The Arrow—Debreu Theory of Contingent Markets

In the previous chapter (see section 1) we noted how one may include the state of nature in the characteristics of a commodity. In this approach a commodity is characterized not merely by its physical attributes, but also the date and state of nature in which it is made available. Using this device we developed some aspects of consumer-choice under uncertainty. We now extend the notion of an intertemporal competitive equilibrium to incorporate such environmental uncertainty.

For ease of exposition suppose time is discrete, and that there are precisely (T+1) periods; t = 0, 1, …, T. Define a state of nature as, ‘…a description of the world…’, from t = 0 to t = T, ‘… so complete that, if true and known, the consequences of every action would be known’. As earlier, let S be the number of states of nature (s = 1, …, S). At the initial date (t = 0), no one knows what the true state of nature is. By hypothesis all uncertainty is resolved for everyone at t = T. Therefore, at T everyone will know precisely what the state of nature is.

It is assumed that with the passage of time all individuals continually receive information about the true state of nature. However, the point to emphasize is that this flow of information is costlessly obtained by all, and is not influenced by policy.