Contingent Commodities

Abstract

The theory of general competitive equilibrium was originally developed for environments where no uncertainty prevailed. Everything was certain and phrases like ‘it might rain’ or ‘the weather might be hot’ were outside the scope of the theory. The idea of contingent commodity, that was introduced by Arrow (1953) and further developed by Debreu (1953), was an ingenious device that enabled the theory to be interpreted to cover the case of uncertainty about the availability of resources and about consumption and production possibilities. Basically, the idea of contingent commodity is to add the environmental event in which the commodity is made available to the other specifications of the commodity. With no uncertainty every commodity is specified by its physical characteristics and by the location and date of its availability. It is fairly clear, however, that such a commodity can be considered to be quite different where two different environmental events have been realized. The following examples clarify this: an umbrella at a particular location and at a given date in case of rain is clearly different from the same umbrella at the same location and date when there is no rain; some ice cream when the weather is hot is clearly different from the same ice cream (and at the same location and date) when the weather is cold; finally, the economic role of wheat with specified physical characteristics available at some location and date clearly depends on the precipitation during its growing season. Thus, specifying commodities by both the standard characteristics and the environmental events seems very natural, whereas the role of the adjective in ‘contingent commodities’ is simply to make it clear that one is dealing with commodities the availability of which is contingent on the occurrence of some environmental event. With this specification the model with contingent commodities is very similar to the classical model of general competitive equilibrium and thus questions like the existence of equilibrium and its optimality (with the additional aspect of efficient allocation of risk bearing) are answered in a similar way. Note that, although this model deals with uncertainty, no concept of probabilities is needed for its formal description.