?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F14028%2F&rft.title=Optimal+Growth%2C+Renewable+Resources+and+Sustainability&rft.creator=Aseev%2C+S.&rft.creator=Manzoor%2C+T.&rft.description=We+study+a+growth+model+for+a+single+resource-based+economy%2C+as+an+in%EF%AC%81nite-horizon+op-timal+control+problem.+The+resource+is+assumed+to+be+governed+by+the+standard+model+of+logistic+growth%2C+and+is+related+to+the+output+of+the+economy+through+a+Cobb-Douglass+type+production+function+with+an+exogenously+driven+knowledge+stock.+The+problem+involves+unbounded+controls+and+the+non-concave+Hamiltonian.+These+preclude+direct+application+of+the+standard+existence+results+and+Arrow%E2%80%99s+su%EF%AC%83cient+conditions+for+optimality.+We+transform+the+original+optimal+control+problem+to+an+equivalent+one+with+simpli%EF%AC%81ed+dy-namics+and+prove+the+existence+of+an+optimal+admissible+control.+Then+we+characterize+the+optimal+paths+for+all+possible+parameter+values+and+initial+states+by+applying+the+ap-propriate+version+of+the+Pontryagin+maximum+principle.+Our+main+%EF%AC%81nding+is+that+only+two+qualitatively+di%EF%AC%80erent+types+of+behavior+of+sustainable+optimal+paths+are+possible+de-pending+on+whether+the+resource+growth+rate+is+higher+than+the+social+discount+rate+or+not.&rft.publisher=WP-16-017&rft.date=2016-11-16&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.rights=cc_by&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F14028%2F1%2FWP-16-017.pdf&rft.identifier=++Aseev%2C+S.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F19.html%3E+%26+Manzoor%2C+T.++(2016).++Optimal+Growth%2C+Renewable+Resources+and+Sustainability.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-16-017+++++