Monopolist Pricing

A monopolist maximizes profit, but unlike a competitive firm, it itself chooses the price (or quantity). How does it do this and what are the consequences?

Demand and Marginal Revenue

The monopolist's demand curve: coincides with the market demand. Downward-sloping — to sell more, it must lower the price.

Marginal revenue (MR): MR < 0. Selling an additional unit requires lowering the price not only on it, but also on all previous units.

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

The second term is negative ($\frac{dP}{dQ}$). For linear demand $P = a - bQ$:

$ TR = P \times Q = aQ - bQ^2 $

$ MR = \frac{dTR}{dQ} = a - 2bQ $

MR has the same intercept, but is twice as steep.

Monopolist Optimum

Rule: $MR = MC$

Procedure:

Find $Q^*$ where $MR = MC$
Determine price $P^$ from the demand curve at $Q^$
Profit = $(P^* - ATC) \times Q^*$

Important: the monopolist does not "choose any price". It is limited by demand. Price selection determines quantity, and vice versa.

Connection to Elasticity

MR and elasticity: $MR = P(1 - 1/|\text{PED}|)$

Consequences:

At $|\text{PED}| = 1$: $MR = 0$
At $|\text{PED}| > 1$ (elastic): $MR > 0$
At $|\text{PED}| < 1$ (inelastic): $MR < 0$

The monopolist operates only on the elastic part of the demand curve! With inelastic demand, $MR < 0$.

Markup and Lerner Index

Lerner Index: measure of market power

$ L = \frac{P - MC}{P} = \frac{1}{|\text{PED}|} $

Interpretation:

$L = 0$: perfect competition ($P = MC$)
$L > 0$: monopoly markup

The less elastic the demand, the higher the markup.

For the investor: gross margin as a proxy for market power. High margin = low elasticity = pricing power.

Deadweight Loss of Monopoly

Comparison with competition:

Competition: $P = MC$, $Q = Q_c$ (efficient quantity)
Monopoly: $P > MC$, $Q = Q_m$

Losses:

Consumer surplus is reduced
Part shifts to the monopolist (profit)
Part is lost irretrievably (DWL)

DWL — the triangle between the demand and MC curves, from $Q_m$ to $Q_c$. Transactions that would have been mutually beneficial do not occur.

Rent-Seeking

Rent-seeking: resources spent to obtain or retain monopoly power.

Lobbying for regulatory protection
Legal costs to defend patents
Blocking entry of competitors

Social costs: rent-seeking is unproductive activity. Resources are spent not on creating value, but on redistribution.

For the Investor

Monopoly profit:

High margin, stable cash flow
Premium valuation — if power is sustainable

Risks:

Regulatory intervention
Antitrust lawsuits
Disruption from new technologies
Public pressure

Analysis:

Source of power and its sustainability
Pricing policy — does the company extract maximum?
Regulatory environment — what are the limitations?