Hildenbrand Distribution Economies as Limiting Empirical Distributions of Random Economies

The present note shows that the concept of a distribution economy (Hildenbrand (1974)) is closely related to a framework of an exchange economy in which the agents’ individual characteristics (i.e. preferences and endowments) are random (Hildenbrand (1971), Bhattacharya and Majumdar (1973), Föllmer (1974)). A random exchange economy is fully specified by the distribution of the family of random variables representing the agents’ individual characteristics. This distribution is a probability measure µ on (SA, B(S)A) with S denoting the space of individual characteristics, B(S) the Borel o-algebra generated by an appropriate topology on S and A a denumerable set of agents. The linkage between a Hildenbrand distribution economy and an ergodic random exchange economy with a countably infinite set of agents endowed with the graph topology of the integer lattice Zd is established in this paper by a convergence result for the empirical distribution of the latter. For any increasing sequence of finite subsets of A exhausting A, the associated sequence of empirical distributions converges almost everywhere on the underlying probability space to some distribution v on (S, B(S)). As far as aggregate variables of the economy, such as the mean demand or the equilibrium price system are concerned, any infinite random exchange economy with converging limiting empirical distribution v is equivalent to a Hildenbrand distribution economy characterized by the same distribution v. This relationship suggests an approach to endogenous modelling of distributions of individual characteristics in General Equilibrium Theory. Thereby, specific distributions of characteristics can be obtained from a specific stochastic microstructure of local interaction between agents affecting their individual characteristics.General Equilibrium Theory, Arrow-Debreu economy, Random Economy, Distribution Economy, Empirical Distribution

Local Interactions as a Decentralized Mechanism Coordinating Equilibrium Expectations

In the context of standard two-period pure-exchange economies with sequential trade, this paper proposes a decentralized coordination mechanism for equilibriumexpectations, facilitated by local interactions between agents. Interactions are modelled stochastically by specifying a family of individual Markov processes on a two-dimensional integer lattice Z2 in continuous time. These processes are interdependent, in that the transition rate of each agent’s expectation also depends on expectations of neighboring agents. The particular specification of transition rates chosen in the present paper is known as the (two-dimensional) Voter Model. The composite process has two extremal invariant measures and a continuum of non-extremal invariant measures. The economic content of the stochastic expectations process is twofold. First, the convergence of the expectations process itself constitutes a “sunspot-device”. While convergence to either one of the extremal invariant measures corresponds to a sunspot-free coordination state, convergence to a convex mixture of invariant measures engenders a sunspot equilibrium. Thus, nonergodicity of the expectations process is related to the occurrence of sunspot equilibria. Second, it explains how coordination of expectations is actually achieved through direct interactions between agents. Any particular coordination state (defined as a limiting measure of the process) can be traced back to a set of initial configurations or more general initial distributions of expectations.Sunspot Equilibria, Voter model, local interactions, coordination

Empirical Regularities in Distributions of Individual Consumption Expenditure

We empirically investigate distributions of individual consumption expenditure f or four commodity categories conditional on fixed income levels. The data stems from the Family Expenditure Survey carried out annually in the United Kingdom. W e use graphical techniques to test for normality and lognormality of these distributions. While mainstream economic theory does not predict any structure for these distributions, we find that in at least three commodity categories individual consumption expenditure conditional on a fixed income level is lognormally distributed.Comment: 9 pages including figures; for Int. J. Mod. Phys. C 13, No.

A Percolation-Based Model Explaining Delayed Take-Off in New-Product Diffusion

A model of new-product diffusion is proposed in which a site-percolation dynamics represents socially-driven diffusion of knowledge about the product's characteristics in a population of potential buyers. A consumer buys the new product if her valuation of it is not below the price of the product announced by the firm in a given period. Our model attributes the empirical finding of a delayed ``take-off'' of a new product to a drift of the percolation dynamics from a non-percolating regime to a percolating regime. This drift is caused by learning-effects lowering the price of the product, or by network-effects increasing its valuation by consumers, with an increasing number of buyers.new-product diffusion, innovation adoption, spatial stochastic processes, percolation