Elsevier

Economics Letters

Volume 124, Issue 1, July 2014, Pages 122-126
Economics Letters

Price vs. quantity competition in a vertically related market

https://doi.org/10.1016/j.econlet.2014.05.002Get rights and content

Highlights

  • We compare Cournot and Bertrand competition in a vertically related market.

  • The standard conclusions about the Cournot–Bertrand comparison are reversed.

  • Cournot competition yields higher prices and lower output than Bertrand competition.

  • Consumer and total welfare are higher with Cournot than with Bertrand competition.

Abstract

This paper demonstrates that the standard conclusions regarding the comparison of Cournot and Bertrand competition are reversed in a vertically related market with upstream monopoly and trading via two-part tariffs. In such a market, downstream Cournot competition yields higher output, lower wholesale prices, lower final prices, higher consumers’ surplus, and higher total welfare than Bertrand competition.

Introduction

The vast majority of products reach the hands of the consumers after going through the various stages of the so-called vertical production chain. Clearly, this implies that a firm which operates in one stage of the vertical chain needs to trade with firms that are active at previous and/or later production stages. According to a number of empirical studies (see e.g., Berto Villa-Boas, 2007; Bonnet and Dubois, 2010), a common way of trading among vertically related firms, i.e., among input producers, final product manufacturers, and retailers, is through non-linear two-part tariff contracts. This paper compares Cournot and Bertrand competition in a vertically related market in which an upstream monopolist trades with two competing downstream firms through two-part tariffs.

A well-known result in oligopoly theory is that a one-tier market is more competitive and efficient when it is characterized by Bertrand competition rather than by Cournot competition. In particular, Bertrand competition results into lower prices and profits and higher output and consumer and total welfare than Cournot competition. Singh and Vives (1984) were the first to establish formally these results. A substantial body of the literature (see e.g., Cheng, 1985; Vives, 1985; Okuguchi, 1987; Dastidar, 1997; Lambertini, 1997; Häckner, 2000, Amir and Jin, 2001) has been developed thereafter extending the Singh and Vives results. For instance,Cheng (1985) and Vives (1985) generalized these results respectively by means of a geographic approach and by considering the n-firm oligopoly case with general demand functions. Dastidar (1997) and Häckner (2000), instead, pointed out the sensitivity of the results in Singh and Vives to the sharing rules governing oligopoly and to the type of product differentiation.1

We demonstrate that the standard conclusions about price and quantity competition can be altered in the context of a vertically related market. In particular, we show that downstream Cournot competition yields more competitive market outcomes than downstream Bertrand competition—it yields higher output and lower prices. The reversal from the standard results is driven by the fact that the upstream monopolist has stronger incentives to increase the aggressiveness of the downstream firms when they compete in quantities than when they compete in prices. Because of this, its incentives to behave opportunistically are more pronounced in the former case. The latter leads, in turn, to lower wholesale prices under Cournot competition that translate into lower marginal costs for the downstream firms, and thus, into higher output and lower prices. Despite the fact that downstream competition is fiercer when it takes place in quantities, still the downstream firms are better off than when they compete in prices. This reveals that the effect of the lower input prices and thus, of the higher efficiency, dominates the effect of the increased competition intensity. Interestingly, in light of the above results, and in contrast to conventional wisdom, we find that Cournot competition is preferable to Bertrand competition from both the consumers’ and the total welfare point of view.

Our analysis extends the above-mentioned extensive literature that compares Cournot and Bertrand outcomes in standard one-tier oligopoly markets by considering a vertically related setting. As such our analysis also complements the literature on contracting in vertically related markets (e.g., O’Brien and Shaffer, 1992; McAfee and Schwartz, 1994, McAfee and Schwartz, 1995; Rey and Vergé, 2004) by analyzing the role of the mode of downstream competition.

Correa-López and Naylor (2004), Correa-López (2007), Arya et al. (2008), Mukherjee et al. (2012), Manasakis and Vlassis (2013), and Chirco and Scrimitore (2013) have also addressed the Cournot–Bertrand debate in the context of a vertically related market. Most of their results are in line with the results of Singh and Vives (1984), and thus, they are different from ours.2 This occurs mainly because all of these papers, in contrast to ours, share a common feature: they compare Cournot and Bertrand downstream competition in markets where trading occurs through linear wholesale prices contracts, and not through the extensively used in practice, as well as in the theoretical literature on vertical contracting, non-linear two-part tariff contracts.

Section snippets

The model

An upstream firm, U, produces, at zero marginal cost, an input which two downstream firms, D1 and D2, use, in one-to-one-proportion, in the production of their final goods. Downstream firms face no other cost than the cost of obtaining the input from U.3

Consumers’ inverse and direct demands for Di’s final good are: pi=aqiγqjandqi=(api)γ(apj)1γ2,i,j=1,2,ij, where pi and qi are respectively Di’s

Equilibrium analysis

We start by solving the last stage of the game, first, under Cournot competition, and then, under Bertrand competition.

(i) Cournot competition: Each Di chooses qi in order to maximize its profits: maxqiπi(wi,wj,qi,qj)=(aqiγqj)qiwiqiFi. The resulting reaction functions are: qi(qj)=awiγqj2. Note that a reduction in the wholesale price charged to Di shifts out its reaction function and turns it into a more aggressive downstream competitor.

Solving the system of reaction functions (2), we

Cournot vs. Bertrand downstream competition

We turn now to the comparison of the equilibrium outcomes under Cournot and Bertrand final market competition.

Proposition 1

The equilibrium wholesale prices and the final prices are higher under Bertrand than under Cournot competition, while the opposite holds for the equilibrium output.

Proof

First, wiC<0<wiB; second, pCpB=aγ34(2γ2)<0; finally, qCqB=aγ34(1+γ)(2γ2)>0. 

Proposition 1 informs us that under Cournot competition the downstream firms obtain the input at better terms than under Bertrand

Conclusion

We have shown that the standard conclusions regarding the comparison of Cournot and Bertrand competition can be reversed in a vertically related market with trading through non-linear contracts. In such a market, the incentives of an upstream monopolist to make its customers more aggressive in the downstream market are stronger when the latter compete in quantities than when they compete in prices. As a result, the upstream monopolist faces a more severe commitment problem under Cournot than

Acknowledgments

We would like to thank an anonymous referee and the associate editor for their helpful comments and suggestions. This research has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)- Research Funding Program (379331): Thalis - Athens University of Economics and Business - “New Methods in the Analysis of Market Competition: Oligopoly,

References (28)

  • L.D. Qiu

    On the dynamic efficiency of Bertrand and Cournot equilibria

    J. Econom. Theory

    (1997)
  • X. Vives

    On the efficiency of Bertrand and Cournot equilibria with product differentiation

    J. Econom. Theory

    (1985)
  • S. Berto Villa-Boas

    Vertical relationships between manufacturers and retailers: inference with limited data

    Rev. Econom. Stud.

    (2007)
  • C. Bonnet et al.

    Inference on vertical contracts between manufacturers and retailers allowing for nonlinear pricing and resale price maintenance

    Rand J. Econ.

    (2010)
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