Why is a perfectly competitive market always in break-even state in the Long Run?

I would firstly begin through making a reference to the assumptions of a perfectly competitive market and explaining how these assumptions help in deriving the graph. For instance, the fact that goods are homogenous means that firms are price takers and are forcer to have a vertical demand curve (because any price charged higher than this would mean that consumers would simply resort to other producers providing the identical goods). Then after explaining this, I would draw out the diagram and refer to the theory of the firm in explaining where producers would produce in the short and long run. After doing this, we will logically try to understand what a producer would do in a certain situation through imagining similar hypothetical situations. For instance, if I am a producer from outside the market and I see that firms in this market are making profits, I will enter this market too (as there are no barriers to entry or exit)! Then, over a period of time, we will see that if other producers continue doing this, there would be a large increase in supply, as producers continue producing this good, which would drive down the price level or the average revenue. Once we have this understanding, we would draw out the graph and see intuitively what would happen. Then we can graphically see that the price level has moved down and that because of this, the firms in the perfectly competitive market go from profit-making to breaking-even in the long run. Conversely, we would do the same with firms that are loss making in the perfectly competitive market.After we have an intuitive understanding from a graphical point of view, we would continue to explain these concepts in words. Then we would be able to have a complete understanding of the subject. We will then finish off the process through looking at some real-life examples and try to apply our new understanding of theory in the real world (for instance the EU agricultural market).