The Dynamics of Bertrand Price Competition with Cost-Reducing Investments

58 Pages Posted: 13 Jun 2013

See all articles by Fedor Iskhakov

Fedor Iskhakov

University of New South Wales (UNSW) - ARC Centre of Excellence in Population Ageing Research (CEPAR)

John Rust

Department of Economics, Georgetown University

Bertel Schjerning

University of Copenhagen - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: March 15, 2013

Abstract

We present a dynamic extension of the classic static model of Bertrand price competition that allows competing duopolists to undertake cost-reducing investments in an attempt to “leapfrog” their rival to attain low-cost leadership – at least temporarily. We show that leapfrogging occurs in equilibrium, resolving the Bertrand investment paradox., i.e. leapfrogging explains why firms have an ex ante incentive to undertake cost-reducing investments even though they realize that simultaneous investments to acquire the state of the art production technology would result in Bertrand price competition in the product market that drives their ex post profits to zero. Our analysis provides a new interpretation of “price wars”. Instead of constituting a punishment for a breakdown of tacit collusion, price wars are fully competitive outcomes that occur when one firm leapfrogs its rival to become the new low cost leader. We show that the equilibrium involves investment preemption only when the firms invest in a deterministically alternating fashion and technological progress is deterministic. We prove that when technological progress is deterministic and firms move in an alternating fashion, the game has a unique Markov perfect equilibrium. When technological progress is stochastic or if firms move simultaneously, equilibria are generally not unique. Unlike the static Bertrand model, the equilibria of the dynamic Bertrand model are generally inefficient. Instead of having too little investment in equilibrium, we show that duopoly investments generally exceed the socially optimum level. Yet, we show that when investment decisions are simultaneous there is a “monopoly” equilibrium when one firm makes all the investments, and this equilibrium is efficient. However, efficient non-monopoly equilibria also exist, demonstrating that it is possible for firms to achieve efficient dynamic coordination in their investments while their customers also benefit from technological progress in the form of lower prices.

Keywords: duopoly, Bertrand-Nash price competition, Bertrand paradox, Bertrand investment paradox, leapfrogging, cost-reducing investments, technological improvement, dynamic models of competition, Markov-perfect equilibrium, tacit collusion, price wars, coordination and anti-coordination games, strategic

JEL Classification: D92, L11, L13

Suggested Citation

Iskhakov, Fedor and Rust, John and Schjerning, Bertel, The Dynamics of Bertrand Price Competition with Cost-Reducing Investments (March 15, 2013). Univ. of Copenhagen Dept. of Economics Discussion Paper No. 13-05. Available at SSRN: https://ssrn.com/abstract=2277601 or http://dx.doi.org/10.2139/ssrn.2277601

Fedor Iskhakov

University of New South Wales (UNSW) - ARC Centre of Excellence in Population Ageing Research (CEPAR) ( email )

Level 6 Central Lobby (enter via East Lobby)
Australian School of Business Building
Sydney, New South Wales NSW 2052
Australia

John Rust

Department of Economics, Georgetown University ( email )

Washington, DC 20057
United States
1-202-687-6806 (Phone)
1-202-687-6102 (Fax)

Bertel Schjerning (Contact Author)

University of Copenhagen - Department of Economics ( email )

Øster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

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