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Endogenous timing in a mixed oligopoly: a forgotten equilibrium
Economics Letters 83 (2004) 147 – 148 www.elsevier.com/locate/econbase
Endogenous timing in a mixed oligopoly: a forgotten equilibrium Armel Jacques * CERESUR, Universite´ de La Re´union, 15, Avenue Rene´ Cassin, BP 7151, F-97715 Saint-Denis Messag Cedex 9, Ile de La Re´union, France Received 2 June 2003; accepted 2 October 2003
Abstract The aim of this note is to slightly correct Proposition 4.1 of [Economic Letters 61 (1998) 181]. D 2004 Elsevier B.V. All rights reserved. Keywords: Mixed oligopoly; Endogenous timing; Stackelberg JEL classification: D00; L00
In a recent issue of this journal, Pal (1998) examines the endogenous timing in a mixed oligopoly. In a model with two time periods, he showed that (1) all firms producing simultaneously in the same time period cannot be sustained as a SPNE outcome, (2) there exists a SPNE outcome where all private firms produce simultaneously in period 1 and the public firm produces in period 2, and (3) if the number of private firms N V 2, there exists a SPNE outcome where the public firm produces in period 1 and the private firms produce in period 2. For N z 3, this configuration cannot be sustained as a SPNE outcome. In Section 4, he extends the analysis to cases with more than two time periods (M > 2). He claims that: If M>2, then there is a UNIQUE SPNE, at which all private firms produce simultaneously in period 1 and the public firm produces in a subsequent period. This last proposition needs to be qualified. This proposition is right when N z 2. However, when N = 1, there is another SPNE, in which the public firm produces in period 1 and the private firm produces in the last period.
* Tel.: +33-2-62938435; fax: +33-2-62938472. E-mail address: [email protected] (A. Jacques). 0165-1765/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2003.10.008
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A. Jacques / Economics Letters 83 (2004) 147–148
Proof: The public firm cannot increase welfare by producing in an other period. If it produces in the last period, the welfare decreases and if it produces in an other period, the welfare stays the same. The private firm cannot increase its profit by producing sooner. If it produces in period 1 its profit decreases and if it produces in an other period, its profit does not change. 5 Reference Pal, D., 1998. Endogenous timing in a mixed oligopoly. Economics Letters 61, 181 – 185.
Endogenous timing in a mixed oligopoly: a forgotten equilibrium Armel Jacques * CERESUR, Universite´ de La Re´union, 15, Avenue Rene´ Cassin, BP 7151, F-97715 Saint-Denis Messag Cedex 9, Ile de La Re´union, France Received 2 June 2003; accepted 2 October 2003
Abstract The aim of this note is to slightly correct Proposition 4.1 of [Economic Letters 61 (1998) 181]. D 2004 Elsevier B.V. All rights reserved. Keywords: Mixed oligopoly; Endogenous timing; Stackelberg JEL classification: D00; L00
In a recent issue of this journal, Pal (1998) examines the endogenous timing in a mixed oligopoly. In a model with two time periods, he showed that (1) all firms producing simultaneously in the same time period cannot be sustained as a SPNE outcome, (2) there exists a SPNE outcome where all private firms produce simultaneously in period 1 and the public firm produces in period 2, and (3) if the number of private firms N V 2, there exists a SPNE outcome where the public firm produces in period 1 and the private firms produce in period 2. For N z 3, this configuration cannot be sustained as a SPNE outcome. In Section 4, he extends the analysis to cases with more than two time periods (M > 2). He claims that: If M>2, then there is a UNIQUE SPNE, at which all private firms produce simultaneously in period 1 and the public firm produces in a subsequent period. This last proposition needs to be qualified. This proposition is right when N z 2. However, when N = 1, there is another SPNE, in which the public firm produces in period 1 and the private firm produces in the last period.
* Tel.: +33-2-62938435; fax: +33-2-62938472. E-mail address: [email protected] (A. Jacques). 0165-1765/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2003.10.008
148
A. Jacques / Economics Letters 83 (2004) 147–148
Proof: The public firm cannot increase welfare by producing in an other period. If it produces in the last period, the welfare decreases and if it produces in an other period, the welfare stays the same. The private firm cannot increase its profit by producing sooner. If it produces in period 1 its profit decreases and if it produces in an other period, its profit does not change. 5 Reference Pal, D., 1998. Endogenous timing in a mixed oligopoly. Economics Letters 61, 181 – 185.