We employ a dynamic framework to study how product innovation activities of a firm are influenced by its production capacity investments for the established product and vice versa. The firm initially has capacity to sell the established product, and it also has the option to start 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 product range. The optimization problem of the firm has two modes. In mode 1 the firm invests in production capacity for the established product as well as in the build-up of its R&D stock. 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.
Once the new product has arrived (mode 2), the firm offers both products and invests in production capacities for both of them.
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 capacities for the established product the firm never invests in R&D and the new product is never introduced, whereas for small initial capacities the firm keeps investing in R&D as long as the innovation has not arrived. In this scenario the new product is always introduced.
Finally, for an intermediate range of capacities 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 threshold phenomenon in the framework of a multi-mode optimization model.