Pricing Externality

The pricing externality in a complementary-goods market is the harm one firm's price hike imposes on the other firms' revenues. When Firm 1 raises $p_1$ by $\Delta$, the total price $P = p_1 + p_2$ rises by $\Delta$, quantity $Q = A-P$ falls by $\Delta$, and Firm 2's revenue $p_2 \cdot Q$ falls by $p_2 \cdot \Delta$ — but Firm 1 ignores this loss in its own optimisation. This is the mechanism behind Double Marginalization.

type: complementary-firms
A: 6

The signature result ($A = 6$): as $N$ rises, total price $P^N = AN/(N+1)$ climbs toward the choke price and industry profit $NA^2/(N+1)^2$ is maximised at $N = 1$. More complementary firms hurt consumers and firms — the opposite of competition among substitutes.

When to use

Use the pricing-externality framing whenever you need to explain why decentralised complementary firms over-price relative to the integrated monopoly benchmark. It is the direct analogue of a pollution externality: individual action harms others, leading to a socially suboptimal outcome. The standard remedies — Vertical Integration, revenue sharing, two-part tariffs — all internalise the externality by giving a single entity control over the full price.