Valuation of adopters based on the Bass model for a new product

This paper shows that a hazard function can be additively decomposed, and with the additively decomposed hazard function, it shows that one can identify the others' effects which come from interactions between potential adopters and the adopters who bought at every adoption time interval. Also, from the additive decomposition of the discrete Bass hazard function, it derives the discrete Bass model which is consistent with the continuous version of Bass model. Furthermore, the coefficients of the derived discrete Bass model are expressed as the functions of coefficients of the continuous Bass model. Based on the derived discrete Bass model, thus, this paper presents a valuation scheme (calculator) for adopter groups which are classified by every observation time. The valuation calculator allows managers to calculate adopters' values only with the estimates of the continuous Bass model.