Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 71, 2022 - Issue 14
135
Views
2
CrossRef citations to date
0
Altmetric
Research Article

Solution existence theorems for finite horizon optimal economic growth problems

Pages 4243-4263 | Received 03 Sep 2020, Accepted 26 May 2021, Published online: 16 Jun 2021

References

  • Ramsey FP. A mathematical theory of saving. Econ J. 1928;38:543–559.
  • Harrod RF. An essay in dynamic theory. Econ J. 1939;49:14–33.
  • Domar ED. Capital expansion, rate of growth, and employment. Econometrica. 1946;14:137–147.
  • Solow RM. A contribution to the theory of economic growth. Q J Econ. 1956;70:65–94.
  • Swan TW. Economic growth and capital accumulation. Econ Record. 1956;32:334–361.
  • Cass D. Optimum growth in an aggregative model of capital accumulation. Rev Econ Stud. 1965;32:233–240.
  • Koopmans TC. On the concept of optimal economic growth. In: Johansen J, editor. The econometric approach to development planning. Amsterdam: North-Holland; 1965. p. 225–295.
  • Romer PM. Increasing returns and long-run growth. J Political Econ. 1986;94:1002–1037.
  • Lucas Jr. RE. On the mechanics of economic development. J Monet Econ. 1988;22:3–42.
  • Spear S, Young W. Optimum savings and optimal growth: the cass-malinvaud-koopmans nexus. Macroecon Dyn. 2014;18:215–243.
  • Spear S, Young W. Two-sector growth, optimal growth, and the turnpike: amalgamation and metamorphosis. Macroecon Dyn. 2015;19:394–424.
  • Spear S, Young W. Generalizations of optimal growth theory: stochastic models, mathematics, and meta-synthesis. Macroecon Dyn. 2017;21:515–544.
  • Spear S, Young W. Macroeconomic dynamics survey: endogenous growth theory and models: the ‘first wave’, 1952–1973. Macroecon Dyn. 2018;22:1695–1720.
  • Barro RJ, Sala-i-Martin X. Economic growth. Cambridge: MIT Press; 2004.
  • Acemoglu D. Introduction to modern economic growth. Princeton: Princeton University Press; 2009.
  • Intriligator MD. Mathematical optimization and economic theory. Englewood Cliffs (NJ): Prentice-Hall Inc.; 1971.
  • Takayama A. Mathematical economics. Hinsdale (IL): The Dryden Press; 1974.
  • Pierre NVT. Introductory optimization dynamics: optimal control with economics and management science applications. Berlin: Springer-Verlag; 1984.
  • Chiang AC, Wainwright K. Fundamental methods of mathematical economics. New York: McGraw-Hill; 2005.
  • Craven BD, Islam SMN. Optimization in economics and finance: some advances in non-linear, dynamic, multi-criteria and stochastic models. Dordrecht: Springer; 2005.
  • d'Albis H, Gourdel P, Le Van C. Existence of solutions in continuous-time optimal growth models. Econ Theory. 2008;37:321–333.
  • Nikolskii MS. Study of an optimal control problem related to the solow control model. Proc Steklov Inst Math. 2016;292:S231–S237.
  • Chakravarty S. Optimal savings with finite planning horizon. Int Econ Rev. 1962;3:338–355.
  • Cesari L. Optimization theory and applications. New York: Springer-Verlag; 1983.
  • Ioffe AD, Tihomirov VM. Theory of extremal problems. Amsterdam: North-Holland Publishing Company; 1979.
  • Kolmogorov AN, Fomin SV. Introductory real analysis. New York: Dovers Publications Inc.; 1970.
  • Lee EB, Markus L. Foundations of optimal control theory. Melbourne: Robert E. Krieger Publishing Co. Inc.; 1986.
  • Balder EJ. An existence result for optimal economic growth problems. J Math Anal Appl. 1983;95:195–213.
  • Rockafellar RT. Convex analysis. Princeton (NJ): Princeton University Press; 1970.
  • Vinter R. Optimal control. Boston (MA): Birkhäuser; 2000.
  • Kinderlehrer D, Stampacchia G. An introduction to variational inequalities and their applications. New York: Academic Press; 1980.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.