SFB 303 Discussion Paper No. A - 280

Author: Hens, Thorsten
Title: On the Structure of Market Excess Demand in an Intertemporal General Equilibrium Model
Abstract: Since Debreu (1974) and the strengthenings of this result by Kirman-Koch (1986), Mantel (1976) and Hildenbrand (1989 b), it is known that in general in the Arrow-Debreu Model of General Equilibrium, the market excess demand function does not obey any structure which leads to an unique or globally stable equilibrium. Considering the theorems of Mantel (1976) and Hildenbrand (1989 b) we show that these results do not simply carry over to Intertemporal General Equilibrium Models with uncertainty and sequential trade. That is to say, we show that there exists a class of economies in which the spot market excess demand function allows for multiple equilibria in the Arrow-Debreu organization of markets, whereas it is monotone in an Intertemporal General Equilibrium Model with homogeneous expectations; thus in the latter model spot market equilibrium is unique and globally stable. The main reason for this result to be true is that in contrary to the Arrow-Debreu model where final consumption allocations for all periods are reached immediately in the first period, in an Intertemporal General Equilibrium Model they are reached via futures and spot markets transactions. The consequence of this two stage allocation process is that the incomes in every period are determined by the evaluation of endowments which are the result of the equilibrium process in futures markets of the period before and thus far away from being arbitrary as in the Arrow-Debreu Model. Considering expectations as heterogeneous, the distinction between complete and incomplete financial markets is decisive. For the complete market case results similar to Mantel (1976) and Hildenbrand (1989 b) can be reestablished. But with incomplete financial markets, heterogeneous expectations lying in an appropriate set of dimension S-L (where S is the number of states of the world and L the number of assets) still lead to a monotone spot market excess demand function. Thus the degree of incompleteness of markets and the degree of homogeneity of expectations play a key role for the structure of market excess demand in an Intertemporal General Equilibrium Model with uncertainty and sequential trade.
Creation-Date: February 1990
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