A model for corporate growth by new product research productivity

A highly simplified model for growth of corporate sales resulting from new product research shows that investment of a fixed annual fraction of profits in new product research and development leads to a feedback effect on growth. When the parameter β(k + S
γ
) exceeds unity, annual sales grow exponentially. For values less than unity, sales reach a steady annual value. The factors in this critical parameter are: β = (total sales of new products)/(dollar of total sales) γ = (sales per old product item)/(sales per new product item) k = years life as a new product S = additional years life as an old product. The qualitative principles involved are of general validity. Although too crude for quantitative prediction of individual product return, the model may have rough quantitative value for whole businesses or large product classes.