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Abstract
Agents' information under uncertainty has not usually been defined in a way allowing isolation of its effects on other economic variables. In particular, its influence as a cost of transactions for which that information is relevant has only recently been studied. Some optimal choice of information by agents should be permitted when information is an explict commodity or when endogenous shifts of information are a major part of the model.
For these problems a mathematically structured space of information is useful. Given a probability space, the space of information is the set of all sub-(sigma)-fields of events. The structure defined here is a complete separable metric on this space whose topology is the weakest one such that for any integrable random variable, the function mapping an information field to the resulting conditional expected value of that random variable is continuous. Set-theoretic convergent (e.g., monotone) sequences of information converge in this metric. In addition, the set of finite partitions of the state space is dense. This metric is weaker and more tractible than the one used by Allen. A different space of information with metric are defined to cover situations where information is decision-relevant in a special way, such as the case of the observation of state plus noise.
When a consumer faces uncertain utility and certain prices for commodities and inital endowment, demand for commodities is shown to be jointly continuous in these parameters and information about the uncertainty affecting utility. The value of information is also continuous is these variables. Costly information acquisition is discussed using straightforward applications of the Maximum Theorem.
An elementary market for information coincident with an asset market is studied. The technology of information production, as well as a moral hazard problem, imply that few producers are active in the market. Since different firms produce different information, they may be presumed to set prices. With two information-producing firms, the possibility of combining information sometimes leads to complementarity effects between their information fields. This in turn allows price reversals in which the firm producing information of lower quality charges the higher price in a Nash-Bertrand equilibrium.
