MR = MC Rule | Econ Academy

The golden rule of profit maximization: produce where Marginal Revenue equals Marginal Cost ( $M R = M C$ ). Why? If $M R > M C$ , producing one more unit adds more to revenue than to cost — profit increases. If $M R < M C$ , the last unit costs more than it brings in — profit falls. The sweet spot is where $M R = M C$ .

Key Term

The MR = MC Rule

A profit-maximizing firm produces the quantity where $M R = M C$ . For a competitive firm, since $M R = P$ , this simplifies to $P = M C$ . The firm expands output as long as each additional unit adds more revenue than cost.

Profit is maximized where the derivative of profit with respect to $Q$ is zero, i.e., $M R = M C$

For a competitive firm, $M R = P$ (as we saw in the previous topic). So the profit-maximization condition becomes simply $P = M C$ . The firm looks at the market price, finds the quantity where its $M C$ curve crosses that price, and produces that much. The profit (or loss) per unit is $P - A T C$ at that quantity.

Worked Example

A competitive firm faces $P = 20$ dollars. Its total cost function is $T C = 50 + 2 Q + 0.5 Q^{2}$ . Find the profit-maximizing quantity and calculate profit.

Interactive — Profit maximization: P = MC, walking down the price line

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Pizza shop with cost curves from the cost-curves topic. Steps through 4 profitable prices to see the profit rectangle shrink as P falls toward min ATC.

Check yourself · no marks

If $M R > M C$ at the current output level, should the firm produce more or less? Why?

Commit to one first. Guessing and being wrong beats reading the answer cold.

Practice · 1 / 4

No penalty for a wrong answer

Apply the

M R = M C

rule:

At the profit-maximizing quantity, if $P > A T C$ , the firm earns:

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