Abstract
Arrow-Debreu’s, and McKenzie’s competitive general equilibrium models can be considered as the finest achievements of economic theory in the 20th century. Like every other general equilibrium model, substantially they are one period models, because of the essential assumptions that all markets are active, and future decisions are definitely taken by all agents in the first period; but in real world economies it is safe to assume that the set of markets is complete only as far as present goods are concerned, while a hypothesis of incomplete markets, or even of missing markets, is much more plausible when considering future production, distribution, and consumption of goods.
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Referece
In spite of the fact that formally they can represent any finite number of time periods.
i.e., Arrow-Debreu-McKenzie’s models on the one hand, and temporary general equilibrium models on the other.
f course, the same very strong assumption of the Arrow-Debreu-McKenzie’s world!
For a model containing an infinite number of periods, see Magill and Quinzii (1994).
Presumably, caused by the very high costs in setting up many future markets; of course, other explanations have been proposed
Both in theory and in practice!
An example of a real asset, at least ideally, is a share of a corporation.
The simplest example of a nominal asset is that of a riskless bond, generally a bond issued by the government, for which one has, with notation of § 29.4.2, m(t) = (1,1,chrw(133),1) for every t, namely, the promise, issued in the first period, to deliver in period t one unit of money in every possible state.
When future markets are formally considered, as in the Arrow-Debreu’s model (1954).
As already noted, it is assumed that all agents know this set.
This implies that the same consumers issue and trade real assets; the model does not contain specialized agents!
Otherwise, consumer j has no bound in issuing assets, thus increasing indefinitely his/her period 1 income. See Magill and Shafer (1991, p. 1534 ).
Magill and Shafer (1991, p.1534).
By the theory of linear spaces, it is plain that for this property to be true it is necessary that one should have A≥v.
As already noted at the end of § 29.4.1.
See § 29.4.2.
Once a no-arbitrage condition is satisfied.
f course, pl(l,s) must be positive; any other positively priced commodity could be employed for this purpose.
It is not inflation-proof.
For some properties, see Magill and Shafer (1991, Theorems 19 and 20).
For instance, the non singularity condition is true if, on the whole, consumers hold some share in every firm, so that one has Ehxkh 1 for every k.
It is, of course, also the share of firm h’s profit distributed to consumer j.
Note that here the box product, D, applies to the subvectors contained in p, c, c, and not to the individual components of each subvector.
The irrelevance of the firms’ decisions about X stems from the fact that, by selling and buying shares, consumers are free to combine, as they like, the income streams they receive from firms.
This disagreement is the main culprit causing Pareto’s inefficiency of a stock-market equilibrium.
Under a state of incomplete markets,namely,A y,contrary to 29.5.2 in general it is no longer possible for all the ris to be equal to one another, because every consumer can have a personal perception of his/her future income stream on every date-event pair.
Such as options on real or nominal assets.
i.e., that Walras’ law and positive homogeneity of zero degree are the only restrictions on excess demand functions;see 16.10.
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© 2000 Springer-Verlag Berlin Heidelberg
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Nicola, P. (2000). Incomplete Markets and Finance. In: Mainstream Mathematical Economics in the 20th Century. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04238-0_29
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DOI: https://doi.org/10.1007/978-3-662-04238-0_29
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