Horizontal and Vertical Differentiation in the Circular City

Horizontal and Vertical Differentiation in the Circular City | 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Research Article Horizontal and Vertical Differentiation in the Circular City Didier Laussel This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9336016/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 We study price, quality, and location competition between two firms on a circular market when consumers differ both horizontally and vertically. Firms choose locations on a circle, qualities from a bounded but costless set, and prices, while consumers have heterogeneous valuations for quality. Transportation costs are quadratic, and the market is fully covered. We show that two distinct equilibrium regimes arise. In a vertical regime, firms maximally differentiate in quality, one choosing the highest feasible quality and the other the lowest. Prices and market shares are pinned down by the vertical differentiation mechanism, and---because of the symmetry of the circle---locations are irrelevant as long as an interior vertical sorting condition holds. In a horizontal regime, firms choose identical (maximal) quality levels and instead differentiate spatially, locating at antipodal points on the circle. We provide exact conditions under which each regime constitutes an equilibrium and characterize the parameter regions where one regime dominates the other. The analysis highlights how vertical differentiation can insulate firms from spatial competition and rationalize co-location, while sufficiently strong transportation costs restore the standard incentive for maximal spatial differentiation. JEL Codes: D4, L13 Other Economics Horizontal and vertical differentiation location product quality Salop's circle Full Text Additional Declarations The authors declare no competing interests. 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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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-9336016","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":618379578,"identity":"24d24a17-17bc-45cb-86a5-593f5a34e1a5","order_by":0,"name":"Didier Laussel","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAklEQVRIie3QMWvCQBTA8RcCmY643mGIX+GJoEvoZ6kIumRwdCpKoZMfIB9Dce1wchCX0KwHDhUCnRyudHFw6CNKKbRnVof7Ey4cxw/uHYDLdY8pQEm/6LKbJrT4cwAJrSbCLjscAwReTcTcRiQg/CKqmYQ7fy0/X4G1skllDJYxvi8WB1MAH1iMUMF0m30A4zrtiwz3Pcy9526mgUfyf4KK0SfpYjoNfIb74Sr3XtrMwBO3XKwmZyIdPam+zvj2Q/hNQsMy1I/Ypte7Em0n9SxLyVm3OPbFEkc9kQ9ploJbSViqjTnJJI539GKn2UMcKrU9mDyxkmt/jxuAy+VyuW72Db57XpNfJMxpAAAAAElFTkSuQmCC","orcid":"","institution":"Aix Marseille Université","correspondingAuthor":true,"prefix":"","firstName":"Didier","middleName":"","lastName":"Laussel","suffix":""}],"badges":[],"createdAt":"2026-04-06 16:54:25","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9336016/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9336016/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":106284331,"identity":"15d16725-dd21-4e28-b769-c7680b50fd70","added_by":"auto","created_at":"2026-04-07 06:42:42","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":329035,"visible":true,"origin":"","legend":"","description":"","filename":"salophortvert.dvi.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9336016/v1_covered_fa609e49-9519-4264-a60b-5f84f21cb1d6.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eHorizontal and Vertical Differentiation in the Circular City\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Aix-Marseille University","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":"Horizontal and vertical differentiation, location, product quality, Salop's circle","lastPublishedDoi":"10.21203/rs.3.rs-9336016/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9336016/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe study price, quality, and location competition between two firms on a circular market when consumers differ both horizontally and vertically. 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