Monopoly

ECON 101H: Introduction to Economics

Sérgio O. Parreiras

Economics Department, UNC at Chapel Hill

Spring 2026

Monopoly P Q 100 200 D P₀ Q₀ P₀

Monopoly

Marginal Revenue

To maximize profits, a firm produces where its marginal revenue equals its marginal cost, regardless of market structure (perfect competition, monopoly, oligopoly, etc.).

What makes the monopoly case different from perfect competition is that the monopolist knows its quantity choice will affect the market price, while firms in perfect competition are price-takers.

In particular, under monopoly, the marginal revenue is not constant and equal to the market price.

Monopoly

Marginal Revenue

Numerical Example: A monopolist sells \(Q = 8\) units at \(P = 30\), but to sell \(Q = 9\), the monopolist must charge \(P = 29.50\).

\[ MR = TR(9) - TR(8) = 29.50 \times 9 - 30 \times 8 = \underbrace{29.50}_{P} + \underbrace{(29.50 - 30)}_{\Delta P} \times \underbrace{8}_{Q} \]

In general:

\[ \boxed{MR = \dfrac{\Delta TR}{\Delta Q} = P + \dfrac{\Delta P}{\Delta Q} \times Q} \]

Notice: \(\Delta P < 0\) which implies that \(MR < P\): the marginal revenue curve lies below the demand curve.

Monopoly Equilibrium P Q D MR MC Q* P*
Welfare Comparison P Q D MR MC QPC PPC CS PS QM PM CS PS DWL

Monopoly

The Mark-up

$$\dfrac{P^* - MC}{P^*} = \dfrac{P^* - MR}{P^*}$$
$$= 1 - \dfrac{MR}{P^*}$$
$$= 1 - \dfrac{P^* + \dfrac{\Delta P}{\Delta Q} \cdot Q^*}{P^*}$$
$$= 1 - 1 + \dfrac{\Delta P}{\Delta Q} \cdot \dfrac{Q^*}{P^*}$$
$$= \dfrac{1}{\eta_{Q,P}}$$
P Q D MR MC Q* P* MC η = -2.33 Mark-up = 42.9%
Demand Elasticity P Q 100 200 D MR 70 60
Total Revenue TR Q 200 4200 60

Monopoly

Patents

TODO

Monopoly

Rent Seeking

TODO

Monopoly

Natural Monopolies

TODO