# 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.

**Keywords**:

**JEL-Classification-Number**:

**Creation-Date**: February 1990

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