The aim of this study is to investigate the level of market power of the Greek manufacturing and services industries over the period 1970-2012. This will be done at a disaggregated level (two and three digit code), with the aim of investigating possible heterogeneity across different subsectors of the above industries. We will also examine possible differences of our results across different periods of the above sample, with the aim of investigating if integration of the Greek economy with the European Union has significantly changed the levels of mark-ups and, hence, the degree of completion in the Greek Economy. The empirical (econometric) methodology that we will implement will include robust methods to the problem of endogeneity that may arise in standard estimation methods, like the method of least squares often employed in practice. The results of our analysis will have a number of interesting implications for the competition policy authorities.