Module 6: Monopoly, Monopolistic Competition, and Strategic Game Theory

Characteristics of a Monopoly

• A monopoly is a market structure defined by several critical characteristics:
  • There is only one seller in the market (the monopolist).
  • Only one product is available with no close substitutes.
  • There are significant barriers to entry.
  • The monopolist faces a decreasing demand curve, as it captures the entire market demand for itself.
  • The monopolist has complete control over the market supply and determines the total quantity offered for sale.
  • The monopolist is not merely part of the supply side; it is the supply side.
  • A monopolist does not have a supply curve; instead, it chooses a specific point on the demand curve that optimizes its own price and quantity.
• Trade-offs in revenue when increasing production:
  • There is an increase in total revenue due to a higher quantity sold.
  • There is a decrease in total revenue because the price must be lowered to sell that higher quantity.

Monopoly: Marginal Revenue and Linear Demand

• Suppose a linear demand curve is defined as:
  • $P(Q) = a - bQ$
• Derived revenue functions:
  • Total Revenue: $TR(Q) = P(Q) \times Q = aQ - bQ^2$
  • Average Revenue: $AR(Q) = \frac{P(Q) \times Q}{Q} = P = a - bQ$
  • Marginal Revenue: $MR(Q) = \frac{d(P(Q) \times Q)}{dQ} = a - 2bQ$
• Relationship between Demand and Marginal Revenue:
  • $P(Q)$ and $MR(Q)$ share the same intercept on the vertical axis (intercept = $a$).
  • The $MR$ curve is steeper, with a slope of $-2b$, while the demand curve slope is $-b$.
  • Consequently, the $MR$ curve always lies below the demand curve.

Monopoly Pricing and Profit Maximization

• Profit is maximized at the output level $Q^*$ where:
  • $MR = MC$
• The price $P^*$ is determined by the demand curve at the quantity $Q^*$.
• The average cost at the profit-maximizing quantity is denoted as $AC^*$.
• Profit Calculation:
  • $\pi^* = P^* \times Q^* - AC^* \times Q^*$
• Marginal Revenue can be expressed using the price elasticity of demand ($E_{D,P}$) via the product rule:
  • $MR(Q) = \frac{dR(Q)}{dQ} = \frac{d(P(Q) \times Q)}{dQ}$
  • $MR(Q) = P + Q \times \frac{dP}{dQ}$
  • $MR(Q) = P + P \times ( \frac{Q}{P} \times \frac{dP}{dQ} )$
  • $MR(Q) = P + P \times ( \frac{1}{E_{D,P}} )$
• At the profit-maximizing point ($MR = MC$):
  • $P + P \times ( \frac{1}{E_{D,P}} ) = MC$

Monopoly Markup Pricing and Lerner's Index

• The markup pricing formula (markup over marginal cost as a percentage of the price) is derived from the profit-maximization condition:
  • $\frac{P - MC}{P} = - \frac{1}{E_{D,P}}$
• Learner's Index of monopoly power is defined as:
  • $L = \frac{P - MC}{P}$
• Observations on elasticity:
  • If $-1 > E_{D,P}$ (demand is very elastic), the price is close to the marginal cost.
  • If $0 > E_{D,P} > -1$ (demand is inelastic), the calculated price would theoretically be negative.
  • Therefore, a monopolist will never choose a price in the inelastic portion of the demand curve.

Social Costs of Monopoly

• Monopoly power allows firms to manipulate prices and quantities, leading to inefficiencies:
  • Price is set above marginal cost ($P > MC$), meaning consumers pay more for the last unit than the cost of production.
  • Production does not occur at the minimum of the Average Cost ($AC$) curve, leading to higher-than-necessary production costs.
• Welfare impacts compared to competitive markets:
  • Lost Consumer Surplus (B): Revenue lost because certain units are not consumed.
  • Surplus transfer (A): Surplus taken from consumers by the producer due to the higher price ($P_m > P_c$).
  • Lost Producer Surplus (C): Surplus lost because the quantity produced is lower than the competitive level.
• Deadweight Loss ($DWL$) from monopoly power is the sum of areas $B + C$.

Price Regulation and Natural Monopolies

• In competitive markets, price regulation usually creates $DWL$, but in a monopoly, it may create efficiency by forcing the monopolist to reduce prices and increase output.
• Natural Monopoly:
  • Characterized by an $AC$ curve that is always decreasing.
  • One large firm can produce total industry output at a lower cost than several small firms.
  • The $MC$ curve is always below the $AC$ curve.
• Regulation Scenarios:
  • Unregulated: Monopolist produces $Q_m$ and charges $P_m$ where $MR = MC$.
  • Competitive Regulation ($P_c = AR = MC$): The firm makes a loss because $AC > AR$.
  • Zero-Profit Regulation ($P_r = AR = AC$): This yields the largest possible output without the firm incurring a loss.
• Regulation Challenges:
  • Regulators need detailed knowledge of demand and cost curves.
  • Rate-of-Return regulation: Allows prices where the return on capital is "fair" or "competitive," though valuing capital is difficult.

