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.