The accusation that competition tends toward inequality is far from true. On the contrary, all artificial inequality is due to the absence of competition; 

Frédéric Bastiat
Economic Harmonies

As an introduction to his chapter on competition, Frédéric Bastiat starts by using a reductio ad absurdum reasoning in order to demonstrate that it is indispensable and inseparable from liberty because “competition is merely the absence of oppression”. Here, he clearly opposes constructivists who have no other choice but impose their views in the hope (or conviction) that they are the best and the fairest. Competition is in fact an essential part of the development of an “emergent order” dear to Hayek and that Bastiat naturally attributed to god given the times in which he was living.

He then goes on in presenting the positive aspects brought by competition linked to the fact that the world is diversified. This latter point constitutes the acceptable inequality and is not suffering from competition (at least, it is not hurt by competition, independently from the sufferings that an individual can encounter for other reasons) but, to the contrary, benefits from it (through economic efficiency that it brings and innovation that it allows). Conversely, repressing competition creates injustice and stymies innovation – these are the artificial inequalities that he is fighting against and often take the form of privileges.

Other quotes from Competition:
Introduction – Part 1 – Part 2 – Part 3 – Part 4 – Part 5 – Part 6 – Conclusion