Microeconomics: General Equilibrium and Monopoly Theory

General Equilibrium and Welfare Economics

Efficiency and Equilibrium Concepts

• Pareto efficient: Any reallocation harms at least one person.
• Partial equilibrium analysis: One market in isolation.
• General equilibrium analysis: How equilibrium is determined in all markets simultaneously.
• Contract curve: The set of all Pareto-efficient bundles.
• First Welfare Theorem: The competitive equilibrium is efficient.
• Second Welfare Theorem: Any efficient allocation can be achieved by competition.

Mutually Beneficial Trades and Production

• Conditions for mutually beneficial trades:
  1. Utility maximization
  2. Usual-shaped indifference curves
  3. No interdependence
• Equilibrium conditions:
  1. Two indifference curves are tangent
  2. MRS_a = MRS_b
  3. No further mutually beneficial trade
  4. Allocation is Pareto efficient
• Efficient production mix: MRT = -P_c/P_w = MRS
• Pareto superior: If people are better off at x and no one else is harmed (must increase welfare).

Welfare and Possibility Frontiers

• Production Possibility Frontier (PPF): The maximum combination of two goods produced given a specific amount of inputs (slope = MRT). Many producers lead to a smooth concave curve. MRT decreases as we move up the PPF. Draw it in a way where those who produce first have a comparative advantage.
• Social welfare function: Combines consumers' utilities to provide a collective ranking of allocation.
• Utility possibility frontier: The set of utility levels corresponding to Pareto-efficient allocations.
• Arrow's Impossibility Theorem:
  1. Social preferences should be complete and transitive.
  2. Society's ranking should depend only on individuals' ordering of these two allocations, not on other alternatives.
  3. Dictatorship is not allowed; this does not mean that democracy must fail.

Monopoly and Market Power

Monopoly Characteristics and Profit Maximization

• Monopoly: It is possible to earn long-run (LR) profit because other firms cannot enter, but it is not guaranteed. Monopolies pick their own prices and have market power (downward-sloping demand). They are not price takers and always operate at elastic demand.
• Profit maximization: MR = MC, but P > MR = MC.
• Regulation failure:
  1. Limited information (setting price ceilings above or below the competitive level).
  2. Ineffective when regulators are captured.
  3. Cannot subsidize.
• Monopolist outcomes: Under-producing, high prices, and society is worse off.
• Shut down decision: P < AVC (Short Run), P < AC (Long Run).
• Market power formula: MR = P(1 + 1/ε) = MC; P/MC = 1 / (1 + 1/ε). The ratio of price to MC depends only on elasticity (ε) at profit-maximizing quantity (q).
• Calculations: ε = (-b)(P/Q); Profit = (P - ATC) × Q.

Price Discrimination

• Conditions for discrimination:
  1. Market power (downward-sloping demand).
  2. Customers must have different willingness to pay (elasticities of demand).
  3. The firm must have some method to identify which consumers have a higher elasticity and which have a low elasticity.
  4. Must be able to prevent resale.
• Perfect price discrimination: Captures all Consumer Surplus (CS). It is more efficient than a single-price monopoly (higher quantity). People who put a very high value are better with a single price, but those with a low value are better with perfect discrimination.