In a perfectly competitive market, how are the market demands taken into consideration? Or is it that the market demand isn't a concept there as such due to a very large market and setting the price more will attract no consumer and less will attract as many consumers as will $p^*$, the market price?
When maximizing profit $\pi_i = pq_i - c(q_i)$ for firm $i$, we do not mention the market (inverse) demand $p(q)$ curve anywhere. This led me to ask this question.
Edit: Slightly unrelated to my main question. While searching for a tag along the lines of perfect-competition, I saw competitive equilibrium. Is perfect competition also a competitive equilibrium?