{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T00:45:18Z","timestamp":1777337118011,"version":"3.51.4"},"reference-count":49,"publisher":"Emerald","issue":"8","license":[{"start":{"date-parts":[[2021,7,16]],"date-time":"2021-07-16T00:00:00Z","timestamp":1626393600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["K"],"published-print":{"date-parts":[[2022,7,22]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to analyze the operational decisions of a manufacturer who produces multiple products and the government's selection of cap-and-trade and carbon tax regulations.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title><jats:p>This paper explores the production decisions of a multi-product manufacturer under cap-and-trade and carbon tax regulations in a cap-dependent carbon trading price setting and compares carbon emission, the manufacturer's profits and social welfare under the two regulations. Game theory and extreme value theory are used to analyze our models.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Findings<\/jats:title><jats:p>First, the authors find that the optimal profit of the manufacturer (the optimal cap) increases and then decreases with the cap (the unit carbon emission of product). Second, if the environmental damage coefficient is moderate, the optimal cap of unit environmental damage coefficient is independent of the product carbon emission or other related product parameters. Ultimately, cap-and-trade regulation always generates more carbon emission than carbon tax regulation. And cap-and-trade regulation (carbon tax regulation) can generate more social welfare if the environmental damage coefficient is low (high), and the social welfare under the two regulations is equal to each other, or otherwise.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title><jats:p>This paper contributes the prior literature by considering the inverse relationship of the allocated cap and the carbon trading price and discusses the social welfare under cap-and-trade and carbon tax regulations. Some important and new results are found, which can guide the government's implementation of the two regulations.<\/jats:p><\/jats:sec>","DOI":"10.1108\/k-09-2020-0610","type":"journal-article","created":{"date-parts":[[2021,7,14]],"date-time":"2021-07-14T13:19:23Z","timestamp":1626268763000},"page":"2554-2577","source":"Crossref","is-referenced-by-count":17,"title":["The choice of cap-and-trade and carbon tax regulations in a cap-dependent carbon trading price setting"],"prefix":"10.1108","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5930-3298","authenticated-orcid":false,"given":"Xiaoping","family":"Xu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yugang","family":"Yu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guowei","family":"Dou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0889-9562","authenticated-orcid":false,"given":"Xiaomei","family":"Ruan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","published-online":{"date-parts":[[2021,7,16]]},"reference":[{"issue":"1","key":"key2022072111313861400_ref001","first-page":"95","article-title":"Contingent claim pricing through a continuous time variational bargaining scheme","volume":"260","year":"2018","journal-title":"Annals of Operations Research"},{"issue":"3","key":"key2022072111313861400_ref002","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/j.reseneeco.2008.01.001","article-title":"Choice and design of regulatory instruments in the presence of green consumers","volume":"30","year":"2008","journal-title":"Resource and Energy Economics"},{"issue":"1","key":"key2022072111313861400_ref003","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10100-009-0120-4","article-title":"On the classical Maki\u2013Thompson rumour model in continuous time","volume":"19","year":"2011","journal-title":"Central European Journal of Operations Research"},{"issue":"1","key":"key2022072111313861400_ref004","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1109\/TASE.2012.2203304","article-title":"Carbon footprint and the management of supply chains: insights from simple models","volume":"10","year":"2013","journal-title":"IEEE Transactions on Automation Science and Engineering"},{"issue":"3","key":"key2022072111313861400_ref005","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1016\/j.ejor.2019.11.052","article-title":"Tax or subsidy? An analysis of environmental policies in supply chains with retail competition","volume":"283","year":"2020","journal-title":"European Journal of Operational