Pricing the razor: A note on two-part tariffs

•This paper studies when a timeless razor-and-blades monopoly would sell razors below cost.•With a uniform distribution of parallel linear demands, it is never optimal to do so.•With two groups of consumers with non-crossing linear demands, it is sometimes optimal to do so.

The “razor-and-blades” pricing strategy involves setting a low price for a durable basic product (razors) and a high price for a complementary consumable (blades). In a timeless model, Oi (1971) showed that if consumers' demand curves differ and do not cross and unit costs are constant, a monopolist should always price blades above cost. This note studies the optimal razor price. With a uniform distribution of parallel linear demand curves it is never optimal to sell the razor below cost, while with two types of consumers and non-crossing linear demands it is optimal to do so for some parameter values.