This paper analyses the difficult development of the European social market economy focusing on state aids and social security. Through the Case Law examined what constitutes the center of all provisions concerning state aids is the definition of "undertaking" and "economic activity". To prevent and solve market failures Member States must enter into the market and guarantee social services such as social security, but this cannot result in an abuse or distortion of competition among other economic operators which need to be put under the same conditions to perform those services that other companies won’t. To this extent, public services may be subject to competition law. What if private companies perform both economic and non-economic activities? What if the same activity can be classified under certain circumstances as economic or under other circumstances as solidarity-oriented? How does the ECJ finally decide whether an entity is an undertaking or not? These questions lead to the case study reported in this paper which also tries to leave a systematization on how to assess what is an undertaking under EU State aid Law and to what extent non-competing sectors can allow the introduction of competition indexes to enhance the quality and efficiency of their services.