A Theory of Continuum Economies with Idiosyncratic Shocks and Random Matchings

Karavaev, Andrei (2008): A Theory of Continuum Economies with Idiosyncratic Shocks and Random Matchings.

Abstract

Many economic models use a continuum of negligible agents to avoid considering one person's effect on aggregate characteristics of the economy. Along with a continuum of agents, these models often incorporate a sequence of independent shocks and random matchings. Despite frequent use of such models, there are still unsolved questions about their mathematical justification. In this paper we construct a discrete time framework, in which major desirable properties of idiosyncratic shocks and random matchings hold. In this framework the agent space constitutes a probability space, and the probability distribution for each agent is replaced by the population distribution. Unlike previous authors, we question the assumption of known identity - the location on the agent space. We assume that the agents only know their previous history - what had happened to them before, - but not their identity. The construction justifies the use of numerous dynamic models of idiosyncratic shocks and random matchings.

• Item Type: MPRA Paper
• Language: English
• Keywords: random matching; idiosyncratic shocks; the Law of Large Numbers; aggregate uncertainty; mixing
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C78 - Bargaining Theory ; Matching Theory; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D83 - Search ; Learning ; Information and Knowledge ; Communication ; Belief ; Unawareness; E - Macroeconomics and Monetary Economics > E0 - General > E00 - General

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