Optimal transfer prices and technology in decentralized business groups

Abstract

Decentralized (parent-affiliates) business groups encompass independent firms sharing production resources under common administrative or financial control. In this paper, we propose a single-leader-multi-follower game where a parent firm (the leader) operates in a competitive single-product market and delegates production to profit-maximizing affiliate firms (the followers). With a view to provide an operational tool for the management of decentralized business groups, the proposed model integrates transfer prices and investment in intangible resources, as incentive mechanisms driving affiliates' production decisions. Based on the parent's control of the value chain, two model specifications and solution approaches are presented: full delegation and partial delegation. For the former, we provide an exact characterization of the equilibrium solution, whereas for business groups operating under partial delegation, we provide tight lower and upper bounds, computable by state-of-the-art optimization methods. As empirically shown using a customized version of the Orbis data set focusing on 40 European parent firms, our methodology not only uncovers how optimal transfer prices and technology are dependent on the parent's control of the value chain, but also gives rise to a computational approach that is efficiently applicable to a wide range of decentralized (parent-affiliates) business groups.

Keywords: Decentralized production, Technology sharing, Leader-follower game, Bilevel programming

JEL Classification: C61, D24, M11, C44