Bertrand, Cournot and monopolistically competitive equilibria
Autor(a) principal: | |
---|---|
Data de Publicação: | 1999 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional do FGV (FGV Repositório Digital) |
Texto Completo: | http://hdl.handle.net/10438/12216 |
Resumo: | Using an example, we study the analogs, for the differentiated product case, of the Cournot and Bertrand equilibria. These equilibria can be shown to exist and be uni que if we impose a sim pie and natural restriction on the elasticities of the demand functions for the differentiated products. Our characterizations of these equilibria make it possible to compare them and to determine how they are affected by the size of the market and the number of firms. We are also able to prove the existence of Cournot free-entry equilibria in which the number of firms is determined endogenously. In addition, we are able to prove that, in a large market, the Cournot free-entry equilibria approximate the Dixit-Stiglitz monopolistically competitive equilibria. The free-entry equilibrium concept we study is an analog of the one studied by Novshek for the case of firms selling products that are perfect substitutes. Our results are extensions of Novshek's. While we were unable to establish a general existence result for Bertrand free-entry equilibria, we were able to prove that, when these equilibria exist, they are unique and that in large markets they also approximate the Dixit-Stiglitz equilibria. |
id |
FGV_f6d751ca5f0dd3550bc7a2f49207b9b0 |
---|---|
oai_identifier_str |
oai:repositorio.fgv.br:10438/12216 |
network_acronym_str |
FGV |
network_name_str |
Repositório Institucional do FGV (FGV Repositório Digital) |
repository_id_str |
3974 |
spelling |
Kihlstrom, RichardEscolas::EPGEFGV2014-10-24T13:33:24Z2014-10-24T13:33:24Z1999-08http://hdl.handle.net/10438/12216Using an example, we study the analogs, for the differentiated product case, of the Cournot and Bertrand equilibria. These equilibria can be shown to exist and be uni que if we impose a sim pie and natural restriction on the elasticities of the demand functions for the differentiated products. Our characterizations of these equilibria make it possible to compare them and to determine how they are affected by the size of the market and the number of firms. We are also able to prove the existence of Cournot free-entry equilibria in which the number of firms is determined endogenously. In addition, we are able to prove that, in a large market, the Cournot free-entry equilibria approximate the Dixit-Stiglitz monopolistically competitive equilibria. The free-entry equilibrium concept we study is an analog of the one studied by Novshek for the case of firms selling products that are perfect substitutes. Our results are extensions of Novshek's. While we were unable to establish a general existence result for Bertrand free-entry equilibria, we were able to prove that, when these equilibria exist, they are unique and that in large markets they also approximate the Dixit-Stiglitz equilibria.engEscola de Pós-Graduação em Economia da FGVSeminários de pesquisa econômica da EPGETodo cuidado foi dispensado para respeitar os direitos autorais deste trabalho. Entretanto, caso esta obra aqui depositada seja protegida por direitos autorais externos a esta instituição, contamos com a compreensão do autor e solicitamos que o mesmo faça contato através do Fale Conosco para que possamos tomar as providências cabíveisinfo:eu-repo/semantics/openAccessBertrand, Cournot and monopolistically competitive equilibriainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleEconomiaMonopóliosConcorrênciareponame:Repositório Institucional do FGV (FGV Repositório Digital)instname:Fundação Getulio Vargas (FGV)instacron:FGVORIGINAL000312740.pdf000312740.pdfapplication/pdf2008804https://repositorio.fgv.br/bitstreams/2ddd8abf-5d79-49d7-9798-4cbcbe95430f/download2084c244e789b5b6ecafefed3e34e78eMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-84707https://repositorio.fgv.br/bitstreams/120267c7-c48e-453b-be31-ffdf673a408b/downloaddfb340242cced38a6cca06c627998fa1MD52TEXT000312740.pdf.txt000312740.pdf.txtExtracted texttext/plain97790https://repositorio.fgv.br/bitstreams/4730cd05-17b0-4d83-9c9d-2fb0f5950e98/download22ace2852472ddec15638fbb7dd9dd80MD57THUMBNAIL000312740.pdf.jpg000312740.pdf.jpgGenerated Thumbnailimage/jpeg4053https://repositorio.fgv.br/bitstreams/beda5921-815b-428f-8b7c-7774d1ed7c84/download200936b3c38e256e68cc2ba6ec502900MD5810438/122162023-11-09 06:29:47.785open.accessoai:repositorio.fgv.br:10438/12216https://repositorio.fgv.brRepositório InstitucionalPRIhttp://bibliotecadigital.fgv.br/dspace-oai/requestopendoar:39742023-11-09T06:29:47Repositório Institucional do FGV (FGV Repositório Digital) - Fundação Getulio Vargas (FGV)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 |
