# Some Properties of the Solution of the Ramsey Model

### Abstract

The main aim of this paper is to improve some results obtained by Smith. We provide here a closed-form solution for the Ramsey model. We prove that if the inverse of the constant elasticity of intertemporal substitution is different to the elasticity of output with respect to physical capital, then the economy described by this model reaches the unique steady-state equilibrium, for any starting values of per-capita consumption. The advantage of the paper over the existing paper is that the arguments here are not local, that is, our hypotheses are most generally possible. Consequently, we can obtain almost all other results as particular cases of our solution. Our approach clarifies why different starting values of per-capita consumption generates the same steady-state equilibrium, but of different periods of time. We also clarifiy some of previous result obtained by other authors as for example Luca Guerrini.### References

Barro, R. N., Mankiw ,G., & Sala-i-Martin, X. (1995). Capital Mobility in Neoclassical Models of Growth. *American Economic Review, 85,* 103-115.

Cass, D. (1965). Optimum Growth in an Aggregative Model of Capital Accumulation. *The Review of Economic Studies, 32*(3), 233 – 240. doi:10.2307/2295827

Guerrini, L. (2010a). The Ramsey model with a bounded population growth rate. *Journal of Macroeconomics, 32*(3), 872–878. doi:10.1016/j.jmacro.2009.08.004

Guerrini, L. (2010b). The Ramsey model with AK technology and a bounded population growth rate*. Journal of Macroeconomics, 32*(4), 1178–1183. doi:10.1016/j.jmacro.2010.05.001

Guerrini, L. (2010c). A closed-form solution to the Ramsey model with logistic population growth. *Economic Modelling, 27*(5), 1178–1182. doi:10.1016/j.econmod.2010.03.002

Koopmans, T. (1968). *On the Concept of Economic Development. The Economic Approach to Development Planning*. Amsterdam, Elsevier.

Kurz, M. (1968). The General Instability of a Class of Competitive Growth Models. *Review of Economic Studies, 35,* 155 - 174.

Mehlum ,H. (2005). A closed form Ramsey saddle path.* The B.E. Journal of Macroeconomics (Contributions), 5 *(1), Article 2. doi:10.2202/1534-6005.1267

Naz, R., Mahomed, F. M., & Chaudhry, A. (2014). A partial Hamiltonian approach for current value Hamiltonian systems. *Communications in Nonlinear Science and Numerical Simulations, 19*(10), 3600–3610. doi:10.1016/j.cnsns.2014.03.023

Ramsey, F. P., (1928). A mathematical theory of savings. *Economic Journal, 38,* 543 - 559.

*Contributions in Macroeconomics, 6*(1), 1–27. doi:10.2202/1534-6005.1356

*Timisoara Journal of Economics and Business*,

*7*(2), 113–122. Retrieved from http://tjeb.ro/index.php/tjeb/article/view/tjeb-vol7-2014-2-01

(CC BY-NC-ND 3.0) (Since 2014)