Lesson preview · Monopoly Basics

MR from Linear Demand — Practice & Proofs

~7 min · Free to read

You’ve seen the rule: for linear demand $P = a - b Q$ , the monopolist’s marginal revenue is $M R = a - 2 b Q$ — same vertical intercept, twice the slope. Now let’s drill it until it’s automatic, and then (optionally) look under the hood to see why the slope doubles.

Tip

The 2× slope rule — one-line recap

If $P = a - b Q$ , then $M R = a - 2 b Q$ . Vertical intercept stays at $a$ . MR hits zero at $Q = a / (2 b)$ — exactly half the demand’s horizontal intercept.

Worked Example

A monopolist faces $P = 80 - 4 Q$ . Write the MR function, then compute MR at $Q = 6$ .

Practice · 1 / 4

Wrong answers cost no XP

Drill the 2× slope rule. Each question re-rolls with fresh numbers every session.

A monopolist faces demand $P = 60 - 2 Q$ . At what quantity does $M R = 0$ ? (Round to 2 decimals.)

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