following the implication that large firms hold greater market share due to their efficiency, demonstrating that the relationship between these efficiency and market share is not clearly defined. Industry Effects Innovation Schumpeter (1950) first recognised the relationship between market concentration and innovation in that a higher concentrated market would facilitate innovation. He reasoned that firms with the greatest market share have the greatest opportunity to benefit from their innovations, particularly through investment into R&D. This can be contrasted with the position taken by Arrow (1962) that a greater market concentration will decrease incentive to innovate because a firm within a monopoly or monopolistic market would have already reached profit levels that greatly exceed costs. In practice, there are complications in observing the direct correlation between market concentration and its effect on. In collecting empirical evidence, issues have also arisen as to how innovation, a firm's control and gaps between R&D and firm size are measured. There has also been a lack of consensus. For example, a negative correlation was established by Connelly and Hirschey (1984) who explained that the correlation evidenced a decreased expenditure on R&D by oligopolistic firms to benefit from greater monopolised profits. However, Blundell et al. observed a positive correlation by tallying the patents lodged by firms. This general observation was also shared by Aghion et al. in 2005. Schumpeter also failed to distinguish between the different technologies that contribute to innovation and did not properly define “creative destruction”. Petit and Teece (2021) argued that technological opportunities, a variable which Schumpeter and Arrow did not include during their time, would be included in this definition as it enables new entrants to make a “breakthrough” into the industry. Research presented by Aghion et al. (2005) suggested an inverted U-shape model that represents the relationship between market concentration and innovation. Delbono and Lambertini modelled empirical evidence onto a graph and found that the pattern demonstrated by the data supported the existence of a U-shaped relationship between these two variables. Alternative Metrics Although, not as common as the Herfindahl–Hirschman Index or Concentration Ratio metrics, various alternative measures of market concentration can also be used. (a) The U Index (Davies, 1980): where is an accepted measure of inequality (in practice the coefficient of variation is suggested), is a constant or a parameter (to be estimated empirically) and N is the number of firms. Davies (1979) suggests that a concentration index should