{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T19:08:56Z","timestamp":1773083336440,"version":"3.50.1"},"reference-count":24,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Operations Research"],"published-print":{"date-parts":[[2011]]},"abstract":"<jats:p>We study empirically and analytically growth and fluctuation of firm size distribution. An empirical analysis is carried out on a US data set on firm size, with emphasis on one-time distribution as well as growth-rate probability distribution. Both Pareto's law and Gibrat's law are often used to study firm size distribution. Their theoretical relationship is discussed, and it is shown how they are complementable with a bimodal distribution of firm size. We introduce economic mechanisms that suggest a bimodal distribution of firm size in the long run. The mechanisms we study have been known in the economic literature since long. Yet, they have not been studied in the context of a dynamic decision problem of the firm. Allowing for these mechanism thus will give rise to heterogeneity of firms with respect to certain characteristics. We then present different types of tests on US data on firm size which indicate a bimodal distribution of firm size.<\/jats:p>","DOI":"10.1155\/2011\/269239","type":"journal-article","created":{"date-parts":[[2011,9,5]],"date-time":"2011-09-05T19:00:58Z","timestamp":1315249258000},"page":"1-21","source":"Crossref","is-referenced-by-count":3,"title":["Fluctuation of Firm Size in the Long-Run and Bimodal Distribution"],"prefix":"10.1155","volume":"2011","author":[{"given":"Hideaki","family":"Aoyama","sequence":"first","affiliation":[{"name":"Graduate School of Science, Kyoto University, Yoshida, Sakyo, Kyoto 606-8501, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lars","family":"Gr\u00fcne","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Frankfurt, Robert Mayer Street 8-10, 60054 Frankfurt, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Willi","family":"Semmler","sequence":"additional","affiliation":[{"name":"Center for Empirical Macroeconomics, 33615 Bielefeld, Germany and New School University, New York, NY 10011, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yoshi","family":"Fujiwara","sequence":"additional","affiliation":[{"name":"Center for Empirical Macroeconomics, 33615 Bielefeld, Germany and New School University, New York, NY 10011, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wataru","family":"Souma","sequence":"additional","affiliation":[{"name":"ATR Human Information Science Laboratories, Kyoto 619-0288, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"13","year":"1932"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2003.12.015"},{"key":"19","year":"2000"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4371(02)01663-1"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/s11151-004-7296-5"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1080\/00036840802400454"},{"key":"20","year":"1948"},{"key":"2","doi-asserted-by":"crossref","first-page":"116","DOI":"10.2307\/2234208","volume":"99","year":"1989","journal-title":"Economic Journal"},{"key":"3","first-page":"92","volume":"262","year":"1990","journal-title":"Scientific America"},{"key":"4","year":"1994"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.2307\/1914229"},{"key":"8","year":"1996"},{"key":"9","year":"1963"},{"key":"18","first-page":"321","volume":"75","year":"2007","journal-title":"Journal of Political Economy"},{"key":"17","volume-title":"Adjustment costs and tobin's q in a model with mutiple steady state","year":"2007"},{"issue":"2","key":"25","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/0022-0531(79)90031-0","volume":"21","year":"1979","journal-title":"Journal of Economic Theory"},{"key":"7","volume-title":"The financial accelerator in a quantitative business cycle framework","year":"1999"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/s00199-003-0442-8"},{"issue":"2","key":"12","doi-asserted-by":"crossref","first-page":"309","DOI":"10.2307\/2118465","volume":"109","year":"1994","journal-title":"The Quarterly Journal of Economics"},{"key":"22","first-page":"449","volume":"2","year":"1974","journal-title":"Journal of Finance"},{"key":"14","doi-asserted-by":"crossref","first-page":"2427","DOI":"10.1016\/j.jedc.2003.11.002","volume":"28","year":"2004","journal-title":"Journal of Economic Dynamics and Control"},{"key":"16","first-page":"1","volume":"1","year":"1993","journal-title":"Booking Papers of Economic Activity"},{"issue":"1","key":"21","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s001910050075","volume":"9","year":"1999","journal-title":"Journal of Evolutionary Economics"},{"key":"23","year":"1897"}],"container-title":["Advances in Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2011\/269239.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2011\/269239.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aor\/2011\/269239.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,20]],"date-time":"2017-06-20T05:47:05Z","timestamp":1497937625000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/aor\/2011\/269239\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"references-count":24,"alternative-id":["269239","269239"],"URL":"https:\/\/doi.org\/10.1155\/2011\/269239","relation":{},"ISSN":["1687-9147","1687-9155"],"issn-type":[{"value":"1687-9147","type":"print"},{"value":"1687-9155","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011]]}}}