The firm is in short-run equilibrium because it is earning supernormal profits, as price $P_1$ is greater than the minimum average cost $P_2$.

The firm is in long-run equilibrium, producing at the profit-maximising output $Q_1$, and exhibits excess capacity equal to $Q_2-Q_1$.

The firm achieves allocative efficiency in the long run because price $P_1$ is equal to average cost at output $Q_1$.

The firm achieves productive efficiency in the long run because it produces at output $Q_2$, where marginal cost equals average cost ($MC=AC$).