Khelifi, Atef (2010): Explicit Solution to Optimal Growth Models. Published in: International Journal of Economics and Finance , Vol. 2, No. 5 (November 2010): pp. 116-121.
Download (347kB) | Preview
This 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.
|Item Type:||MPRA Paper|
|Original Title:||Explicit Solution to Optimal Growth Models|
|Keywords:||Ramsey-Cass-Koopmans model; Explicit saddle path; Saving rate; optimal growth model|
|Subjects:||O - Economic Development, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O41 - One, Two, and Multisector Growth Models
D - Microeconomics > D9 - Intertemporal Choice and Growth
D - Microeconomics > D9 - Intertemporal Choice and Growth > D91 - Intertemporal Consumer Choice; Life Cycle Models and Saving
O - Economic Development, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity
O - Economic Development, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O40 - General
|Depositing User:||Atef KHELIFI|
|Date Deposited:||25. Oct 2010 00:38|
|Last Modified:||25. Feb 2013 09:15|
- Zou Heng-Fu (1994), “'The Spirit of Capitalism' And Long-Run Growth”, European Journal of Political Economy, 1994 (vol. 10, pp.279-293)
- Max Weber (1905). “The Protestant Ethic and the Spirit of. Capitalism”; Unwin Hyman, London & Boston, 1930
- Cass D., (1965), “Optimal Growth in an Aggregate Model of Accumulation of Capital”, Review off Economic Studies 32, 233-240.
- Koopmans T. (1965), “On the Concept of Optimal Growth”, The Econometric Approach to Development Planning, Chap 4, p225. North Holland Publishing Co.
- Ramsey F. (1928), “A Mathematical Theory of the Saving”, Economic Newspaper 38 (152), 543-559
- Solow R. (1956), “A Contribution to the Economic Theory of Growth”, Quaterly Newspaper off Economics 70, 65-94.
- Dorfman R. (1969), “An Economic Interpretation of Optimal Control Theory”, The American Economic Review, Vol.59, n°5, pp 817-831
- Phelps E. (1961), "The Golden Rule of Capital Accumulation", The American Economic Review, vol. 51, pp 638-643
-Shell K. (1969), “Applications of Pontryagin's Maximum Principle to Economics” in Mathematical Systems Theory and Economics, I (H.W. Kuhn and G.P. Szegö, eds.), Berlin: Springer Verlag, 1969, 241-292.
- Pontryagin LS. (1962) “Ordinary Differential Equations”, Reading Mass.: Addison-Wesley
- Pontryagin LS. (1962) “The Mathematical Theory of Optimal Processes”, New York and London : Interscience Publishers
- J.Benhabib & A.Rustichini (1994), “A Note on a NewClass of Solutions to Dynamic Programing Problems Arising in Economic Growth”, Journal of Economic Dynamics and Control, 18, 808-813
- H.Mehlum (2005), “A Closed Form Ramsey Saddle Path”, Contributions to Macroeconomics, Vol.5-1, Article 2
- RJ.Barro & Sala-i-Martin (2004), “Economic Growth”, 2d Edition, MIT Press
Available Versions of this Item
Standard Explicit Solution to Optimal Growth Models. (deposited 13. May 2010 05:50)
- Explicit Solution to Optimal Growth Models. (deposited 25. Oct 2010 00:38) [Currently Displayed]