Courtnot’s Price and Bertrand’s Price Models for Complementary Products for Deteriorating items and Incorporating Tax on Purchasing and Sales:Decisions on Demand and Green Lot Size

Courtnot’s Price and Bertrand’s Price Models for Complementary Products for Deteriorating items and Incorporating Tax on Purchasing and Sales:Decisions on Demand and Green Lot Size | 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 Courtnot’s Price and Bertrand’s Price Models for Complementary Products for Deteriorating items and Incorporating Tax on Purchasing and Sales:Decisions on Demand and Green Lot Size C.K. Sivashankari This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6624644/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract In this paper, Cournot’s and Bertrand’s price models for complementary products for deteriorating items and incorporating tax on purchasing and sales are considered in third order equation. Two models are developed: mode-1 is considered Cournot’s price model with Advertisement-sales return-Cournot’s price as a demand function and optimal demand and lot size are decisions variables, and in the model-2, developed Bertrand’s price model with Advertisement-sales return-Bertrand’s price as a demand function and optimal pricing and lot size are decisions variables. In both models, a comparative study has been executed between incorporating tax along with without tax. It is evident that a gradual increase in tax rate, from 1 to 10 percent, significantly impacts and reduces the total profit. In both the models, price break even point is established, and law of demand has been confirmed in two models and highest possible profit has been calculated from the three alternative variables. Transporation cost, a carbon emission cost, green technology invesment cost, are introduced to reduce carbon emissions. Finding the optimum demand, optimal pricing along lot size for maximizing overall profit is purpose of this paper. Numerical examples demonstrate this model's applicability. To evaluate stability of this suggested model, a sensitivity analysis of the optimum solutions is provided. The data are generated by using Visual Basic 6.0 Production Tax Sales Tax Cournot’s Demand Advertisement Sales return Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 03 Jun, 2025 Reviews received at journal 30 May, 2025 Reviews received at journal 27 May, 2025 Reviewers agreed at journal 20 May, 2025 Reviewers agreed at journal 16 May, 2025 Reviewers agreed at journal 15 May, 2025 Reviewers agreed at journal 14 May, 2025 Reviewers agreed at journal 14 May, 2025 Reviewers invited by journal 14 May, 2025 Editor assigned by journal 13 May, 2025 Submission checks completed at journal 13 May, 2025 First submitted to journal 08 May, 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. 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-6624644","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":456830807,"identity":"8a4e8a5d-1318-4d4e-ace1-781f5acad6da","order_by":0,"name":"C.K. 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Two models are developed: mode-1 is considered Cournot\u0026rsquo;s price model with Advertisement-sales return-Cournot\u0026rsquo;s price as a demand function and optimal demand and lot size are decisions variables, and in the model-2, developed Bertrand\u0026rsquo;s price model with Advertisement-sales return-Bertrand\u0026rsquo;s price as a demand function and optimal pricing and lot size are decisions variables. In both models, a comparative study has been executed between incorporating tax along with without tax. It is evident that a gradual increase in tax rate, from 1 to 10 percent, significantly impacts and reduces the total profit. In both the models, price break even point is established, and law of demand has been confirmed in two models and highest possible profit has been calculated from the three alternative variables. Transporation cost, a carbon emission cost, green technology invesment cost, are introduced to reduce carbon emissions. Finding the optimum demand, optimal pricing along lot size for maximizing overall profit is purpose of this paper. Numerical examples demonstrate this model's applicability. To evaluate stability of this suggested model, a sensitivity analysis of the optimum solutions is provided. 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