Oligopoly model with recurrent renewal of capital revisited

The aim of the present paper is to investigate an oligopoly market, modelled by using CES production function in combination with the isoelastic demand function. It is supposed that the competitors act not under constant, but eventually decaying returns, and thus, from time to time they need to renew their capital equipment, choosing its optimal amount according to the current market situation. It is shown that the asymptotic trajectories depend essentially on the value of the global capital durability, and are also sensitive to the initial choice of individual inactivity times. In particular, the firms may merge into different groups renewing their capitals simultaneously, which lead to distinct dynamical patterns. It is also studied how the capital wearing out rate influences the system behaviour.