General equilibrium is an approach in economics for analyzing simultaneous equilibrium in all markets within an economy. For general equilibrium, all markets must be in equilibrium, and no change of actions in any market must reward any agent. General equilibrium contrasts with the partial equilibrium approach, which considers some part of the economy while taking other markets as given. This concept is fundamental in understanding how economies function in totality.
Historical Context
The concept of general equilibrium has its roots in classical economics, but it was formally developed in the late 19th and 20th centuries. Léon Walras, a French economist, is credited with laying the foundational work for general equilibrium theory.
- Léon Walras (1834-1910): Introduced the notion of a general equilibrium in his book “Elements of Pure Economics” (1874-1877). He formulated the idea that supply and demand in multiple markets simultaneously reach a state of equilibrium.
- Arrow-Debreu Model: In the 1950s, economists Kenneth Arrow and Gérard Debreu expanded upon Walras’ ideas to create a more comprehensive and mathematically rigorous model of general equilibrium. Their model, known as the Arrow-Debreu Model, became a cornerstone of modern economic theory.
Types/Categories
- Static General Equilibrium: Analyzes the equilibrium in a single time period.
- Dynamic General Equilibrium: Considers the evolution of economic variables over multiple time periods.
- Partial Equilibrium vs. General Equilibrium: Partial equilibrium focuses on a single market, while general equilibrium considers all markets in an economy simultaneously.
Key Events
- 1874-1877: Publication of Léon Walras’ “Elements of Pure Economics.”
- 1954: Arrow and Debreu publish their influential paper, “Existence of an Equilibrium for a Competitive Economy.”
Detailed Explanations
Walrasian Equilibrium
A Walrasian or competitive equilibrium is a situation in an economy where the supply equals demand in all markets. Formally, the conditions for a Walrasian equilibrium are:
- Market Clearing: For every commodity, the total quantity supplied must equal the total quantity demanded.
- Feasibility: The consumption and production plans must be feasible given the available resources.
- Optimization: Each agent (consumer or firm) must be optimizing given their preferences and constraints.
Arrow-Debreu Model
The Arrow-Debreu Model incorporates uncertainty and shows that under certain conditions, an equilibrium exists and is Pareto efficient. The model uses a set of assumptions:
- Preferences: Preferences are complete, transitive, and continuous.
- Technology: Production sets are convex.
- Initial Endowments: Each consumer has an initial endowment of goods.
- Markets: Complete markets exist for all future states of the world.
Mathematical Models
The basic model can be expressed as:
Where:
- \( x_{ij} \) is the amount of good \( j \) consumed by agent \( i \).
- \( y_{ij} \) is the amount of good \( j \) produced by agent \( i \).
Chart: General Equilibrium Model
graph TD
A[Consumers] -->|Demand| B[Markets]
B -->|Supply| C[Producers]
C -->|Goods| A
B --> D[Equilibrium]
D -->|Feedback| B
Importance and Applicability
General equilibrium models are essential for:
- Policy Analysis: Helps in evaluating the impact of policy changes on the entire economy.
- Economic Predictions: Useful in forecasting economic conditions and market reactions.
- Resource Allocation: Assists in understanding how resources are distributed efficiently in an economy.
Examples
- Tax Policy: Analyzing the impact of tax changes on multiple markets.
- Trade Policy: Assessing the effects of tariffs and trade restrictions.
Considerations
- Assumptions: The accuracy of a general equilibrium model depends on the assumptions made about preferences, technology, and initial endowments.
- Computational Complexity: Solving these models can be mathematically and computationally intensive.
Related Terms
- Pareto Efficiency: An allocation is Pareto efficient if no individual can be made better off without making someone else worse off.
- Partial Equilibrium: Focuses on equilibrium in a single market, holding other markets constant.
Comparisons
| Aspect | Partial Equilibrium | General Equilibrium |
|---|---|---|
| Scope | Single market | All markets |
| Interdependencies | Ignored | Considered |
| Complexity | Lower | Higher |
Interesting Facts
- Mathematical Proof: The Arrow-Debreu model provided the first complete mathematical proof of the existence of a general equilibrium.
- Nobel Prize: Kenneth Arrow and Gérard Debreu both won the Nobel Prize in Economics for their contributions to general equilibrium theory.
Inspirational Stories
Kenneth Arrow’s pioneering work, despite initial skepticism, transformed economics. His dedication and rigorous approach to proving the existence of a general equilibrium inspired a generation of economists to explore complex interdependencies in economic systems.
Famous Quotes
“Every economic theory that has ever been of real use is primarily a theory of general equilibrium.” - Kenneth Arrow
Proverbs and Clichés
- Proverb: “All things in moderation.”
- Cliché: “Everything is connected.”
Expressions, Jargon, and Slang
- Market Clearing: The process through which supply equals demand.
- Edgeworth Box: A tool used to depict the exchange process between two agents.
FAQs
Q: What is the difference between partial and general equilibrium?
A: Partial equilibrium examines a single market in isolation, whereas general equilibrium analyzes all markets in an economy simultaneously.
Q: Why is the Arrow-Debreu Model important?
A: It provides a rigorous mathematical framework for understanding the conditions under which a general equilibrium exists.
References
- Arrow, K. J., & Debreu, G. (1954). Existence of an Equilibrium for a Competitive Economy. Econometrica, 22(3), 265-290.
- Walras, L. (1874-1877). Elements of Pure Economics.
Final Summary
General equilibrium theory provides a comprehensive framework for understanding how different markets within an economy interact and achieve equilibrium. From its historical roots with Léon Walras to its rigorous formalization by Arrow and Debreu, the theory has become fundamental in economic analysis. Despite its complexity, general equilibrium remains vital for policymakers, economists, and scholars in assessing the full implications of economic activities and policies.
