In this article, we present a model of economic growth through demand creation in the face of demand saturation, by representing demand saturation by an S-shaped logistic function and reckoning the firm's R&D as an activity to determine the probability of product innovation, that is, of demand creation. By defining the parameter of birth rate of a new product as the probability that a new product is derived from an existing one and identifying the time path of this parameter with the firm's R&D plan, we derive the optimal R&D plan and examine the growth rate of the firm's expected total revenue along this optimal plan. We then find that the optimal birth rate of a new product is influenced positively by the speed of diffusion of demand and the initial level of demand but negatively by the unit cost of production and the interest rate and that the growth rate of the firm converges to the optimal birth rate of a new product.