Background
The Arrow–Debreu state price is a fundamental concept in economic theory, particularly in the context of general equilibrium analysis. It allows economists to evaluate the efficiency and welfare implications of different economic arrangements involving future uncertainties.
Historical Context
Introduced by Kenneth Arrow and Gérard Debreu in the early 1950s, the Arrow-Debreu model received significant attention as it provided rigorous foundations for the theory of competitive equilibrium in markets considering all possible future states of the world. Arrow (1953) and Debreu (1959) each made pivotal contributions to the mutual development of a formal structure for economies under uncertainty. Their collaborative work eventually led to their receipt of the Nobel Memorial Prize in Economic Sciences.
Definitions and Concepts
The Arrow–Debreu state price refers specifically to the price today of a contingent claim that pays one unit of a commodity if a particular state of the world is realized in the future. Essentially, it is a price assigned to a “state-contingent contract” intended to cover all possible eventualities, thus facilitating optimal allocations in uncertain and dynamic contexts.
Major Analytical Frameworks
Classical Economics
In classical economics, future uncertainties were often abstracted away because the focus was on static models of supply and demand without considering stochastic elements.
Neoclassical Economics
The Arrow-Debreu model firmly roots itself in neoclassical economics. It offers insight into how markets could function effectively under uncertainties, extending the principles of competitive equilibrium and Pareto efficiency.
Keynesian Economics
Keynesian economists often focus on aggregate demand and drivers of economic stability rather than individual state prices in determining consumption across different states of the world.
Marxian Economics
Marxian economics traditionally do not directly engage with the mathematical formalism introduced by the Arrow-Debreu state prices but rather with broader socio-economic dynamics including capitals, labor, and surplus value.
Institutional Economics
Institutional economics emphasizes the role of legal frameworks, contracts, and norms, which dovetail into considerations about Arrow-Debreu markets and state prices but focus less on the mathematical pricing methods for future state consumption.
Behavioral Economics
Behavioral economists might critique Arrow-Debreu state prices by questioning the rationality assumptions about human behavior inherent in Arrow-Debreu models.
Post-Keynesian Economics
Post-Keynesians often critique neoclassical models and stress radical uncertainty, contrasting with the structured probabilities used in Arrow-Debreu state pricing.
Austrian Economics
Austrian economists may challenge the Arrow-Debreu framework for its assumptions about knowledge and prediction of future states and prefer dynamic, process-oriented models of market operation.
Development Economics
State pricing mechanisms could apply to interpretations of risk and consumption in developing economies, though real-world frictions might mean broader models are required.
Monetarism
Monetarists, with an emphasis on the role of monetary supply in the economy, might include Arrow-Debreu state prices in understanding and predicting market outcomes under monetary constraints.
Comparative Analysis
Different schools of thought provide contrasting viewpoints about the rigorous mathematical abstraction level evident in Arrow-Debreu state prices, with proponents seeing state pricing as a path to efficiency and detractors pointing out its idealized assumptions.
Case Studies
Case studies could involve examining the implementation of state contingent contracts in finance and insurance markets, where Arrow-Debreu ideas come to life in options and derivatives trading.
Suggested Books for Further Studies
- “Theory of Value: An Axiomatic Analysis of Economic Equilibrium” by Gérard Debreu
- “General Competitive Analysis” by Kenneth J. Arrow and Frank H. Hahn
- “Arbitrage Theory in Continuous Time” by Tomas Björk
Related Terms with Definitions
- Arrow-Debreu Economy - A theoretical model of an economy where resources and goods are allocated to derive an optimal allocation under conditions of pure competition and complete markets.
- Pareto Efficiency - An economic state where resources are allocated in a way that no individual’s welfare can be made better off without making someone else worse off.
- Contingent Claim - A financial instrument or contract that pays off based on a certain state of the world occurring.
