🧃Intermediate Microeconomic Theory Unit 7 – General Equilibrium & Economic Welfare

Key Concepts

• General equilibrium analyzes the behavior of multiple markets simultaneously and how they interact with each other
• Pareto efficiency is a state where no one can be made better off without making someone else worse off
• Competitive equilibrium is a situation where all markets clear and no agent has an incentive to change their behavior
• Edgeworth box is a graphical tool used to analyze the efficiency of resource allocation between two individuals or groups
• First Welfare Theorem states that under certain assumptions, a competitive equilibrium leads to a Pareto efficient allocation of resources
  • Assumes perfect competition, complete markets, and no externalities or public goods
• Second Welfare Theorem states that under certain assumptions, any Pareto efficient allocation can be achieved through a competitive equilibrium with appropriate initial redistributions
• Social welfare function is a way to aggregate individual preferences into a measure of overall social welfare

Market Interactions

• In a general equilibrium setting, changes in one market can have spillover effects on other markets through price adjustments and resource reallocation
• Substitution effect occurs when a change in the price of one good leads consumers to substitute towards or away from other goods
• Income effect occurs when a change in the price of a good affects consumers' real income and thus their demand for all goods
• Feedback loops can amplify or dampen the effects of market disturbances as they propagate through the economy
  • Positive feedback loops (e.g., increased demand leading to higher prices, which further increases demand) can lead to instability
  • Negative feedback loops (e.g., increased supply leading to lower prices, which reduces supply) can help stabilize markets
• Interdependence of markets means that analyzing one market in isolation may lead to incorrect conclusions about the overall impact of policy changes or other shocks

General Equilibrium Model

• Walrasian general equilibrium model assumes perfect competition, complete markets, and no externalities or public goods
  • Agents are price-takers and have complete information about prices and qualities of goods
  • No market power, transaction costs, or barriers to entry or exit
• Equilibrium is characterized by a set of prices such that supply equals demand in all markets simultaneously
  • Excess demand (supply) in one market puts upward (downward) pressure on prices until equilibrium is reached
• Existence of equilibrium can be proven under certain assumptions using fixed-point theorems (e.g., Brouwer's or Kakutani's)
• Uniqueness of equilibrium is not guaranteed in general, but can be shown under more restrictive assumptions (e.g., gross substitutability)
• Stability of equilibrium depends on the adjustment process and the properties of excess demand functions
  • Tatonnement process adjusts prices in proportion to excess demand, but may not always converge to equilibrium
  • Non-tatonnement processes allow for trading at disequilibrium prices and may have different stability properties

Efficiency in Production and Consumption

• Productive efficiency occurs when it is impossible to produce more of one good without producing less of another (i.e., on the production possibility frontier)
  • Marginal rate of technical substitution (MRTS) must be equal across all firms producing the same goods
• Allocative efficiency occurs when resources are allocated to their highest-valued uses (i.e., marginal benefit equals marginal cost)
  • Marginal rate of substitution (MRS) must be equal across all consumers consuming the same goods
• In a competitive equilibrium, both productive and allocative efficiency are achieved
  • Firms maximize profits by setting MRTS equal to input price ratios
  • Consumers maximize utility by setting MRS equal to output price ratios
• Edgeworth box can be used to illustrate efficient allocations as points on the contract curve where MRS is equal for both consumers
• Production possibility frontier (PPF) shows the maximum combinations of goods that can be produced given available resources and technology
  • Points inside the PPF are inefficient, while points outside are unattainable

