Pricing with markups under horizontal and vertical competition

We study the effect of competition on markups for producers of both substitutes and complements. We model a market for a single product, or product bundle, where producers compete to provide all or some portion of the product. In our game, each firm adopts a price function proportional to its per-unit costs by deciding on the size of a markup. Customers then choose a set of providers that offers the lowest combined price. For quadratic production costs and general series- parallel market structures, a producer's optimal markup corresponds to the price in a redefined market, which we derive explicitly. We characterize equilibrium markups for inelastic and elastic demand. When bundle demand is inelastic, a unique equilibrium exists if and only if the market has a 3-edge-connected network structure. We study comparative statics of equilibria with respect to changes in the market design. When production is divided among decentralized firms that compete vertically, markups increase throughout the market. Reduced competition in the market for any bundle component leads to a higher bundle price, but social efficiency in component markets need not coincide with overall efficiency of production. Furthermore, the effect on an individual producer's profit is seen to depend on its market position.