{"title":"Optimality of a Linear Decision Rule in Discrete Time AK Model","authors":"Myungkyu Shim","doi":"10.1515/bejte-2021-0061","DOIUrl":null,"url":null,"abstract":"Abstract Surprisingly, formal proof on the optimality of a linear decision rule in the discrete time AK model with a CRRA utility function has not been established in the growth literature while that in the continuous time counterpart is well-established. This note fills such a gap: I provide a formal proof that consumption being linearly related to investment is a sufficient and necessary condition for Pareto optimality in the discrete time AK model.","PeriodicalId":44773,"journal":{"name":"B E Journal of Theoretical Economics","volume":"23 1","pages":"519 - 527"},"PeriodicalIF":0.3000,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"B E Journal of Theoretical Economics","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1515/bejte-2021-0061","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ECONOMICS","Score":null,"Total":0}
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Abstract
Abstract Surprisingly, formal proof on the optimality of a linear decision rule in the discrete time AK model with a CRRA utility function has not been established in the growth literature while that in the continuous time counterpart is well-established. This note fills such a gap: I provide a formal proof that consumption being linearly related to investment is a sufficient and necessary condition for Pareto optimality in the discrete time AK model.
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