Why does a monopoly produce where MR = MC?

The two numbers that decide every unit

For each extra unit the firm could make, two numbers matter. Marginal revenue (MR) is the extra money the sale brings in. Marginal cost (MC) is the extra money it costs to make. The firm compares them one unit at a time.

1. If $MR>MC$, the unit adds more revenue than cost, so it adds to profit — make it.
2. If $MR<MC$, the unit costs more than it earns, so it shrinks profit — skip it.
3. Profit stops climbing exactly where $MR=MC$. That is the profit-maximizing quantity.
4. To get the price, go up from that quantity to the demand curve and read it off. The price is higher than MR.

Why MR sits below the price

Here is the part that trips people up. A monopolist charges one price to everyone. To sell one extra unit, it has to drop that price a little — and the drop applies to every unit, not just the new one. So the extra sale brings in its own price but quietly shaves a bit off all the units already being sold. After that markdown, the true gain — marginal revenue — comes out below the price on the tag.

Worked example

Suppose demand is $P=100-Q$ and each unit costs a flat 20 dollars to make, so $MC=20$.

The monopolist makes half as much (40 versus 80) and charges three times as much (60 versus 20). Same costs, same demand — the difference is entirely that MR sits below price, so the firm stops sooner.

Why not produce one more?

At $Q=40$ the next unit would bring in marginal revenue of $100-2(41)=18$ dollars but cost 20 dollars to make. That unit loses 2 dollars. Every unit past 40 loses more. Stopping at $MR=MC$ is not the firm being timid — it is the firm refusing to make units that bleed money.

Common misconception

Frequently asked questions

Why does a monopoly produce where MR = MC?

Because that is the last unit worth making. While marginal revenue beats marginal cost ($MR>MC$), each extra unit adds to profit, so the firm keeps going. Once marginal cost passes marginal revenue ($MR<MC$), each extra unit loses money. The crossover point, $MR=MC$, is exactly where profit stops rising — the profit-maximizing quantity.

Why is marginal revenue below the price for a monopolist?

A single-price monopolist must lower the price on every unit to sell one more, not just on the last one. So the extra unit brings in its own price but costs the firm a small markdown on all the units it was already selling. That markdown pulls marginal revenue below the price the buyer pays.

How do you find the monopoly price?

First find the profit-maximizing quantity where $MR=MC$. Then go straight up from that quantity to the demand curve and read the price there. The price sits above marginal revenue, because the demand curve tells you the most buyers will pay for that quantity.

Does a monopolist charge the highest price it possibly can?

No. At a sky-high price almost nobody buys, so profit is tiny. The monopolist instead picks the quantity where $MR=MC$, and that quantity sets one specific price on the demand curve — high, but far from the maximum a single desperate buyer might pay.

Is the MR = MC rule the same in perfect competition?

The rule is universal: every profit-maximizing firm produces where $MR=MC$. The difference is that a competitive firm is a price taker, so its marginal revenue equals the market price and the rule collapses to $P=MC$. A monopolist has $MR<P$, so it produces less and charges more than a competitive industry would.

What is the marginal revenue formula for a linear demand curve?

If demand is $P=a-bQ$, marginal revenue is $MR=a-2bQ$ — the same intercept but twice the slope. That is why the MR line always lies below the demand curve and hits the quantity axis at half the demand-curve quantity.

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