Duopoly (Price and Output Determination)

1) Meaning: what is duopoly?

A duopoly is a market structure in which two firms dominate the market for a product.

Key feature: strategic interdependence.
Each firm’s decision (price/output) affects the other firm’s demand, revenue, and profit. So each firm must consider the rival’s likely response.

CUET PG focus: Most questions target the basic logic of major duopoly models—especially Cournot and Bertrand—and sometimes Stackelberg.

2) Why duopoly is special: strategic behavior

In monopoly:

firm chooses output given market demand.

In perfect competition:

firm takes price as given.

In duopoly:

each firm chooses a strategy while anticipating the rival’s reaction. This is the foundation for oligopoly models too.

3) Cournot Duopoly (quantity competition) – high-yield model

3.1 Core assumptions

Two firms produce a homogeneous product.
Firms choose quantities simultaneously.
Each firm assumes the rival’s output is fixed when deciding its own output.
Market price depends on total output:

Q = q_1 + q_2,\quad P = P(Q)

Each firm has a cost function (often constant MC in basic versions).

3.2 Reaction function

Each firm chooses its best output given the other’s output:

q_1 = R_1(q_2),\quad q_2 = R_2(q_1)

The intersection of reaction functions gives Cournot equilibrium $(q_1^*, q_2^*)$ .

3.3 Key results (standard intuition)

Total output in Cournot is greater than monopoly output but less than competitive output.
Price is lower than monopoly price but higher than competitive price.
Each firm earns positive profits (usually).

Ranking (very testable):

Q_{PC} > Q_{Cournot} > Q_{Monopoly}

P_{PC} < P_{Cournot} < P_{Monopoly}

3.4 Symmetric Cournot (common conceptual conclusion)

If firms are identical (same costs), they split output equally:

q_1^* = q_2^* = \frac{Q^*}{2}

4) Bertrand Duopoly (price competition) – classic “Bertrand paradox”

4.1 Core assumptions

Two firms sell a homogeneous product.
Firms choose prices simultaneously.
Consumers buy from the firm with lower price.
If prices equal, firms split the market.
Firms have constant marginal cost (often assumed).
Unlimited capacity (in simplest version).