Research"},{"key":"key2022072111313861400_ref006","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.tre.2017.09.011","article-title":"Decentralization or integration: distribution channel selection under environmental taxation","volume":"113","year":"2018","journal-title":"Transportation Research E: Logistics and Transportation Review"},{"issue":"2","key":"key2022072111313861400_ref007","doi-asserted-by":"crossref","first-page":"95","DOI":"10.5547\/ISSN0195-6574-EJ-Vol24-No2-4","article-title":"Are differentiated carbon taxes inefficient? A general equilibrium analysis","volume":"24","year":"2003","journal-title":"The Energy Journal"},{"key":"key2022072111313861400_ref008","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1016\/j.jclepro.2017.07.251","article-title":"Optimal production and carbon emission reduction level under cap-and-trade and low carbon subsidy policies","volume":"167","year":"2017","journal-title":"Journal of Cleaner Production"},{"key":"key2022072111313861400_ref009","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.tre.2016.11.007","article-title":"Manufacturer and retailer coordination for environmental and economic competitiveness: a power perspective","volume":"97","year":"2017","journal-title":"Transportation Research Part E: Logistics and Transportation Review"},{"key":"key2022072111313861400_ref010","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.tre.2013.03.006","article-title":"Local sourcing and fashion quick response system: the impacts of carbon footprint tax","volume":"55","year":"2013","journal-title":"Transportation Research Part E: Logistics and Transportation Review"},{"issue":"11","key":"key2022072111313861400_ref011","doi-asserted-by":"crossref","first-page":"2646","DOI":"10.1016\/j.cor.2013.04.017","article-title":"Optimal apparel supplier selection with forecast updates under carbon emission taxation scheme","volume":"40","year":"2013","journal-title":"Computers and Operations Research"},{"key":"key2022072111313861400_ref012","volume-title":"Cutting Carbon in Europe: The 2020 Plans and the Future of the EU ETS","year":"2008"},{"issue":"2","key":"key2022072111313861400_ref013","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1007\/s10479-013-1514-1","article-title":"Sustainability investment under cap-and-trade regulation","volume":"240","year":"2016","journal-title":"Annals of Operations Research"},{"issue":"6","key":"key2022072111313861400_ref014","doi-asserted-by":"crossref","first-page":"1006","DOI":"10.1111\/poms.12523","article-title":"Technology choice and capacity portfolios under emissions regulation","volume":"25","year":"2016","journal-title":"Production and Operations Management"},{"key":"key2022072111313861400_ref015","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.enpol.2012.09.042","article-title":"Emission-dependent supply chain and environment-policy-making in the \u2018cap-and-trade\u2019system","volume":"57","year":"2013","journal-title":"Energy Policy"},{"issue":"1","key":"key2022072111313861400_ref016","first-page":"1","article-title":"Allocation policy considering firm's time-varying emission reduction in a cap-and-trade system","volume":"290","year":"2020","journal-title":"Annals of Operations Research"},{"key":"key2022072111313861400_ref049","volume-title":"The EU Emissions Trading System (EU ETS)","author":"EC","year":"2013"},{"issue":"2","key":"key2022072111313861400_ref017","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/0165-1765(95)00666-4","article-title":"The dual political economy of taxes and tradable permits","volume":"49","year":"1995","journal-title":"Economics Letters"},{"key":"key2022072111313861400_ref018","first-page":"1449","article-title":"Inventory management under joint product recovery and cap-and-trade constraints","volume":"167","year":"2017","journal-title":"Journal of Cleaner Production"},{"issue":"4","key":"key2022072111313861400_ref019","doi-asserted-by":"crossref","first-page":"908","DOI":"10.1287\/opre.2013.1189","article-title":"Optimal production planning with emissions trading","volume":"61","year":"2013","journal-title":"Operations Research"},{"key":"key2022072111313861400_ref020","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/j.jclepro.2014.08.102","article-title":"Production lot-sizing and carbon emissions under cap-and-trade and carbon tax regulations","volume":"103","year":"2015","journal-title":"Journal of Cleaner Production"},{"issue":"9","key":"key2022072111313861400_ref021","doi-asserted-by":"crossref","first-page":"1094","DOI":"10.1057\/s41274-016-0123-1","article-title":"Optimal