In a perfectly competitive market, how are the market demands taken into consideration?

Question

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.

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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?

Answer 1

No, market demand is in there. The assumption of perfectly competitive market is that firm is a price taker. Consequently market demand is perfectly elastic so the inverse demand function that individual firm faces is given by:

$$p(q_i)= \bar{p}$$

Once you substitute this inverse demand into profit function you get:

$$\Pi = p(q_i)q_i - c(q_i)=\bar{p}q_i-c(q_i)$$

I use $\bar{}$ to emphasize that price is fixed but most undergraduate textbooks just use $p$. Nonetheless, the demand is still there, just the demand one single firm faces is always perfectly elastic and independent of production of a single firm (even if demand for whole market isn't).

Is perfect competition also a competitive equilibrium?

Perfect competition is a model. A competitive equilibrium can be an equilibrium found in perfectly competitive model, but equilibrium itself is balance of various forces (e.g. supply-demand, revenue-costs etc.) or situation where players play their best response to what other players are playing.