Ebook Existence of Solutions and Asset Pricing Bubbles in General Equilibrium Models
The theory of general equilibrium is the branch of economic theory that studies the interactions between demand and supply of the different goods in the different markets in order to determine the prices of these goods (while the partial equilibrium analysis considers only the relations between demand and supply of a specific good and the price of the same good).
In general equilibrium analysis some simplifications are usually introduced, in particular it is assumed that:
- markets are competitive and individuals are optimizing;
- there is no production (at least in first approximation), agents have fixed endowments of the goods and they must determine only the quantities to exchange (pure exchange economy).
One of the central features of modern economics is then the introduction of time and uncertainty, and the consequent attempt to analyse an environment characterized by the presence of these elements. The main consequence for the behaviour of individuals is that they have only a limited ability to make decisions in such an environment; with reference to the theory of general equilibrium, in particular, this implies that, when agents have limited knowledge and ability to face uncertainty, they trade sequentially (i.e. periods by periods) and use a system of contracts which involve only limited commitments into the future.
The traditional Arrow-Debreu general equilibrium model (whose objective is the study of the allocation of resources achievable through a system of markets and whose central result is that, when there are markets and associated prices for all goods and services in the economy, no externalities or public goods, and no informational asymmetries, then competitive markets allocate resources efficiently) can be adapted to take into account the presence of time and uncertainty, assuming the existence, at the initial date, of a complete set of contingent markets (i.e. a market for each good produced or consumed in every possible future contingency). Nevertheless, this is an idealization that is not realistic (since the individuals do not have full knowledge of all possible future events and the society cannot costlessy monitor and enforce the commitments of agents), and for this reason it is necessary to consider an extension of this model, introducing a sequence of spot markets (for the exchange of goods and services) and a sequence of financial markets (in which contracts that allow to transfer resources across time are negotiated); typically, there is a limited number of these markets, i.e. there is a situation of incomplete markets.
The equilibrium solution of these models (if it exists) gives the values of prices and quantities (of the goods and of the financial activities) in correspondence of which the individuals solve their optimization problem and the (real and financial) markets clear (i.e. demand equals supply on these markets). A first important problem is therefore represented by the analysis of conditions that guarantee the existence of solutions in this kind of models.
These models can then be used to analyse the issue of asset pricing, and in particular the relation between the equilibrium price of an asset and the stream of future dividends on which the asset represents a claim. What emerges is that, while in the finite-horizon case the equilibrium price equals the fundamental value of the asset (i.e. the discounted sum of future dividends), in the infinite-horizon case this is not necessarily true (in particular, it is possible for the price to be larger than the fundamental value, and in this case the price of the asset is said to involve a speculative bubble). A second important question is therefore represented by the analysis of conditions that allow to exclude the presence of such bubble components, together with the study concerning the fragility of this phenomenon.
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