Dynamic optimal control of a firm’s product-process innovation with expected quality effects in a monopoly exhibiting network externality

This paper develops a dynamic model to study a firm’s product and process innovation with expected quality effects in a monopoly exhibiting network externality. The significant features of our work are: (i) considering the customers’ expected quality effects in a monopoly exhibiting network externality; (ii) the demand structure depends on price, product quality, and expected quality; and (iii) discussing a special case where the network size is proportional to the demand. Our results show: (i) there exists a unique saddle-point steady-state equilibrium under monopoly and social planning; (ii) as the forgetting parameter increases, the effort of process innovation is greater than that of product innovation; (iii) the social incentive towards both efforts is always larger than the private (monopolist) incentive; however, when the network size is proportional to demand, the social incentive towards the effort in product innovation (process innovation) is always smaller (larger) than the private (monopolist) incentive; (iv) sensitivity analysis shows that the both efforts and price are more sensitive towards the unit variable strength of network externality than the fixed strength of network externality, while the forgetting parameter has little effect on the both efforts and price; (v) the effort in product (process) innovation is increasing (decreasing) with the proportional coefficient.