Why does a firm make profit in a perfect competition market I'm solving a problem about $n=180$ firms in a perfect competition market, where demand is given by $D(p)=100-5p$. A firm's cost function is $c(q_i) = 2 \cdot (q_i)^2$. Using $p = c'(q_i)$ and the demand function, I was able to derive the equilibrium quantity $q^* = \frac{1}{2}$ and price $p^* = 2$.
When asked about the profit each firm makes, I calculated a positive result for the individual profit in equilibrium $\pi_i^* = p^*\cdot q_i^* - c(q_i^*) = \frac{1}{2}&gt;0$.
How is this possible? Is there not the assumption that a firm does not make profits in a perfect competition market? I know that there can be short term profits, but we assumed the market is in equilibrium here from the start. I'm new to microeconomics, coming from a mathematical background.
The first order condition for profits here (with respect to quantity, since firms are price-takers) is
$$p - 4q_i = 0 \implies q_i^* = \frac 1 4 p,$$
which is the supply function of its firm. So market Supply is
$$nq_i^* = \frac{180}{4} p = 45p,$$
and equilibrium market price
$$45 p = 100 - 5 p \implies p^* = 2$$
and equilibrium market quantity
$$Q* = nq_i^* = 180 \cdot\frac 1 4 (2) = 90$$
Per identical firm we have
$$q^*_i = 0.5$$
The profits are
$$(2)*(0.5) - 2* (0.5)^2 = 0.5$$
...indeed.
So what happens here?
Well &quot;perfectly competitive market&quot; among others things means costless and free entry. But the problem above was solved for a fixed number of firms.
At this number of firms, each firm makes an economic profit. This will induce other firms to enter the market, driving equilibrium price down and economic profits to zero.
I guess the OP can understand how one can compute the number of firms required so as to have zero economic profits (hint: it is not finite).