Arrow-Debreu economy

3 key takeaways

• An Arrow-Debreu economy models a complete and competitive market with all possible goods, states, and time periods.
• It demonstrates how prices can achieve equilibrium where supply equals demand for all goods.
• The model helps in understanding the allocation of resources and the effects of uncertainty and time on market outcomes.

What is an Arrow-Debreu economy?

An Arrow-Debreu economy is a highly abstract and theoretical construct used in general equilibrium theory to model an economy where every conceivable good, including contingent and future goods, is traded in a complete market. The model assumes perfect competition, where all agents are price-takers, and markets exist for every possible state and time period. This allows for the comprehensive analysis of how resources are allocated across different times and states of the world, considering both uncertainty and intertemporal choices.

Importance of an Arrow-Debreu economy

The Arrow-Debreu model is foundational in economic theory because it provides rigorous conditions under which markets can reach a general equilibrium, where all markets clear simultaneously (supply equals demand for all goods). It forms the basis for modern economic theories of market behavior, resource allocation, and welfare economics. The model also helps in understanding the role of financial markets in sharing risks and smoothing consumption over time.

How an Arrow-Debreu economy works

Complete markets: The model assumes that there are markets for all conceivable goods, including those contingent on future states of the world. For example, there are markets not just for wheat today but also for wheat next year if it rains, wheat next year if it doesn’t rain, etc.

General equilibrium: Prices adjust to ensure that all markets clear. This means that for every good, the total quantity demanded equals the total quantity supplied.

Consumers and producers: Economic agents in the model (consumers and producers) are assumed to be rational and have complete information. Consumers maximize utility, while producers maximize profit.

Intertemporal and contingent choices: Agents make decisions based on their preferences for consumption over time and under different states of the world, allowing for a thorough analysis of how uncertainty and time affect economic outcomes.

Examples of Arrow-Debreu economy applications

• Risk sharing: The model illustrates how complete markets allow individuals to share risks efficiently. For example, farmers can trade contingent claims on their crops to hedge against bad weather.
• Resource allocation: By modeling an economy with multiple goods and time periods, the Arrow-Debreu model shows how resources can be allocated optimally over time, ensuring that future needs are met efficiently.
• Policy analysis: Economists use the Arrow-Debreu framework to analyze the effects of policy changes on resource allocation and welfare. For instance, they can study how introducing new financial instruments affects market completeness and risk distribution.

Real-world application

Consider a simplified version of an Arrow-Debreu economy with two goods (apples and oranges), two time periods (today and tomorrow), and two states of the world (rain and no rain). In this economy, there are markets for:

• Apples today
• Oranges today
• Apples tomorrow if it rains
• Oranges tomorrow if it rains
• Apples tomorrow if it doesn’t rain
• Oranges tomorrow if it doesn’t rain

Prices adjust so that in each of these markets, supply equals demand. Consumers and producers make decisions based on their preferences and expectations about future states (rain or no rain), leading to an equilibrium allocation of apples and oranges across both time periods and states of the world.

Understanding the Arrow-Debreu economy is crucial for advanced economic theory and provides a foundation for various practical applications in finance, policy analysis, and risk management. It offers insights into how markets can achieve efficient outcomes even under uncertainty and over time.

Related topics you might want to learn about include general equilibrium theory, welfare economics, and financial markets. These areas provide further insights into the theoretical foundations and practical implications of the Arrow-Debreu model.