Profit Maximisation

Profit Maximisation: The Core Objective

A firm’s fundamental goal is to maximise its profit. Profit, denoted by the Greek letter $\pi$, is the difference between what the firm earns from selling its output and what it spends to produce that output.

The firm wants to find the specific quantity of output, call it $q_0$, at which this gap between total revenue and total cost is the largest. At any other quantity, profit will be strictly less than at $q_0$. The entire problem of profit maximisation boils down to one question: how do we identify this special quantity $q_0$?

The Three Conditions for Maximum Profit

The textbook lays down three precise conditions that must hold simultaneously at the profit-maximising output $q_0$. These are not arbitrary rules; they follow from the logic of comparing the benefit of producing one more unit with its cost.

Condition 1: Price Equals Marginal Cost ($p = MC$)

Marginal cost ($MC$) is the addition to total cost from producing one extra unit. In perfect competition, the firm is a price taker — it can sell any amount at the market price $p$. So the addition to total revenue from selling one more unit is exactly $p$.

If $p > MC$, the extra revenue from the next unit exceeds its extra cost. Producing that unit adds to profit, so the firm should increase output. If $p < MC$, the extra cost of the next unit exceeds its extra revenue. Producing it would reduce profit, so the firm should decrease output. Only when $p = MC$ is there no incentive to change output in either direction. This is the first-order condition for a maximum.

Condition 2: Marginal Cost Must Be Non-Decreasing at $q_0$

This is the second-order condition that ensures the point identified by $p = MC$ is a maximum and not a minimum. Think of the typical U-shaped marginal cost curve. As output increases, $MC$ first falls, reaches a minimum, and then rises.

If $p = MC$ on the downward-sloping portion of the $MC$ curve, then just to the left of that point $MC > p$ (the last unit added more to cost than to revenue, so profit was falling), and just to the right $MC < p$ (one more unit adds more to revenue than to cost, so profit rises). Such a point is actually a local minimum of profit, not a maximum.

For a true maximum, $MC$ must be rising (or at least not falling) at the point where it equals price. In other words, the $MC$ curve must cut the price line from below. This is why the condition is that marginal cost must be non-decreasing at $q_0$.

Condition 3: The Shutdown Condition

Even if $p = MC$ and $MC$ is rising, the firm might still be making a loss. The third condition determines whether the firm should produce at all or shut down temporarily. …