I have introduced the notion of absorptive capacity into an innovation-driven growth model. The model features firms with heterogeneous size and innovation capability. The economy`s aggregate output growth rate is driven by the growth of the productivity index of firm`s intermediate goods. There are firms already operating at least one active product line and potential entrants not owning a product line, but engaged in research in order to innovate and enter the economy. Each firm engages in R&D activities to improve upon existing intermediate good or to discover a completely new one. An incumbent firm may exit the economy exogenously and more importantly endogenously due to creative destruction or due to obsolescence. The consideration of the firm`s absorptive capacity in Cohen and Levinthal`s sense shaped the specifications of the innovation production functions for entrants and incumbents. I have set a proxy for the firm`s absorptive capacity that considers the quality level of active product lines owned by the firm, their number and their closeness. Then, incumbent firm`s absorptive capacity confers to the it an innovation efficiency advantage compared to potential entrant, in improving upon its own product lines or in innovating in a product line not existing in its portfolio. For potential entrants, the average quality level of intermediate good in the economy acts as an extra difficulty they must overcome since the did not participate in building that economy`s average level of quality, and lack then the absorptive capacity that an average incumbent firm in the economy would possess. Although the general structure of the equilibrium growth rate obtained is the same as in the basis model (Acemoglu et al. 2013), however, the content of incumbents` rate of innovation and the rate of entry for potential entrants is different and more likely to deliver different values in equilibrium. This framework may be useful in studying empirically the effects of R&D subsidies on economic growth and lead to different results obtained by the main reference article, that found that subsidies to incumbents` R&D are pervasive for the growth of the economy.