dc.title.eng.fl_str_mv |
Bertrand, Cournot and monopolistically competitive equilibria |
title |
Bertrand, Cournot and monopolistically competitive equilibria |
spellingShingle |
Bertrand, Cournot and monopolistically competitive equilibria Kihlstrom, Richard Economia Monopólios Concorrência |
title_short |
Bertrand, Cournot and monopolistically competitive equilibria |
title_full |
Bertrand, Cournot and monopolistically competitive equilibria |
title_fullStr |
Bertrand, Cournot and monopolistically competitive equilibria |
title_full_unstemmed |
Bertrand, Cournot and monopolistically competitive equilibria |
title_sort |
Bertrand, Cournot and monopolistically competitive equilibria |
author |
Kihlstrom, Richard |
author_facet |
Kihlstrom, Richard |
author_role |
author |
dc.contributor.unidadefgv.por.fl_str_mv |
Escolas::EPGE |
dc.contributor.affiliation.none.fl_str_mv |
FGV |
dc.contributor.author.fl_str_mv |
Kihlstrom, Richard |
dc.subject.area.por.fl_str_mv |
Economia |
topic |
Economia Monopólios Concorrência |
dc.subject.bibliodata.por.fl_str_mv |
Monopólios Concorrência |
description |
Using an example, we study the analogs, for the differentiated product case, of the Cournot and Bertrand equilibria. These equilibria can be shown to exist and be uni que if we impose a sim pie and natural restriction on the elasticities of the demand functions for the differentiated products. Our characterizations of these equilibria make it possible to compare them and to determine how they are affected by the size of the market and the number of firms. We are also able to prove the existence of Cournot free-entry equilibria in which the number of firms is determined endogenously. In addition, we are able to prove that, in a large market, the Cournot free-entry equilibria approximate the Dixit-Stiglitz monopolistically competitive equilibria. The free-entry equilibrium concept we study is an analog of the one studied by Novshek for the case of firms selling products that are perfect substitutes. Our results are extensions of Novshek's. While we were unable to establish a general existence result for Bertrand free-entry equilibria, we were able to prove that, when these equilibria exist, they are unique and that in large markets they also approximate the Dixit-Stiglitz equilibria. |
publishDate |
1999 |
dc.date.issued.fl_str_mv |
1999-08 |
dc.date.accessioned.fl_str_mv |
2014-10-24T13:33:24Z |
dc.date.available.fl_str_mv |
2014-10-24T13:33:24Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10438/12216 |
url |
http://hdl.handle.net/10438/12216 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartofseries.por.fl_str_mv |
Seminários de pesquisa econômica da EPGE |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Escola de Pós-Graduação em Economia da FGV |
publisher.none.fl_str_mv |
Escola de Pós-Graduação em Economia da FGV |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional do FGV (FGV Repositório Digital) instname:Fundação Getulio Vargas (FGV) instacron:FGV |
instname_str |
Fundação Getulio Vargas (FGV) |
instacron_str |
FGV |
institution |
FGV |
reponame_str |
Repositório Institucional do FGV (FGV Repositório Digital) |
collection |
Repositório Institucional do FGV (FGV Repositório Digital) |
bitstream.url.fl_str_mv |
https://repositorio.fgv.br/bitstreams/2ddd8abf-5d79-49d7-9798-4cbcbe95430f/download https://repositorio.fgv.br/bitstreams/120267c7-c48e-453b-be31-ffdf673a408b/download https://repositorio.fgv.br/bitstreams/4730cd05-17b0-4d83-9c9d-2fb0f5950e98/download https://repositorio.fgv.br/bitstreams/beda5921-815b-428f-8b7c-7774d1ed7c84/download |
bitstream.checksum.fl_str_mv |
2084c244e789b5b6ecafefed3e34e78e dfb340242cced38a6cca06c627998fa1 22ace2852472ddec15638fbb7dd9dd80 200936b3c38e256e68cc2ba6ec502900 |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 |
repository.name.fl_str_mv |
Repositório Institucional do FGV (FGV Repositório Digital) - Fundação Getulio Vargas (FGV) |
repository.mail.fl_str_mv |
|
_version_ |
1810023821525123072 |