Supply curve for a competitive firm with constant MC I know that for a perfectly competitive firm, the supply curve is given by $p=MC \ge AVC$, where $AVC$ is the average variable cost. 
Now I get really confused when the $MC$ comes out to be a constant. How do I determine the supply curve in that scenario?
Consider a firm with constant marginal cost $c$ that chooses to supply a quantity $q \in [0, \bar{x}]$ when taking the price $p$ as given. The profits of such a firm can be written as

$$ \text{total revenue} - \text{total cost}  = q p - c q = q(p - c).$$

From this, we can immediately infer the optimal supply $q^*$:


If $p&lt;c$, then $q^* = 0$.
If $p=c$, then any $q \in [0, x]$ is optimal.
If $p&gt;c$, then $q^* = \bar{x}$ (the maximum possible quantity).


Notice we need a constraint like $q \in [0, \bar{x}]$ for the supply correspondence to be well-defined. If we had simply restricted $q$ to $\mathbb{R}^+$ (the non-negative real numbers), as is more usual, then there would be no solution to the profit maximisation problem in the case of $p&gt;c$.