Complementary Monopolist

A complementary monopolist is a firm with monopoly power over one component of a complementary bundle — for instance, one of two sequential toll-road operators, or a video-game console maker selling alongside an independent game publisher. Each complementary monopolist sets the price of its component while taking the others' prices as given, leading to Double Marginalization.

type: reaction-functions
kind: price
br1: 5,-0.5
br2: 5,-0.5

Best responses in prices (not quantities). Both slope down, and the equilibrium $p_1 = p_2 = A/3$ gives a total $P = 2A/3$ — higher than the integrated monopoly price $A/2$.

When to use

The complementary-monopolist label is what makes the Topic 4 result memorable: $N$ complementary monopolists yield $P^N = AN/(N+1)$, individual profit $A^2/(N+1)^2$, and total industry profit $NA^2/(N+1)^2$ — maximised at $N=1$ and falling monotonically as the chain fragments. Use the term when contrasting with a substitute-goods oligopoly, where more firms drive price toward marginal cost.