🧃Intermediate Microeconomic Theory Unit 7 – General Equilibrium & Economic Welfare
General equilibrium theory examines how multiple markets interact and reach equilibrium simultaneously. It explores concepts like Pareto efficiency, competitive equilibrium, and the Edgeworth box to analyze resource allocation and market interactions.
The First and Second Welfare Theorems link competitive equilibrium to Pareto efficiency, providing insights into market outcomes. Social welfare functions aggregate individual preferences, while market interdependencies and feedback loops complicate economic analysis and policy decisions.
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
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