We employ a dynamic framework to study how product innovation activities of a firm are influenced by its investments in production capacity of an established product and vice versa. The firm initially has capacity to sell an established product. Additionally, it also has the option to undertake an R&D project, which upon completion allows the firm to introduce a new vertically and horizontally differentiated product to the market, thereby extending its current product range. The breakthrough probability of detecting the new product depends on both the value of the firm's R&D stock and its current R&D investment. It is shown that the initial production capacity for the established product influences the intensity of R&D activities of the firm. In particular, there are constellations such that for large initial production capacity for the established product the firm never invests in R&D and the new product is never introduced. For small initial capacity the firm keeps investing in R&D implying that eventually the new product is always introduced. Finally, for an intermediate range of initial capacity levels the firm initially invests in product R&D, but then reduces these investments to zero. In this scenario the new product is introduced with a positive probability, which is however substantially smaller than 1. From a technical perspective this analysis gives the example of a new type of Skiba threshold phenomenon in the framework of a multi-mode optimization model.
- Product innovation
- Multi-product firm
- Piecewise deterministic optimal control
- Skiba curve