Abstract
In this paper we consider equilibrium under uncertainty in a sequence of markets. In each market goods are bought both by traders and firms. Firms must buy today the vector of inputs which will determine their production choice set tomorrow. To cover the cost of these inputs, firms sell bonds. A situation where a producer defaults on bonds issued in the previous period occurs when his revenue from production and from the sales of new bonds does not cover liabilities to bondholders from the previous period plus new purchases of inputs. The producer is then said to be bankrupt, and bondholders become the shareholders in the firm, replacing the shareholders from the previous period. Although the time-event structure of the model is known to all, each individual and firm may have different information (and hence subjective probabilities) of the various states at each time. Equilibrium is said to exist if for a given vector of commodity, bond, and share prices, individual consumption and investment plans are optimal, firms maximize a concave function of implicit shareholder and bondholder firm valuations, and supply and demand of commodities, shares and bonds are equal. Several features of the model are taken from Radner [1972], and its results may be seen to complement those proven there as well as results obtained by Dreze [1974]. The structure and proofs of the model are taken largely from the Arrow-Debreu model of economic equilibrium (see, for example, Arrow [1964] and Debreu [1959]). The paper is divided as follows: Section 1 discusses the time-state structure of the model, which is wholly derived from Radner. We go on to discuss production, and in Section 3, we discuss the stock market. Section 4 deals with
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