SFB 303 Discussion Paper No. B - 80


Author: Werner, Jan
Title: Structure of Financial Markets and Real Indeterminacy of Equilibria.
Abstract: This paper studies an exchange economy extending over a sequence of dates under uncertainty. There are two alternative structures of complete markets for such an economy. The first one consists of contingent commodity markets at date 0 for all commodities available for consumption within the time interval under consideration (see Debreu (1959, ch.6)). The second one consists of spot commodity markets at each date and in each state of nature, and markets for financial assets of a special form: for every state, there is an asset that yields one unit of account in this state and nothing in other states (see Arrow (1953)). These two structures are allocation equivalent.

An interesting observation on the model of Arrow (1953) is that there is an indeterminacy of equilibrium prices of assets - every positive asset price vector can be embedded in equilibrium. This indeterminacy is, however, entirely nominal - it does not affect the allocation of commodities. A model of a sequence of markets with an arbitrary (possibly incomplete) structure of financial assets has been analyzed by Cass (1984), Werner (1985), and Duffie (1987). Such a model has an equilibrium under standard assumptions, and the same feature that every arbitrage-free asset price system can be embedded in an equilibrium. It turns out, however, that this indeterminacy of asset prices is in general real, i.e. it affects the equilibrium allocaton of commodities, when markets are incomplete.

The indeterminacy of equilibrium allocations with financial assets has been analyzed by Geanakoplos and Mas-Colell (1985), Balasko and Cass (1986), and Werner (1986). The present paper generalizes previous results of Werner (1986) in two aspects: in provides a description of real indeterminacy for a two period model with an arbitrary asset structure (no assumptions on the return matrix), and for a multiperiod model with trade of financial assets at every date. The importance of the first generalization lies in the fact that the previously imposed restriction to return matrices in general position is restrictive from the economic point of view.
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Creation-Date: July 1987
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