market equilibrium quantity $\ne$ firm profit maximising quantity? Consider a perfectly competitive market with equilibrium price $P_{eq}$ and quantity $Q_{eq}$ and firm with profit maximising quantity $Q_f$ as illustrated below:







I guess any firm in the market would have the same demand, marginal revenue and average revenue (or am I wrong?), but what about profit maximising quantity $Q_f$? It seems to depend on $MC$. Is $MC$ different for each firm?


If so, then $Q_f$ is not necessarily the same for each firm?
If not, why?
In intro micro you usually assume that every firm in a perfectly competetive market has the same costs and production function etc. Hence, the MCs are the same for every firm. Under this assumptions, every firm will produce the same quantity in equilibrium.