Wage Bargaining and Capital Accumulation: A Dynamic Version of the Monopoly Union Model

Wage Bargaining and Capital Accumulation: A Dynamic Version of the Monopoly Union Model | 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 Wage Bargaining and Capital Accumulation: A Dynamic Version of the Monopoly Union Model Marco Guerrazzi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5446636/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this paper, I explore the relationship between wage bargaining and capital accumulation by developing a differential game in which a monopolistic union sets the wage of its members by taking as given the optimal employment strategy of a representative firm and the way in which capital is evaluated over time. Under the assumption that investment amounts to a constant share of produced output, I show that a meaningful open-loop Stackelberg equilibrium requires the union to be more patient than the firm. Moreover, relying on some numerical simulations, I show that although adjustments towards the steady-state equilibrium occur through damped oscillations, after an initial period of decline, the model predicts a stable union wage premium. JEL Classification: J31; J51; J52. Monopoly union model Capital accumulation Binding wage contracts Differential games Open-loop Stackelberg equilibrium Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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-5446636","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":382300452,"identity":"770513f3-12d6-4514-9769-b3e03c4ea6c8","order_by":0,"name":"Marco Guerrazzi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEElEQVRIiWNgGAWjYDADNvYGKANMGgAxMyEtPAcwtBDSI5GAIYRdi3xE8rHPFTV19nySjw9++LjDJpqP/QCbdEFBrRwDO/8BbFoMb6QlzzxzjI2ZTTotWXLmmbTcNp4ENukZBseNcTnMcEaOMWMDGw8bm3SOGTNv2+HcNgagFh6DY4kNOLXkf2Zs+CfBwyZ5/htEC/8DsJZ6XFrkJXKYGRvbDCTYgLogWiTAttQk4HKYAc8zY8bGvgQDNp40Y8mZbUC/SDxstuYxOGDYxsxsgNWW9uTHjA3f6uzl2w8//PCxzSZ3fn/ywds8f+rk+fkPPsBqywFMMcYGIHEYGqdYbGnAIVGHQ3wUjIJRMApGIAAABOZO3X9pwDwAAAAASUVORK5CYII=","orcid":"","institution":"University of Genoa","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Marco","middleName":"","lastName":"Guerrazzi","suffix":""}],"badges":[],"createdAt":"2024-11-13 11:38:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5446636/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5446636/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":79309843,"identity":"caf94035-cb19-4200-a246-04e3cc6acad9","added_by":"auto","created_at":"2025-03-27 00:46:28","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1478492,"visible":true,"origin":"","legend":"","description":"","filename":"SubmissionDGA.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5446636/v1_covered_0de1da66-b226-48f3-b178-df6024e6595f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Wage Bargaining and Capital Accumulation: A Dynamic Version of the Monopoly Union Model","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Monopoly union model, Capital accumulation, Binding wage contracts, Differential games, Open-loop Stackelberg equilibrium","lastPublishedDoi":"10.21203/rs.3.rs-5446636/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5446636/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, I explore the relationship between wage bargaining and capital accumulation by developing a differential game in which a monopolistic union sets the wage of its members by taking as given the optimal employment strategy of a representative firm and the way in which capital is evaluated over time. 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