Profit Maximization: Marginal Revenue and Marginal Cost

Profit is $\pi(Q)=TR(Q)-TC(Q)$. Comparing totals can find the largest gap, but marginal reasoning explains the choice:

If $MR>MC$, the next unit increases profit. If $MR<MC$, it reduces profit. The firm expands through units with positive marginal profit and stops before the first unit whose MC exceeds MR. With smooth curves and an interior solution, this becomes $MR=MC$ on rising MC.

For a competitive firm

Because $MR=P$, the rule is

at the chosen positive output, provided the firm should operate. Equality alone is insufficient when MC is falling: a crossing where MC continues downward can be a profit minimum. The relevant crossing lies on rising MC.

Fixed cost affects the level of profit but not the output that maximizes short-run profit, because fixed cost does not change with one more unit. It can still matter for long-run entry and exit.

Profit versus revenue and average cost

Producing the quantity with greatest revenue ignores cost. Producing at minimum ATC minimizes cost per unit, not necessarily total profit. Profit is maximized where the vertical gap between TR and TC is greatest, equivalently where marginal additions change from positive to negative.

The rule works for losses too. “Profit maximization” means choosing the least negative attainable profit when every option loses money. The next lesson determines whether that choice is positive production or temporary shutdown.

Verify the rule with totals

Suppose price and MR are 14, while marginal costs for seven units are 8, 7, 8, 10, 13, 17, and 22. Units one through five each add to profit because their MC does not exceed 14. Unit six would reduce profit by 3, so the firm stops at five.

Adding the marginal profits gives the same answer as comparing total revenue and total cost. The marginal method is usually clearer because it explains exactly why production stops.

Use two decisions, not one

The $MR=MC$ rule identifies the best positive output. It does not by itself prove that operating is better than producing zero. After finding the candidate quantity, the firm must apply the shutdown test. This two-stage procedure prevents the common mistake of producing at an MR–MC crossing even when revenue cannot cover variable cost.

Another common error is choosing minimum ATC output. Minimum ATC finds the lowest cost per unit; maximum profit finds the largest total gap between revenue and cost. They coincide only by accident.