🔎 How to solve perfect competition problems (three steps)

On the homework/exam, you often solve a perfect competition problem in three steps:

1. Use $P = MC$ to find $q^*$. (or $P \geq MC$ for discrete goods)

2. Shut down if $P < AVC$ when you produce $q^*$.

   1. if you shut down, then $q = 0$

   2. if you don’t shut down, then $q = q^*$.

3. Complete rest of problem.

   1. $\text{profit} = q \times (P - AC)$

Here are the same three steps, broken down with explanations:

1. Find the optimal quantity to produce if you don’t want to shut down, $q^*$: Use $MR = P = MC$ to find $q^*$. (or $P \geq MC$ for discrete goods)

   1. This step anchors everything that comes later, because, if they produce anything, they produce $q^*$ units.

2. Will you make $q^*$ units or will you shut down? Shut down if $P < AVC$. ← use the AVC for when you produce $q^*$.

   1. if you shut down, then $q = 0$

   2. if you don’t shut down, then $q = q^*$.

3. Once you know q, you can plug q into any equation that you like. For example:

   1. $\text{profit} = q \times (P - AC)$

🧭 ↑↑ we will follow similar steps with monopolies and monopolistic competition as well. For all models, we will determine quantity by setting $MR = MC$. Perfect competition is special only in that $P = MR$ in perfect competition, so we can set $P = MR = MC$.