand curve.
3. Since each firm’s profit depends on both its own and its competitor’s output, firms adjust their quantities in response to each other’s decisions.
4. The process continues until a stable Nash equilibrium is reached, where neither firm has an incentive to change its output.

Cournot Equilibrium:

At equilibrium, each firm produces the quantity that maximizes its profit given the competitor’s output level. This results in a stable market output where firms have no incentive to change their production.

2. Bertrand Model (1883)

Developed by: Joseph Bertrand
Type: Price competition

Assumptions:

• Few firms (n) producing homogeneous products.

• Firms set prices simultaneously and independently.

• Consumers buy from the lowest-priced firm.

• Perfect information and no transaction costs.

Outcome:

• Firms undercut each other’s prices until price = marginal cost.

• Known as the Bertrand Paradox: even with few firms, the outcome resembles perfect competition.

• Assumes no product differentiation.

3. Stackelberg Model

Developed by: Heinrich von Stackelberg
Type: Quantity competition with sequential moves

Assumptions:

• Two firms: Leader and Follower.

• The leader sets output first; the follower responds after observing the leader’s decision.

• Firms produce homogeneous products.

• Goal is profit maximization.

Outcome:

• The leader has first-mover advantage and earns higher profits.

• The follower reacts optimally based on the leader’s choice.

• Total market output is higher than Cournot, but less than perfect competition.

4. Sweezy’s Kinked Demand Curve Model (1939)

Developed by: Paul Sweezy
Focus: Price rigidity in oligopoly

Assumptions:

• Few firms produce homogeneous products.

• If a firm raises price, others do not follow → loss of market share.

• If a firm lowers price, others follow → no real gain in share.

Outcome:

• Creates a kink in the demand curve at the current price.

• Demand curve is:

  • Elastic above the kink (price increase → large loss in demand)

  • Inelastic below the kink (price decrease → little gain)

• Result: Price stability, even without collusion.