Reaction Function

Definition

A reaction function is a mathematical representation that describes how one firm's optimal output decision reacts to the output levels chosen by other firms in a market. This concept is crucial in analyzing strategic interactions among firms, particularly in oligopoly settings where decisions are interdependent. Understanding reaction functions allows firms to predict competitors' behavior and adjust their strategies accordingly to maximize their own profits.

5 Must Know Facts For Your Next Test

1. In the Stackelberg leadership model, the leader firm sets its output first, and the follower firm responds based on its reaction function.
2. Reaction functions can be derived from firms' profit maximization conditions, considering how changes in one firm's output affect others.
3. The shape of the reaction function can indicate whether firms are close substitutes or complements in their products.
4. Graphically, reaction functions are often represented as curves showing the relationship between two firms' outputs in an oligopolistic market.
5. Understanding reaction functions helps firms anticipate competitors' responses and strategically decide their own output levels.

Review Questions

• How do reaction functions help firms in predicting competitors' behavior in an oligopoly?
  • Reaction functions provide a way for firms to understand how their output decisions impact and are impacted by their competitors. By analyzing these functions, a firm can anticipate how changes in its output will influence its rivals' output levels, allowing it to strategically adjust its own production to optimize profits. This predictive capability is crucial in an oligopoly where firms' decisions are interdependent.
• Discuss the role of reaction functions in determining the equilibrium outcomes in the Stackelberg model compared to Cournot competition.
  • In the Stackelberg model, one firm acts as a leader and sets its output first, which then influences the follower's output through its reaction function. This creates a sequential decision-making process where the leader anticipates the follower's response. In contrast, Cournot competition involves simultaneous decision-making where each firm's output is determined based on expectations of rivals' outputs as represented by their respective reaction functions. The Stackelberg model typically results in higher profits for the leader compared to Cournot outcomes due to this first-mover advantage.
• Evaluate how changes in market conditions might affect reaction functions and subsequently impact firm strategy in an oligopolistic setting.
  • Changes in market conditions, such as shifts in consumer demand or production costs, can significantly alter the shape and position of reaction functions. For instance, if production costs rise for one firm, it may reduce its optimal output level, which would shift its reaction function accordingly. This change could prompt rival firms to adjust their strategies as well, leading to new equilibrium outputs. Firms must continuously analyze these shifts to remain competitive, demonstrating the dynamic nature of strategic interactions in oligopolies.

Related terms

Nash Equilibrium: A situation in a strategic game where no player can benefit from unilaterally changing their strategy, given the strategies of other players.

Cournot Competition: An oligopoly model where firms compete on the quantity of output they produce, with each firm's output decision influencing the market price.

Best Response: The strategy that yields the highest payoff for a player, given the strategies chosen by other players in the game.