Wealth-driven competition in a speculative financial market: Examples with maximizing agents

This paper demonstrates how both quantitative and qualitative results of general, analytically tractable asset-pricing model in which heterogeneous agents behave consistently with a constant relative risk aversion assumption can be applied to the particular case of linear investment choices. In this way it is shown how the framework developed in Anufriev and Bottazzi (2005) can be used inside the classical setting with demand derived from utility maximization. Consequently, some of the previous contributions of the agent-based literature are generalized. In the course of the analysis of asymptotic market behavior the main attention is paid to a geometric approach which allows to visualize all possible equilibria by means of a simple one-dimensional curve referred as the Equilibrium Market Line. The case of linear (particularly, mean-variance) investment functions thoroughly analyzed in this paper allows to highlight those features of the asymptotic dynamics which are common to all types of the CRRA-investment behavior and those which are specific for the linear investment functions.