Dynamic monopoly with multiple continuously distributed time delays

Two time delays are assumed in a boundedly rational monopoly. The characteristic equation is derived for the general case, and a complete stability analysis is conducted both analytically and numerically in two special cases. In the first case, wherein the continuously distributed time delays have different weights, it is shown that a monopoly equilibrium is destabilized to generate a limit cycle via Hopf bifurcation. In the second case in which one delay is continuously distributed and the other is fixed, it is demonstrated that the stability of the monopoly equilibrium can change finite number of times and eventually becomes periodically or aperiodically unstable. It is of interest to notice that the two delay dynamics can be qualitatively different from the one delay dynamics.