Lesson preview · Monopoly Pricing

Solving Q* and P* — Practice & Proofs

~7 min · Free to read

Two steps. Set $M R = M C$ and solve for $Q_{m}$ . Plug $Q_{m}$ into the demand curve to read $P_{m}$ . With $M R = a - 2 b Q$ for linear demand, the algebra is short.

Tip

Closed form for linear demand and constant MC

If $P = a - b Q$ and $M C = c$ (constant), the answer has a closed form:

$Q_{m} = \frac{a - c}{2 b}, P_{m} = \frac{a + c}{2}$ .

The monopoly price is the midpoint of the demand intercept $a$ and the marginal cost $c$ .

Worked Example

A monopolist faces $P = 120 - 4 Q$ with $M C = 20$ . Find $Q_{m}$ and $P_{m}$ , then verify with the closed form.

Practice · 1 / 4

Wrong answers cost no XP

Drill the MR = MC recipe. Each question re-rolls with fresh numbers.

A monopolist faces $P = 130 - 4 Q$ with $M C = 15$ (constant). Find $Q_{m}$ . (Round to 2 decimals.)

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