production planning and cap setting under cap-and-trade regulation","volume":"68","year":"2017","journal-title":"Journal of the Operational Research Society"},{"issue":"1","key":"key2022072111313861400_ref022","first-page":"96","article-title":"Dual-mode production planning for manufacturing with emission constraints","volume":"25","year":"2016","journal-title":"European Journal of Operational Research"},{"issue":"2","key":"key2022072111313861400_ref023","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.ijpe.2011.03.024","article-title":"Managing carbon footprints in inventory management","volume":"132","year":"2011","journal-title":"International Journal of Production Economics"},{"issue":"1","key":"key2022072111313861400_ref024","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1080\/00207543.2019.1641239","article-title":"The production decisions and cap setting with wholesale price and revenue sharing contracts under cap-and-trade regulation","volume":"58","year":"2020","journal-title":"International Journal of Production Research"},{"key":"key2022072111313861400_ref025","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/j.eneco.2015.03.015","article-title":"A method for analyzing pollution control policies: application to SO2 emissions in China","volume":"49","year":"2015","journal-title":"Energy Economics"},{"issue":"4","key":"key2022072111313861400_ref026","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1108\/K-04-2018-0169","article-title":"Impact of carbon permit allocation rules on incentive contracts for carbon emission reduction","volume":"49","year":"2018","journal-title":"Kybernetes"},{"issue":"3","key":"key2022072111313861400_ref027","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1016\/j.ejor.2011.11.027","article-title":"Consumer environmental awareness and competition in two-stage supply chains","volume":"218","year":"2012","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"key2022072111313861400_ref028","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1111\/deci.12265","article-title":"Contract design with information asymmetry in a supply chain under an emissions trading mechanism","volume":"49","year":"2018","journal-title":"Decision Sciences"},{"issue":"4","key":"key2022072111313861400_ref029","doi-asserted-by":"crossref","first-page":"34","DOI":"10.2478\/ngoe-2018-0021","article-title":"Gaming for introducing social challenges and responsibility to Young people","volume":"64","year":"2018","journal-title":"Na\u0161e gospodarstvo\/Our Economy"},{"issue":"1","key":"key2022072111313861400_ref030","first-page":"437","article-title":"Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration","volume":"260","year":"2018","journal-title":"Annals of Operations Research"},{"key":"key2022072111313861400_ref031","first-page":"983","article-title":"The symmetry between controlling pollution by price and controlling it by quantity","year":"1992","journal-title":"Canadian Journal of Economics"},{"issue":"3","key":"key2022072111313861400_ref032","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1016\/j.ejor.2014.10.057","article-title":"The steel industry: a mathematical model under environmental regulations","volume":"242","year":"2015","journal-title":"European Journal of Operational Research"},{"key":"key2022072111313861400_ref033","unstructured":"Sartor, O. (2012), \u201cThe EU ETS carbon price: to intervene or not to intervene? Climate Brief No 12\u201d, from CDC Climate available at: http:\/\/www.cdcclimat.com\/IMG\/pdf\/12-02_climate_brief_12_-_the_eu_ets_carbon_price_-_to_intervene_or_not_to_intervene.pdf (accessed 26 May 2014)."},{"issue":"2","key":"key2022072111313861400_ref034","doi-asserted-by":"crossref","first-page":"696","DOI":"10.1007\/s10957-017-1159-3","article-title":"A stochastic maximum principle for a Markov regime-switching jump-diffusion model with delay and an application to finance","volume":"179","year":"2018","journal-title":"Journal of Optimization Theory and Applications"},{"key":"key2022072111313861400_ref035","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.tre.2016.10.007","article-title":"Capacity and production planning with carbon emission constraints","volume":"97","year":"2017","journal-title":"Transportation Research Part E: Logistics and Transportation Review"},{"issue":"2","key":"key2022072111313861400_ref036","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1007\/s10479-015-1858-9","article-title":"How supply chain coordination affects the environment: a carbon footprint