On an “Important Principle” of Arrow and Debreu
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Arnis Vilks
Abstract
In their seminal 1954 paper on the existence of competitive equilibrium, Arrow and Debreu state what they call an “important principle”, namely that it is necessary for the existence of equilibrium that every consumer has some asset or can supply some labour service which has a positive price at equilibrium. It does not seem to have been noticed that this claim is incorrect. We provide a very simple model of a private ownership economy with three goods where a competitive equilibrium exists, but consumers who have nothing to sell but their labour end up with zero wealth in equilibrium. As zero wealth must be taken to mean non-survival, and the Arrow–Debreu model is frequently interpreted as assuming that all consumers can survive without trade, we also briefly discuss the issue of non-survival in equilibrium. We finally point out that our example illustrates the possibility that technological progress may result in a situation where the value of work becomes negligible.
Acknowledgement
Helpful comments by Tony Bryant and Harald Wiese on an earlier version of this paper are gratefully acknowledged.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Research Articles
- Skepticism and Credulity: A Model and Applications to Political Spin, Belief Formation, and Decision Weights
- Expert Panels with Selective Investigation
- Self-Control Preferences and Status-Quo Bias
- Passive Cross-Holding in a Stackelberg Oligopoly
- A Rehabilitation of the Law of Diminishing Marginal Utility: An Ordinal Marginal Utility Approach
- Workplace Heterogeneity and the Returns to Versatility
- Single- and Double-Elimination Tournaments under Psychological Momentum
- Cheap Talk with Multiple Experts and Uncertain Biases
- Legal Environment and Contractual Choice
- Politically Connected Firms and the Environment
- Injurers versus Victims: (A)Symmetric Reactions to Symmetric Risks
- Notes
- On an “Important Principle” of Arrow and Debreu
- A Note on the Existence of the Competitive Equilibrium in Grossman and Shapiro (1984)
- Endogenous Expectations Management with Network Effects: A Note
Artikel in diesem Heft
- Frontmatter
- Research Articles
- Skepticism and Credulity: A Model and Applications to Political Spin, Belief Formation, and Decision Weights
- Expert Panels with Selective Investigation
- Self-Control Preferences and Status-Quo Bias
- Passive Cross-Holding in a Stackelberg Oligopoly
- A Rehabilitation of the Law of Diminishing Marginal Utility: An Ordinal Marginal Utility Approach
- Workplace Heterogeneity and the Returns to Versatility
- Single- and Double-Elimination Tournaments under Psychological Momentum
- Cheap Talk with Multiple Experts and Uncertain Biases
- Legal Environment and Contractual Choice
- Politically Connected Firms and the Environment
- Injurers versus Victims: (A)Symmetric Reactions to Symmetric Risks
- Notes
- On an “Important Principle” of Arrow and Debreu
- A Note on the Existence of the Competitive Equilibrium in Grossman and Shapiro (1984)
- Endogenous Expectations Management with Network Effects: A Note
