Cournot and Bertrand models explore how firms compete in oligopolies. Cournot focuses on quantity competition, where firms choose output levels. Bertrand examines price competition, with firms setting prices for identical products.

These models reveal how strategic decisions impact market outcomes. They show how firms maximize profits by anticipating competitors' moves, leading to different equilibrium prices and quantities depending on the type of competition.

Cournot Competition Model

Oligopoly Structure and Quantity Competition

• Cournot competition describes a market structure where firms compete based on the quantity of output they produce
• Oligopoly market structure consists of a small number of firms that have significant market power and influence on market outcomes
• Quantity competition involves firms simultaneously choosing their output levels, taking into account the expected output of their competitors
• Firms make production decisions independently and simultaneously, without knowing the decisions of their competitors

Best Response Functions and Reaction Curves

• Best response functions represent a firm's optimal output level given the output levels of its competitors
• Each firm aims to maximize its profits, taking into account the expected output of other firms in the market
• Reaction curves graphically depict the best response functions of firms, showing how each firm's optimal output varies with the output of its competitors
  • For example, if firm A increases its output, firm B's reaction curve will show how much it should adjust its own output in response to maximize profits

Nash Equilibrium and Market Equilibrium

• Nash equilibrium in Cournot competition occurs when each firm is producing its best response output given the output levels of its competitors
  • At the Nash equilibrium, no firm has an incentive to unilaterally change its output level
• Market equilibrium in Cournot competition is determined by the intersection of the firms' reaction curves
  • The equilibrium output levels and market price are determined by the simultaneous optimization of all firms in the market
• In Cournot equilibrium, firms typically produce more than the perfectly competitive output level but less than the monopoly output level

Bertrand Competition Model

Oligopoly Structure and Price Competition

• Bertrand competition describes a market structure where firms compete based on the prices they set for their products
• Oligopoly market structure in Bertrand competition also involves a small number of firms with significant market power
• Price competition means that firms simultaneously choose the prices they will charge for their products, taking into account the expected prices of their competitors

Homogeneous Products and Pricing Strategies

• Bertrand competition assumes that firms produce homogeneous products, meaning that the products are identical or perfect substitutes
  • Consumers view the products as interchangeable and have no preference for one firm's product over another
• Firms engage in price undercutting to attract customers, as consumers will choose the firm offering the lowest price
  • For example, if firm A lowers its price, firm B must match or undercut that price to avoid losing market share

Nash Equilibrium and Market Equilibrium

• Nash equilibrium in Bertrand competition occurs when each firm is setting its profit-maximizing price given the prices set by its competitors
  • At the Nash equilibrium, no firm has an incentive to unilaterally change its price
• Market equilibrium in Bertrand competition is characterized by firms setting prices equal to their marginal costs
  • This leads to zero economic profits for firms in the long run, as they cannot sustain prices above marginal cost without being undercut by competitors
• Bertrand competition typically results in lower prices and higher consumer welfare compared to Cournot competition

Strategic Interactions and Profit Maximization

Profit Maximization and Strategic Behavior

• Profit maximization is the primary objective of firms in both Cournot and Bertrand competition models
• Firms choose their output levels or prices to maximize their profits, given the strategic behavior of their competitors
• Strategic interactions among firms involve anticipating and responding to the decisions of competitors to achieve the best possible outcome

Strategic Substitutes and Complements

• Strategic substitutes occur when an increase in one firm's strategic variable (e.g., output or price) leads to a decrease in the optimal level of the other firm's strategic variable
  • In Cournot competition, outputs are typically strategic substitutes, meaning that if one firm increases its output, the optimal response of the other firm is to decrease its output
• Strategic complements arise when an increase in one firm's strategic variable leads to an increase in the optimal level of the other firm's strategic variable
  • In Bertrand competition, prices are often strategic complements, implying that if one firm raises its price, the optimal response of the other firm is to also raise its price

Best Response Functions and Reaction Curves in Strategic Interactions

• Best response functions and reaction curves capture the strategic interactions among firms in Cournot and Bertrand competition
• Firms optimize their decisions based on the expected actions of their competitors, leading to interdependent decision-making
• The slope and shape of the reaction curves depend on whether the strategic variables are substitutes or complements
  • In Cournot competition, reaction curves are typically downward-sloping, reflecting the strategic substitute nature of outputs
  • In Bertrand competition, reaction curves are often upward-sloping, indicating the strategic complement nature of prices