An Extended Goodwin Model for Skill-Polarized Economies under Technological Change

An Extended Goodwin Model for Skill-Polarized Economies under Technological Change | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article An Extended Goodwin Model for Skill-Polarized Economies under Technological Change Mazin Alahmadi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8006631/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract We extend Goodwin’s classical growth-cycle model into a five-dimensional integrodifferential system that captures the dynamic competition between high- and low-skilled labor pools under skill-biased technological change. We develop a dynamic optimal framework to stabilize wage-employment cycles, addressing volatility driven by automation and labor market polarization. Mathematically, we establish the existence of endogenous cycles via a supercritical Hopf bifurcation, thereby formalizing Goodwin’s conjecture within a skill-differentiated economy. We derive Hamiltonian conditions for optimal policy intervention, demonstrating how targeted skill subsidies and automation taxes can suppress bifurcations and guide the system toward a stable equilibrium. The model’s prediction accuracy is empirically confirmed using labor market data from Saudi Arabia (2018–2023) and the OECD (2020–2025), particularly in predicting the rebound in high-skilled wages following the 2008 financial crisis. Our results provide a robust mathematical foundation for cost-effective policy tools, such as robotic taxation and workforce retraining, that promote employment stability while sustaining productivity growth. These insights are particularly relevant for economies undergoing rapid transformation, including those aligned with strategic initiatives like Saudi Vision 2030. Distributed delay differential equations Stability Periodic solutions Optimal control Hopf bifurcation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 05 Feb, 2026 Reviews received at journal 04 Feb, 2026 Reviews received at journal 11 Dec, 2025 Reviewers agreed at journal 10 Nov, 2025 Reviewers agreed at journal 06 Nov, 2025 Reviewers invited by journal 06 Nov, 2025 Editor assigned by journal 06 Nov, 2025 Submission checks completed at journal 04 Nov, 2025 First submitted to journal 01 Nov, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8006631","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":542776312,"identity":"0d276336-88da-4970-8676-fa7e6865b920","order_by":0,"name":"Mazin Alahmadi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6klEQVRIiWNgGAWjYDAC5gOMBxgbgIzDzIchIgcIaWFLYIBqYUsmVcsBHmPitOi2MT848HPHNnm+4zyfDX62Mcjx3Uhg/vADjxazY2wGB3vP3DaceZh3c2JvG4Ox5I0ENskefFruNxgc4G27zbgBqAXIYEjcANTCwIPXFvYPB/+23bbfcJjnMZDBUA/UwvzxD14tPAaHgbYkArUwJwNtSTC4kcAgjd8WnoLDsm23k2ceZjM2ljknYTjzzMM2aRn8Dtv48G3bbdu+84cfS74pswEGXfLhj2/waEEHEkAMjqZRMApGwSgYBZQAAMImWeUUdf9aAAAAAElFTkSuQmCC","orcid":"","institution":"King Abdulaziz University","correspondingAuthor":true,"prefix":"","firstName":"Mazin","middleName":"","lastName":"Alahmadi","suffix":""}],"badges":[],"createdAt":"2025-11-01 15:23:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8006631/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8006631/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":96125329,"identity":"00be5533-b5fd-4655-b10b-5243da7950d4","added_by":"auto","created_at":"2025-11-17 23:34:12","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3197,"visible":true,"origin":"","legend":"","description":"","filename":"d1ab35ca97c349ab9261d2797a7ab27c.json","url":"https://assets-eu.researchsquare.com/files/rs-8006631/v1/ef8072453f53433e8f43c4e4.json"},{"id":96248399,"identity":"a3b7a2da-27d7-44e8-b8af-d1ccd600de21","added_by":"auto","created_at":"2025-11-19 07:28:25","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1172526,"visible":true,"origin":"","legend":"","description":"","filename":"mazinjee1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8006631/v1_covered_22ba96d3-3e7e-473b-affa-eacd8318cb32.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"An Extended Goodwin Model for Skill-Polarized Economies under Technological Change","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-evolutionary-economics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jeec","sideBox":"Learn more about [Journal of Evolutionary Economics](http://link.springer.com/journal/191)","snPcode":"191","submissionUrl":"https://submission.nature.com/new-submission/191/3","title":"Journal of Evolutionary Economics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Distributed delay differential equations, Stability, Periodic solutions, Optimal control, Hopf bifurcation","lastPublishedDoi":"10.21203/rs.3.rs-8006631/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8006631/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":" We extend Goodwin’s classical growth-cycle model into a five-dimensional integrodifferential system that captures the dynamic competition between high- and low-skilled labor pools under skill-biased technological change. 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