Pareto Optimality

• Pareto improvement is a change that makes at least one person better off without making anyone else worse off
• Pareto optimal (or Pareto efficient) allocation is one where no Pareto improvements are possible
  • All gains from trade have been exhausted
• First Welfare Theorem states that a competitive equilibrium is Pareto optimal under certain assumptions
  • Intuition: if there were any Pareto improvements left, agents would have an incentive to trade until they were achieved
• Second Welfare Theorem states that any Pareto optimal allocation can be achieved as a competitive equilibrium with appropriate initial redistributions
  • Intuition: by redistributing endowments, we can "choose" which of the many possible Pareto optimal allocations to implement
• Pareto criterion is often used as a normative benchmark for evaluating policy changes or market outcomes
  • However, it does not address distributional concerns or make interpersonal comparisons of utility

Welfare Economics

• Social welfare function (SWF) is a way to aggregate individual preferences into a measure of overall social welfare
  • Different SWFs embody different value judgments about inequality, fairness, and interpersonal comparisons
  • Examples: utilitarian (sum of utilities), Rawlsian (maximize utility of worst-off individual), Nash (product of utilities)
• Arrow's Impossibility Theorem shows that no SWF can satisfy a set of seemingly reasonable axioms simultaneously
  • Axioms include Pareto principle, independence of irrelevant alternatives, unrestricted domain, and non-dictatorship
• Compensation principles (Kaldor-Hicks, Scitovsky) try to extend Pareto criterion to evaluate changes that create winners and losers
  • A change is an improvement if winners could hypothetically compensate losers and still be better off
  • However, actual compensation may not occur, and principles can lead to inconsistent rankings
• Social choice theory studies how individual preferences can be aggregated into collective decisions (e.g., voting rules)
  • Condorcet paradox shows that majority voting can lead to intransitive social preferences
  • Arrow's theorem applies to social choice as well, limiting the scope for rational collective decision-making

Real-World Applications

• Computable general equilibrium (CGE) models are used to simulate the effects of policy changes or other shocks on the economy
  • Based on calibrated parameters and functional forms, solved numerically
  • Examples: trade liberalization, tax reforms, environmental regulations
• Input-output analysis studies the interdependence of industries in an economy and how changes in one sector affect others
  • Based on input-output tables showing flows of goods and services between sectors
  • Can be used to calculate multipliers and analyze supply chain disruptions
• Urban economics applies general equilibrium concepts to the spatial structure of cities and the location decisions of firms and households
  • Monocentric city model explains land rent gradients and commuting patterns
  • Agglomeration economies and congestion externalities can lead to multiple equilibria and path dependence
• International trade theory uses general equilibrium models to analyze the causes and consequences of trade between countries
  • Ricardian model explains trade based on differences in technology and opportunity costs
  • Heckscher-Ohlin model explains trade based on differences in factor endowments and intensities
  • Gains from trade, distributional effects, and optimal trade policies can be studied in a general equilibrium framework

Limitations and Critiques

• Assumptions of perfect competition, complete markets, and no externalities are rarely satisfied in reality
  • Market power, asymmetric information, transaction costs, and missing markets are common
  • Public goods and externalities (e.g., pollution, congestion) create wedges between private and social costs/benefits
• Behavioral economics challenges the assumption of rational, self-interested agents with stable preferences
  • Bounded rationality, cognitive biases, and social preferences can lead to deviations from standard model predictions
  • Nudges and choice architecture can be used to influence behavior and improve outcomes
• Dynamic and stochastic aspects of the economy are often neglected in static, deterministic general equilibrium models
  • Intertemporal choices, uncertainty, and expectations formation can have important implications for equilibrium outcomes
  • Overlapping generations models and dynamic stochastic general equilibrium (DSGE) models try to address these issues
• General equilibrium analysis is often criticized for being too abstract and unrealistic, and for neglecting important institutional and historical factors
  • Partial equilibrium analysis may be more appropriate for some research questions and policy issues
  • Comparative statics results may not hold in the presence of multiple equilibria or non-convexities
• Distributional concerns and normative judgments are not fully captured by the Pareto criterion or competitive equilibrium
  • Equity-efficiency tradeoffs and interpersonal comparisons of well-being require additional value judgments
  • Social welfare functions and compensation principles have their own limitations and controversies