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In long-run equilibrium firms earn zero economic profit

In long-run equilibrium, all of the firms in the industry earn zero economic profit.  Why is it true?

The theory of perfect competition explicitly supposes that there are no entry or exit barriers to new participants in any industry.  With free entry, positive economic profits induce new entrants.  As these firms enter, the supply curve shifts towards the right, causing a drop in the equilibrium price of the product.  Entry will stop, and equilibrium will be obtained, when economic profits have fallen to zero.

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