It's unclear how market equilibrium is reached in case of overproduction Let's assume that there is disequilibrium, namely that $P=P_2$, thus $Q_s &gt; Q_d$. In other words, there is overproduction. This is perfectly competitive market, so competition between producers will make them lower prices in order to get rid of excessive production, thus allowing the market equilibrium (in the point $E$) to be reached. But wait a second! When we said that producers will change price we said nothing about quantity of production. But you can clearly see that in point $L$ (before producers lowered prices) the quantity was equal to $Q_2$, while in point $E$ it's equal to $Q'$, and $Q' &lt; Q_2$. 

What happened with all these ${\bf Q}_2$ minus ${\bf Q}'$ goods? It looks like producers collectively decided to destroy part of their excessive goods in order to reach the point of equilibrium. Because if producers will change only price of their goods (i.e. $Q_s$ is constant) there is NO way they can reach equilibrium without moving their supply curve (or alternatively - without moving the demand curve).
You are basically asking a dynamic question on the basis of a static model, although this often done for convenience. In a real static model, over production is impossible.

You answered the first part of your question yourself: In the short run the Q2-Q'goods got sold off at a lower price. For the long run: recall that the supply curve is also the industry's marginal cost curve. If producers lower their prices below P2, some of them will start to operate at less than max profit and either go out of business or reduce production, to operate at max profit level again. In the long run we thus move along the supply curve, downwards to point E.