Discrete-time delay dynamics of boundedly rational monopoly

This paper discusses the delay dynamics of monopoly with discrete timescales. It is assumed that a monopoly has delayed and limited information on demand. It is also assumed that the firm wants to react to an average of past data instead of reacting to sudden market changes and this average is used to determine the marginal profit. In the case of one-step delay, the output of the previous time period is selected. In the cases of two and three delays where data at one, two, and three previous time periods are available, it is shown that the steady state undergoes to complex dynamics through either a period-doubling or a Neimark–Sacker bifurcation, depending on the specified values of the parameters. Numerical examples illustrate the theoretical results. Finally, the case of geometric delay is also analyzed to show the birth of the period-doubling bifurcation.     

A heterogeneous agent model of asset price dynamics with two time delays

This study constructs a heterogeneous agents model of a financial market in a continuous-time framework. There are two types of agents, fundamentalists and chartists. The former follows the traditional efficiency market theory and has a linear demand function, whereas the latter experiences delays in the formation of price trends and possesses a S-shaped demand function. The main feature of this study is a theoretical investigation on the effects caused by two time delays in a price adjustment process. In particular, two main results are demonstrated: One is that the stability switching curves are analytically derived, and the other is that the stability losses and gains can repeatedly occur when the shape of the curves are meandering. Although it is well known that a time delay has a destabilizing effect, these results imply that multiple delays can stabilize and destabilize a market price generating persistent deviations from the stationary price.     

Entry and Merger in Commercial Fishing with Multiple Markets

Received May 23, 2001; revised version received October 22, 2001