Oligopoly and duopoly Models

(i) The Cournot (duopoly) Model

In the Cournot Duopoly Model, two firms (Firm A and Firm B) compete in a market with high demand for mineral water. Here’s how they interact:

• Firm A decides how much water to produce, aiming to maximize profit based on the market price, which is influenced by the total supply.
• Firm B observes Firm A’s production and then produces half of the unsupplied market to maximize its own profit, assuming Firm A’s output is fixed.
• Back-and-Forth: Both firms adjust their production in response to each other, with Firm A and Firm B each producing a portion of the market until equilibrium is reached.
• Equilibrium: Both firms end up producing one-third of the total market demand, together supplying two-thirds of the market.

Missed Opportunity: If they cooperated (colluded), they could act as a monopoly, producing less to drive up prices and split the market equally, with each firm producing just a quarter of the total supply.

(ii) The Bertrand Model

In the Bertrand Duopoly, two firms, Firm A and Firm B, sell identical products (e.g., smartphones) and engage in a price war to attract customers. Here’s how it plays out:

• Price Competition: Consumers always buy from the firm with the lower price. If Firm A sets a price of ₹10,000 and Firm B sets it at ₹10,500, customers will flock to Firm A.
• Undercutting: Firm B, seeing this, lowers its price to ₹9,999, and Firm A responds by lowering its price further. The price keeps dropping as both firms try to outdo each other.
• Zero Profit: The price eventually drops to the point where it equals the marginal cost of production, meaning neither firm makes a profit.
• Outcome: This leads to a perfectly competitive market outcome where prices are driven down to marginal cost, and both firms earn zero profit.

The Bertrand Model illustrates how price competition in a duopoly can result in a race to the bottom, leading to no profit for either firm, similar to a perfectly competitive market.

(iii) The Chamberlin (duopoly) Model

In the Chamberlin Duopoly Model, two firms produce differentiated products, meaning their goods are not identical but slightly different. This product differentiation allows each firm to have some degree of monopoly power, yet they still compete with each other.

Key Features:

• Product Differentiation: The firms’ products are not perfect substitutes. Consumers might prefer one over the other, giving the firms some control over pricing.
• Imperfect Competition: Unlike perfect competition, firms face a downward-sloping demand curve rather than a perfectly elastic one, due to product differentiation.
• Strategic Pricing: Firms must carefully choose their prices and quantities, considering the impact of their decisions on their competitor.

Equilibrium:

• Profit Maximization: Each firm maximizes profit where Marginal Cost (MC) = Marginal Revenue (MR).
• Price and Output: Due to competition, firms charge a price higher than in perfect competition, but lower than a monopoly would.
• Market Outcome: The output produced is lower than in perfect competition, and prices are higher than in perfect competition but lower than a monopoly, resulting in economic profits for both firms.

(iv) Sweezy’s Kinked Demand Curve Model

The Sweezy’s Kinked Demand Curve Model explains price rigidity in oligopoly markets, where a few firms dominate. Developed by Paul Sweezy, it shows why firms are hesitant to change prices due to how competitors react.

Key Features:

• Kinked Demand Curve: The demand curve facing each firm is kinked due to two assumptions:
  • Price Increase: If a firm raises its price, competitors won’t follow, causing the firm to lose many customers as consumers switch to lower-priced alternatives.
  • Price Decrease: If a firm lowers its price, competitors will match the price cut, preventing the firm from gaining many customers and reducing its profit margins.
• Price Rigidity:
  • Firms avoid raising prices because they risk losing customers.
  • Firms also avoid lowering prices because competitors will match, leading to reduced profits.
• Price Stability: As a result of these dynamics, the market experiences price stability. Even if costs change, prices remain rigid, and firms focus more on non-price competition (like advertising and product differentiation) to attract customers.

This model highlights how oligopolistic firms prefer maintaining stable prices to avoid the risks of losing customers or engaging in price wars.

(v) Edgeworth Model

The Edgeworth Duopoly Model, developed by Francis Ysidro Edgeworth, allows two firms to compete not just in terms of price or quantity, but both. Unlike other duopoly models, this one assumes non-linear demand where firms can adjust both the price and output.

In this model:

• Firms A and B compete by choosing the right combination of price and quantity to maximize their profits.
• The market has a limited capacity, and each firm’s decision affects the other’s.
• The Edgeworth Box represents all possible combinations of price and quantity, and the equilibrium is found where both firms’ indifference curves are tangent.

This model leads to unstable equilibrium, with the possibility of price wars (where firms lower prices to compete) or tacit collusion (where firms cooperate without explicit agreement).

The Edgeworth model highlights the complexity of duopoly competition when firms have the freedom to adjust both price and quantity, leading to strategic interactions that can drive prices down or allow firms to coordinate their actions.

(vii) Stackelberg Model

The Stackelberg Model is a strategic oligopoly model where firms compete based on quantity, not price, and one firm (the leader) gains a competitive advantage by moving first. Developed by Heinrich von Stackelberg in 1934, this model highlights the leader-follower dynamic in decision-making.

Key Features:

• Leader-Follower Dynamic:
  • One firm acts as the leader, setting its output level first.
  • The other firm is the follower, adjusting its output based on the leader’s decision.
• First Mover Advantage:
  • The leader firm gains a competitive edge by deciding its quantity first, anticipating the follower’s reaction. This allows it to optimize profits.
  • The follower firm adjusts its production accordingly, often leading to a suboptimal outcome compared to the leader.
• Reaction Function:
  • The follower’s quantity is determined by a reaction function, which indicates how the follower will adjust its output in response to the leader’s output.
• Market Equilibrium:
  • Equilibrium is achieved when the leader maximizes its profit by considering the follower’s reaction, and the total market quantity determines the price.
• Profit Distribution:
  • The leader generally earns higher profits due to its ability to set the market’s quantity first, capturing a larger share, while the follower earns less profit.

The Stackelberg model emphasizes the strategic advantage gained by firms that move first in quantity competition.

(viii) Price-leadership Model

The Price-Leadership Model is a strategy used in oligopolistic markets where one dominant firm sets the price for the entire industry, and other firms follow its lead. This model suggests that a dominant firm (the price leader) has the power to influence the prices in the market, while the following firms (the price followers) adjust their prices accordingly to maintain market share. Here’s a brief breakdown:

Key Features of the Price-Leadership Model:

• Dominant Firm: The leader has significant market power, often due to lower costs or better market understanding, and sets the price without fear of competitors undercutting it.
• Price Followers: Smaller firms follow the leader’s price to avoid price wars, typically engaging in non-price competition like product differentiation or advertising.
• Market Outcome: The price leader maintains control over prices, stabilizing the market. Followers align their prices with the leader.
• Collusion: The model can result in tacit collusion, where the leader indirectly influences market prices, benefiting all firms with higher prices and profits.

Types of Price Leadership:

• Barometric Price Leadership: The leader sets prices based on general market trends or economic conditions.
• Dominant Firm Price Leadership: The largest firm (with the most market power) sets the price.
• Reverse Price Leadership: In some cases, a smaller firm with innovative products or lower costs may lead, causing the larger firms to follow suit.