Week 8 Oligopoly Part A1 What Is Oligopoly What Is Duopoly

Week 8 Oligopolypart A1 What Is Oligopoly What Is Duopoly2 What

Identify and explain the concepts of oligopoly and duopoly. Discuss the role of game theory in understanding the behavior of firms within these market structures. Describe how equilibrium strategies are determined in a duopoly setting. Explain the Cournot model of quantity competition, including an analysis of the market for bricks, where two firms produce identical products under cost and demand conditions. Include the derivation of reaction functions, equilibrium quantities, prices, and profits for each firm.

Provide an overview of the Stackelberg model, illustrating the sequential move nature of quantity competition, and analyze the equilibrium outcomes when one firm acts as a leader and the other as a follower. Address the profitability of potential mergers in this context. Describe the Bertrand model of price competition, detailing how firms choose prices simultaneously, and analyze the equilibrium prices and profits when products are homogeneous and costs are given.

Discuss differentiated product duopoly with example of gourmet restaurants, illustrating how demand functions depend on both prices. Derive reaction functions, equilibrium outputs, prices, and profits for each firm based on their demand functions and costs.

Paper For Above instruction

Oligopoly and duopoly are two fundamental market structures characterized by a small number of firms exerting significant influence over the market outcomes. An oligopoly exists when a few firms dominate the market, and their strategic interactions determine pricing and output decisions. Conversely, a duopoly is a specific form of oligopoly involving only two firms competing directly with each other. Understanding these structures is crucial for analyzing competitive strategies and market power.

Game theory plays a central role in explaining firms' strategic decision-making in oligopolistic markets. By modeling interactions as strategic games, it allows us to analyze how firms anticipate rivals’ responses and choose optimal strategies accordingly. The core component of game theory in this context is the concept of equilibrium, notably the Nash equilibrium, where no firm can improve its payoff by unilaterally changing its strategy. In a duopoly, equilibrium strategies can be determined through best response functions, leading to stable outcomes where each firm's strategy is optimal given the other firm's choice.

The Cournot model offers insight into quantity competition in a duopoly with homogeneous products and simultaneous decision-making. In the case of brick production, the market demand is given by P = 1 - (x + y), with costs C1(x) = 0.03x and C2(y) = 0.02y. To determine the reaction functions, each firm maximizes its profit while considering the other firm's output. By differentiating the profit functions concerning its own output, each firm derives its reaction function: for firm 1, y = R1(x); for firm 2, x = R2(y). Solving these simultaneously yields the equilibrium quantities.

Calculations show that in equilibrium, Firm 1 produces approximately 11.56 units, and Firm 2 produces about 16.09 units. The resulting market price is roughly $0.575, with profits of approximately $0.23 for Firm 1 and $0.32 for Firm 2. The technology advantage of firm 2 impacts the equilibrium, granting it a higher output and profit share.

The Stackelberg model extends this analysis by introducing sequential decision-making, where the leader moves first, and the follower responds optimally. Assuming firm 1 is the leader and firm 2 the naive follower, both firms adjust their outputs based on the earlier stage strategies. The equilibrium involves the leader anticipating the follower's best response, resulting in higher production and profits compared to the Cournot scenario for the leader.

In the studied example, the Stackelberg equilibrium indicates that firm 1 will produce approximately 13 units, and firm 2 will produce about 14.5 units, with corresponding prices around $0.477. Profits are marginally increased for the leader compared to the Cournot outcome, illustrating the strategic advantage of moving first. Mergers between firms could potentially enhance market power, leading to higher prices and profits; however, such integrations are subject to antitrust regulations and market considerations.

The Bertrand model offers an alternative framework where firms compete by setting prices simultaneously. In the brick production scenario with costs of $0.02 per unit, the equilibrium price converges to marginal cost levels, leading to zero economic profits for both firms under perfect competition assumptions. Any attempt to set higher prices would result in losing all customers to the cheaper rival, enforcing price competition at the cost floor.

Finally, considering a differentiated product duopoly with restaurants, the demand functions depend on both prices, reflecting customer preferences and brand loyalty. The firms’ rival demand functions are x = 100 - 4p1 + 2p2 and y = 100 - 4p2 + 2p1. Deriving reaction functions based on profit maximization yields equilibrium prices of approximately $13 for restaurant 1 and $14.25 for restaurant 2, with corresponding outputs and profits. These results underscore how product differentiation influences strategic pricing and market share, producing outcomes distinct from homogeneous product models.

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