In this paper, we examine the relationship of innovative inputs to innovative output using a knowledge production framework approach. Following the line of research first developed by Griliches, the main concept is that innovation input (research effort) could lead to the knowledge generation, which could be reflected on a new or an improved product. We adopt, as the main innovative input, the innovation expenditure per sales and as the innovative output, the share of innovative products in the total of sales. We test the hypothesis that innovation expenditure is related non-linearly to knowledge growth (in terms of the share of new products in total sales), forming an inverted U-shaped curve at the firm level in a short-term period. Innovation activity is not the only factor influencing the generation of new knowledge and it is accepted that it can lead to knowledge growth. It is therefore of interest to look at the knowledge growth problems faced by enterprises when trying to carry out innovation. The analysis is based on the data set of the research: "Women and Innovation: Determinant Factors and Obstacles of Innovative Activity of Greek Firms, 2004- 2006," ARCHIMEDES research project, Technological Educational Institute of Athens, Greece.