Standard Explicit Solution to Optimal Growth Models
AbstractThis paper shows that the standard optimal growth model can be solved explicitly by using a utility function describing preferences for consumption and savings. Such a maximising criterion including the flow of savings can actually be strongly motivated by two arguments. First, the basic assumption of a representative agent who wishes to consume and save a part of his income each time, can be interpreted as an implicit assumption of some degree of preference for thriftiness. Second, this function formalizes also the concept of Max Weber’s spirit of capitalism (with a direct preference for wealth), which makes the model similar to the one of Heng-Fu Zou (1994) except that his specification includes the capital stock. The resulting model offers an interesting application of the Pontryagin’s Maximum Principle, as well as elegant closed form solutions.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 22610.
Date of creation: Sep 2010
Date of revision:
Ramsey-Cass-Koopmans model; Explicit saddle path; Saving rate; optimal growth model;
Find related papers by JEL classification:
- O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
- D9 - Microeconomics - - Intertemporal Choice
- D91 - Microeconomics - - Intertemporal Choice - - - Intertemporal Household Choice; Life Cycle Models and Saving
- O4 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity
- O40 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General
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- Mehlum Halvor, 2005. "A Closed Form Ramsey Saddle Path," The B.E. Journal of Macroeconomics, De Gruyter, vol. 5(1), pages 1-15, April.
- Zou, Heng-fu, 1994.
"'The spirit of capitalism' and long-run growth,"
European Journal of Political Economy,
Elsevier, vol. 10(2), pages 279-293, July.
- Heng-fu Zou, 1991. "The spirit of capitalism and long-run growth," Policy Research Working Paper Series 630, The World Bank.
- Heng-fu Zou, 1995. "'The spirit of capitalism' and long-run growth," CEMA Working Papers 94, China Economics and Management Academy, Central University of Finance and Economics.
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