[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-202130-105":59,"doc-detail-202130-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","to-bubble-or-not-to-bubble-asset-price-dynamics-and-optimality-in-olg-economies","To Bubble or Not to Bubble - Asset Price Dynamics and Optimality in OLG Economies","","Research studies an overlapping generations (OLG) exchange economy in which an asset provides dividends and determines when equilibria are bubbleless or bubbly. Using exogenous parameters, it derives three scenarios for equilibrium existence and fully characterizes equilibrium price dynamics under stationary endowments. It then proves necessary and sufficient conditions for Pareto optimality. Finally, it links asset price behavior to equilibrium optimality criteria.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/to-bubble-or-not-to-bubble-asset-price-dynamics-and-optimality-in-olg-economies/202130/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/to-bubble-or-not-to-bubble-asset-price-dynamics-and-optimality-in-olg-economies/202130.png","ImageObject",300,407,{"name":92,"@type":93},"Aria Callaghan","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-25","2026-09-04",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",17,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What are the three equilibrium scenarios identified for the OLG economy with a dividend-yielding asset?","Question",{"text":113,"@type":114},"The study derives three cases: only bubbleless equilibria exist; a bubbleless equilibrium coexists with a continuum of bubbly equilibria; or all equilibria are bubbly.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"When does a bubbly equilibrium exist under stationary endowments and standard assumptions?",{"text":118,"@type":114},"A bubbly equilibrium exists if and only if the interest rate in the economy without the asset is strictly lower than the population growth rate and the sum of per-capita dividends is finite.",{"name":120,"@type":111,"acceptedAnswer":121},"What conditions are provided for Pareto optimality in this framework?",{"text":122,"@type":114},"The paper establishes necessary and sufficient conditions for Pareto optimality and then investigates how asset price behavior relates to whether equilibria are optimal.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},202130,1788542645,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145,"preview_page_count":4},962084926284,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Munich Personal RePEc Archive  \nTo Bubble or Not to Bubble: Asset Price Dynamics and Optimality in OLG Economies  \nPham, Ngoc Sang and Le Van, Cuong and Bosi, Stefano  \nEM Normandie Business School, Métis Lab, CNRS, PSE, Université d’Evry, Université Paris-Saclay  \n4 August 2025  \nOnline at [https://mpra. ub. uni-muenchen. de/125605/](https://mpra. ub. uni-muenchen. de/125605/)  \n[MPRA Paper No. 125605](MPRA Paper No. 125605) , [posted 07 Aug 2025 18:17 UTC](posted 07 Aug 2025 18:17 UTC)  \nTo Bubble or Not to Bubble: Asset Price Dynamics  \nand Optimality in OLG Economies ∗ Stefano BOSI† Cuong LE VAN‡ Ngoc-Sang PHAM§  \nAugust 5, 2025  \nAbstract  \nWe study an overlapping generations (OLG) exchange economy with an asset that yields dividends. First, we derive general conditions, based on exogenous parameters, that give rise to three distinct scenarios: (1) only bubbleless equilibria exist,(2) a bubbleless equilibrium coexists with a continuum of bubbly equilibria, and (3) all equilibria are bubbly. Under stationary endowments and standard assumptions, we provide a complete characterization of the equilibrium set and the associated asset price dynamics. In this setting, a bubbly equilibrium exists if and only if the interest rate in the economy without the asset is strictly lower than the population growth rate and the sum of per capita dividends is finite.  \nSecond, we establish necessary and sufficient conditions for Pareto optimality.  \nFinally, we investigate the relationship between asset price behaviors and the optimality of equilibria.  \nKeywords: exchange economy, overlapping generations, asset price bubble, fundamental value, low interest rate, Pareto optimal.  \nJEL Classifications: C6, D5, D61, E4, G12 .  \n1 Introduction  \nThe asset valuation and its effects on welfare, either negative or positive, are long-standing questions in economics. The seminar paper of Tirole (1985) studies the price formation of asset yielding non-negative dividends and shows its impact on the Pareto optimality of equilibrium allocations.  \nAccording to the traditional literature (Tirole, 1982 , 1985 ; Santos and Woodford, 1997), given a dividend-paying asset with positive supply, its rational bubble is said to exist if the asset’s market price exceeds its fundamental value, typically defined as  \n∗We thank Alexis Akira Toda for his comments.  \n†Université d’Evry, Université Paris-Saclay. Email: [stefano.bosi@univ-evry.fr](stefano.bosi@univ-evry.fr)  \n‡CNRS, PSE. Email: [Cuong.Le-Van@univ-paris1.fr](Cuong.Le-Van@univ-paris1.fr)  \n§ EM Normandie Business School, Métis Lab. Emails: [npham@em-normandie.com](npham@em-normandie.com), [pns.pham@gmail.com](pns.pham@gmail.com)  \nthe sum of the discounted stream of future dividends.1 An equilibrium is referred tobe bubbly (bubbleless) if a bubble exists (does not exist), to be asymptotically bubbly ifa bubble exists and its bubble component does not converge to zero over time.  \nLet n, Gd and R∗ denote, respectively, the gross population growth rate, the gross dividend growth rate and the steady-state interest rate of the economy without asset. Assuming a constant dividend (i.e. , Gd = 1), the main insights from Proposition 1 in Tirole (1985) can be summarized as follows.  \n1. Insight 1: No bubbly equilibrium exists if 1 \u003C n \u003C R∗ .2  \n2. Insight 2: A continuum of equilibria (including both bubbly and bubbleless equilibria) exists if 1 \u003C R∗ \u003C n.  \n3. Insight 3: Every equilibrium is bubbly if R∗ \u003C 1 \u003C n.3  \nFurthermore, Proposition 2 in Tirole (1985) claims (without providing a formal proof)4 that: if R∗ \u003C n, then the asymptotically bubbleless equilibria are not Pareto optimal and the asymptotically bubbly equilibrium is Pareto optimal.  \nFollowing Tirole (1985), much of the subsequent literature has focused on the case of pure bubble assets, i.e., assets that pay no dividends but nonetheless have strictly positive prices. These works have extended Tirole’s framework across various economic settings.  \nA s","cbCaiuH1xNPERiUY","https://ap.wps.com/l/cbCaiuH1xNPERiUY","pdf",1079672,65,"English","# Introduction\n## Asset valuation, bubbles, and welfare\n## Fundamental value and bubbly vs bubbleless equilibria\n## Scenarios under population growth, dividend growth, and interest rate","[{\"question\":\"What are the three equilibrium scenarios identified for the OLG economy with a dividend-yielding asset?\",\"answer\":\"The study derives three cases: only bubbleless equilibria exist; a bubbleless equilibrium coexists with a continuum of bubbly equilibria; or all equilibria are bubbly.\"},{\"question\":\"When does a bubbly equilibrium exist under stationary endowments and standard assumptions?\",\"answer\":\"A bubbly equilibrium exists if and only if the interest rate in the economy without the asset is strictly lower than the population growth rate and the sum of per-capita dividends is finite.\"},{\"question\":\"What conditions are provided for Pareto optimality in this framework?\",\"answer\":\"The paper establishes necessary and sufficient conditions for Pareto optimality and then investigates how asset price behavior relates to whether equilibria are optimal.\"}]","To Bubble or Not to Bubble - Asset Price Dynamics and Optimality in OLG Economies | PDF",164]