Introduction

In the now classical extension of the general competitive model to include time and uncertainty, it was observed that if at time 0 (today) there are markets for future delivery of all goods contingent on the date and state of nature, then the resulting equilibrium allocation will be Pareto efficient. Moreover, in such an equilibrium future spot markets would not need to be active; the future would simply consist of agents fulfilling their promises (see Debreu 1959). In the event that there is not a complete system of contingent commodity contracts at time 0, then a new problem arises; there will be reason for future spot markets to be active, so that agents making decisions at the current data need to make expectations about what future prices will be. Thus a new equilibrium concept is required, and that is the topic of this essay. Following the basic paper of Arrow (1964), Roy Radner, in a fundamental series of papers (1967, 1968, 1972), developed the concept of an equilibrium of plans, prices, and price expectations for the sequence of markets that will arise when there is not a complete set of contingent contracts at time 0 – a concept that has led to a substantial amount of research in the last two decades. It is the purpose of this essay in honor of Roy Radner to review this research program that his pioneering work has spawned, and to assess its future. A substantial number of interesting issues arise if all uncertainty is not resolved at the initial date.