Market Power Factors

• Market power (the ability to set prices) depends on:
  • Price elasticity of market demand.
  • Number of potential competitors (industry concentration).
  • Barriers to entry (Setup costs, patents, protective laws).
  • Product heterogeneity (Quality differences, advertising).
  • Interaction forms (Fierce competition vs. collusion).
• Note: High market power does not automatically guarantee high profits, as profit depends on cost structures.

Monopolistic Competition

• Characteristics:
  • Product Differentiation: Similar but non-equivalent goods (close but imperfect substitutes). Cross-price elasticity is high but finite.
  • Free Entry and Exit: Low barriers to entry/exit; many firms exist.
  • Examples include toothpaste, soap, and sporting goods.
• Short-run vs. Long-run:
  • Short-run: Firms can earn positive economic profit.
  • Transition: Positive profits attract new firms, shifting the individual firm's demand curve ($D$) downward and changing the $MR$ curve.
  • Long-run Equilibrium: 1) Profit is maximized ($MR = MC$), and 2) Economic profit is zero ($P = AC$).
• Comparison to Perfect Competition:
  • Monopolistic Competition: $P > MC$ (leading to deadweight loss) and $AC > MC$ (production not at minimal average cost/unused capacity).
  • Perfect Competition: $P = MC$ (no deadweight loss) and $AC = MC$ (minimal average cost).

Game Theory Terminology and Strategies

• Game: A situation where rational economic agents (players) make strategic decisions.
• Strategy: A complete plan of actions and reactions.
• Payoff: The benefit (utility or profit) from a combination of strategies.
• Optimal Strategy: A strategy that maximizes a player's payoff given the actions of others.
• Dominant Strategy: A strategy that is optimal regardless of what other players do.
• Dominated Strategy: A strategy a player will never use because another strategy is always better.
• Nash Equilibrium:
  • A situation where each player chooses an action that is optimal against the action the other player will choose.
  • Any equilibrium in dominant strategies is a Nash Equilibrium, but not all Nash Equilibria involve dominant strategies.

Strategic Games and Behavior

• Advertising Game Example:
  • (Advertise, Advertise) is an equilibrium in dominant strategies if both firms find advertising always yields higher payoffs than not advertising.
• Battle of the Sexes (Ajax vs. Ballet):
  • Wife prefers Ajax; Husband prefers Ballet. Disagreement results in staying home ($0, 0$).
  • Two Nash Equilibria exist: (Ajax, Ajax) and (Ballet, Ballet).
• Prisoner's Dilemma:
  • Dominant strategy for both is to Confess ($-5, -5$).
  • This result is inefficient; both would prefer (Don't Confess, Don't Confess) at ($-2, -2$), but that combination is unstable.
• Maximin Behavior:
  • Players minimize risk by looking for the worst possible outcome of each strategy and choosing the one with the "least bad" result (maximizing the minimum payoff).

Oligopoly Models

• Characteristics: Small number of firms, significant barriers to entry (natural or strategic).
• Cournot Duopoly:
  • Each firm chooses its profit-maximizing output based on what it believes its competitor will produce.
  • Reaction Curve: Shows a firm's profit-maximizing output for every possible output level of the competitor.
  • Cournot-Nash Equilibrium: The intersection of the two firms' reaction curves where both firms' assumptions are correct and they react optimally.
• Collusion:
  • Firms agree to maximize joint profits (acting like a monopoly).
  • Often illegal and inherently unstable because the monopoly agreement is not a Nash Equilibrium; firms have an incentive to unilaterally deviate to increase private profit.

Price Rigidity and Dominant Firm Pricing

• Kinked Demand Curve (Oligopoly):
  • Firms believe rivals will follow price decreases but not price increases.
  • This creates a demand curve kinked at the current price ($P^*$), resulting in a discontinuous $MR$ curve.
  • Cost increases (from $MC$ to $MC'$) may not change price or quantity if they stay within the gap of the $MR$ curve.
• Dominant Firm Model:
  • One dominant firm sets the price; smaller "fringe" firms are price takers ($S_F$).
  • The dominant firm's demand ($D_D$) is the market demand minus fringe supply ($D_D = D - S_F$).
  • The dominant firm produces where its marginal revenue ($MR_D$) equals its marginal cost ($MC_D$).