Profit Maximization

Definition

Any firm, in any market structure (PC, monopoly, oligopoly), maximizes its profit where $MR = MC$.

• The maths ($\Pi = TR - TC$, $\frac{d\Pi}{dq} = MR - MC = 0$) assumes nothing about the market.
• Only what MR equals differs: PC $MR = P$ → $P = MC$; Monopoly $MR < P$ → $P > MC$.

Situational reasoning

Example: P = €8

Extra unit	MC of this unit	Profit change	Produce?
11th	€5	+€3	Yes, margin left
12th	€8	€0	Yes, break-even on this unit
13th	€10	−€2	No, loses money

→ Keep producing until MC rises to P, then stop: $P = MC$. MC initially gets low, but from one point, bottleneck occurs, so MC increases. Until the MC is too high so that it is no longer profitable, the total profit is accumulated positive number. So max profit is when $MR-MC=0$, thus $MR = MC$.

Mathematical reasoning:

$\Pi(q) = TR(q) - TC(q)$ $\frac{d\Pi}{dq}=MR-MC=0. \therefore MR=MC.$

• From this reasoning, this condition is called the First Order Condition(FOC) of profit maximization.
• For profit maximizing, Second Order Condition(SOC) is also required: $\frac{d^2\Pi}{dq^2}<0. TC''>0$
  • $TC''>0$: $MC$ must be rising
• And $P = MR$ in Perfect Competition, so $P = MC$.
  • General rule $MR = MC$. Price taker → each extra unit sells at $P$ → $MR = P$ → $P = MC$.

For SR three cases and LR chains, see Short-run and Long-run Equilibrium.

Related: Shutdown Rule, Monopoly