perspective","volume":"250","year":"2017","journal-title":"Annals of Operations Research"},{"issue":"1","key":"key2022072111313861400_ref037","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1080\/00207543.2013.836615","article-title":"Joint decisions on inventory replenishment and emission reduction investment under different emission regulations","volume":"52","year":"2014","journal-title":"International Journal of Production Research"},{"key":"key2022072111313861400_ref038","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1016\/j.ijpe.2016.08.029","article-title":"Supply chain coordination with green technology under cap-and-trade regulation","volume":"183","year":"2017","journal-title":"International Journal of Production Economics"},{"key":"key2022072111313861400_ref039","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1016\/j.omega.2015.08.006","article-title":"Production and pricing problems in make-to-order supply chain with cap-and-trade regulation","volume":"66","year":"2017","journal-title":"Omega"},{"key":"key2022072111313861400_ref040","doi-asserted-by":"publisher","DOI":"10.1108\/K-10-2019-0714","article-title":"Government investment strategy and platform pricing decisions with the cross-market network externality","year":"2020","journal-title":"Kybernetes"},{"key":"key2022072111313861400_ref041","doi-asserted-by":"publisher","DOI":"10.1080\/00207543.2021.1897175","article-title":"The selection of marketplace mode and reselling mode with demand disruptions under cap-and-trade regulation","year":"2021","journal-title":"International Journal of Production Research"},{"key":"key2022072111313861400_ref042","doi-asserted-by":"publisher","DOI":"10.1080\/00207543.2021.1894367","article-title":"Coordination of a supply chain with online platform considering green technology in the blockchain era","year":"2021","journal-title":"International Journal of Production Research"},{"issue":"2","key":"key2022072111313861400_ref043","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1016\/j.ejor.2020.04.006","article-title":"Collecting mode selection in a remanufacturing supply chain under cap-and-trade regulation","volume":"287","year":"2020","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"key2022072111313861400_ref044","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.ejor.2015.08.020","article-title":"Managing new and remanufactured products to mitigate environmental damage under emissions regulation","volume":"249","year":"2016","journal-title":"European Journal of Operational Research"},{"key":"key2022072111313861400_ref045","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1016\/j.apnum.2020.07.002","article-title":"Strong-order conditions of Runge-Kutta method for stochastic optimal control problems","volume":"157","year":"2020","journal-title":"Applied Numerical Mathematics"},{"issue":"1","key":"key2022072111313861400_ref046","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.ijpe.2013.01.024","article-title":"Multi-item production planning with carbon cap and trade mechanism","volume":"144","year":"2013","journal-title":"International Journal of Production Economics"},{"issue":"2","key":"key2022072111313861400_ref047","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1080\/0740817X.2015.1011357","article-title":"Dynamic multi-technology production-inventory problem with emissions trading","volume":"48","year":"2016","journal-title":"IIE Transactions"},{"issue":"8","key":"key2022072111313861400_ref048","doi-asserted-by":"crossref","first-page":"1699","DOI":"10.1108\/K-06-2018-0339","article-title":"The joint dynamic green innovation and pricing strategies for a hybrid system of manufacturing and remanufacturing with carbon emission constraints","volume":"48","year":"2019","journal-title":"Kybernetes"}],"container-title":["Kybernetes"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/K-09-2020-0610\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/K-09-2020-0610\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T21:50:11Z","timestamp":1753393811000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/k\/article\/51\/8\/2554-2577\/261897"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,16]]},"references-count":49,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2021,7,16]]},"published-print":{"date-parts":[[2022,7,22]]}},"alternative-id":["10.1108\/K-09-2020-0610"],"URL":"https:\/\/doi.org\/10.1108\/k-09-2020-0610","relation":{},"ISSN":["0368-492X"],"issn-type":[{"value":"0368-492X","type":"print"}],"subject":[],"published":{"date-parts":[[2021,7,16]]}}}