Arrow-Debreu Economy

Published Apr 5, 2024

Definition of Arrow-Debreu Economy

An Arrow-Debreu economy is a model of an economy that describes how equilibrium prices allow for efficient allocation of resources within a perfectly competitive market. Named after economists Kenneth Arrow and Gérard Debreu, this model incorporates a complete set of markets for goods and services, as well as for future and contingent claims. The Arrow-Debreu model assumes perfect information, no transaction costs, and that all markets clear (supply equals demand) at some set of prices.

Example

Consider an economy where there are only two goods: apples and oranges. In this simplified Arrow-Debreu model, every consumer has preferences regarding how many apples and oranges they wish to consume, and each producer has a technology that determines how efficiently they can produce these goods. Furthermore, let’s assume there is a futures market where individuals can buy or sell apples and oranges that will be delivered in the future under certain conditions (for example, a good harvest or a poor harvest).

In this economy, the Arrow-Debreu theorem postulates that there exists a set of prices for apples and oranges today, as well as for each possible future state of the world, where supply and demand balance and all markets clear. These prices guide efficient production, consumption, and risk allocation decisions. Producers know how much to produce based on current and future prices, while consumers can optimally allocate their income across different goods and time periods to maximize utility.

Why Arrow-Debreu Economy Matters

The Arrow-Debreu model provides a foundational framework for modern economic theory and financial markets. It offers insights into how markets can, under certain conditions, lead to an efficient allocation of resources. This includes the allocation of risk, where individuals can insure against unfavourable future states of the world by trading in contingent claims markets. Hence, the Arrow-Debreu model serves as a benchmark for understanding economic efficiency, helping economists to identify market failures and explore how real-world markets deviate from the ideal.

Frequently Asked Questions (FAQ)

How does the Arrow-Debreu model handle uncertainty?

The Arrow-Debreu model addresses uncertainty by introducing markets for contingent claims, which are essentially financial instruments that pay off in different states of the world. These markets allow individuals and firms to buy and sell claims that pay off under specific conditions, effectively allowing them to hedge against future risks and uncertainties.

What are the limitations of the Arrow-Debreu model?

Although highly influential, the Arrow-Debreu model has limitations. Its assumptions of perfect information, no transaction costs, and a complete set of markets are rarely met in reality. Many markets, especially those for contingent claims on future states of the world, are incomplete or nonexistent. Additionally, the model does not accommodate imperfect competition, market power, or strategic interaction among agents.

How has the Arrow-Debreu model influenced modern economics?

The Arrow-Debreu model has significantly influenced economic theory, particularly in the fields of general equilibrium theory and financial economics. It has provided a foundation for the development of models that incorporate time and uncertainty into economic analysis, including options pricing and the theory of corporate finance. Moreover, it has inspired economists to explore the implications of market imperfections, guiding regulatory policies aimed at promoting more efficient and stable markets.