Monopoly

The Price Maker

A monopoly is a single seller — it faces the entire market demand curve and chooses its price (or equivalently, its quantity). Unlike a competitive firm, the monopolist is a price maker.

Key insight: marginal revenue is less than price. To sell one more unit, the monopolist must lower the price on ALL units (not just the marginal one):

$$MR = P + Q \cdot \frac{dP}{dQ} < P$$

For a linear demand $P = a - bQ$: $TR = (a - bQ)Q = aQ - bQ^2$, so:

$$MR = a - 2bQ$$

MR has twice the slope of the demand curve — it falls faster and hits zero at half the demand-curve intercept.

Profit maximisation: $MR = MC$, then read the price from the demand curve above:

$$\pi = (P - AC) \times Q$$

Deadweight loss: the monopolist restricts output below the competitive level ($Q_m < Q_c$) and charges a higher price ($P_m > P_c$). Units between $Q_m$ and $Q_c$ have willing buyers and affordable production costs but are NOT produced — this is the deadweight loss triangle.

Price discrimination:

• First degree (perfect): charge each consumer their maximum willingness to pay — captures all surplus.
• Second degree: offer different packages (bulk discounts, versioning) — consumers self-select.
• Third degree: charge different prices to different groups (student discounts, peak pricing) — requires identifiable segments with different elasticities.

Sources of monopoly power: legal barriers (patents, licences), economies of scale (natural monopoly), control of essential resources, network effects.

Monopoly vs competition

Common pitfall: Reading the monopoly price off the $MR$ curve. The sequence is: find $Q^*$ where $MR = MC$, then climb up to the demand curve to read the price customers will pay for that quantity.