Document Type : Research Article


1 Department of Mathematics and Computer Sciences, Damghan University, Damghan, Iran

2 The University of Zurich and Swiss Finance Institute

3 Department of mathematics and computer sciences, Damghan University, Damghan, Iran


In this paper, we address the problem of analyzing and computing all steady states of an overlapping generation (OLG) model with production and many generations. The characterization of steady states coincides with a geometrical representation of the algebraic variety of a polynomial ideal, and, in principle, one can apply computational algebraic geometry methods to solve the problem. However, it is infeasible for standard methods to solve problems with a large number of variables and parameters. Instead, we use the specific structure of the economic problem to develop a new algorithm that does not employ the usual steps for the computation of Grobner basis such as the computation of successive S-polynomial and expensive division.


[1] David Altig, Alan J Auerbach, Laurence J Kotlikoff, Kent A Smetters, and Jan Walliser, Simulating Fundamental Tax Reform in the United States, American Economic Review (2001),
[2] Alan J Auerbach and Laurence J Kotlikoff, National Savings, Economic Welfare, and the
Structure of Taxation, Behavioral Simulation Methods in Tax Policy Analysis, University of
Chicago Press, 1983, pp. 459–498.
[3] , Dynamic fiscal policy, vol. 11, Cambridge University Press Cambridge, 1987.
[4] Eberhard Becker, Teo Mora, Maria Grazia Marinari, and Carlo Traverso, The shape of
the shape lemma, Proceedings of the international symposium on Symbolic and algebraic
computation, 1994, pp. 129–133.
[5] Thomas Becker and Volker Weispfenning, Gr¨obner bases, volume 141 of graduate texts in
mathematics, 1993.
[6] A.Lans Bovenberg and Ben J Heijdra, Environmental tax policy and intergenerational distribution, Journal of Public Economics 67 (1998), no. 1, 1–24.
[7] Egbert Dierker, Two remarks on the number of equilibria of an economy, Econometrica:
Journal of the Econometric Society (1972), 951–953.
[8] Jean Charles Faug`ere, A new efficient algorithm for computing gr¨obner bases without reduction to zero (f 5), Proceedings of the 2002 international symposium on Symbolic and
algebraic computation, 2002, pp. 75–83.
[9] Stephie Fried, Kevin Novan, and William B Peterman, The distributional effects of a carbon
tax on current and future generations, Review of Economic Dynamics 30 (2018), 30–46.
[10] Shuhong Gao, Yinhua Guan, and Frank Volny IV, A new incremental algorithm for computing gr¨obner bases, Proceedings of the 2010 International Symposium on Symbolic and
Algebraic Computation, 2010, pp. 13–19.
[11] Timothy J Kehoe and David K Levine, Comparative statics and perfect foresight in infinite
horizon economies, Econometrica: Journal of the Econometric Society (1985), 433–453.
[12] Timothy J Kehoe and David K Levine, The economics of indeterminacy in overlapping
generations models, Journal of Public Economics 42 (1990), no. 2, 219–243.
[13] Timothy J Kehoe, David K Levine, Andreu Mas-Colell, and Michael Woodford, Gross substitutability in large-square economies, Journal of Economic Theory 54 (1991), no. 1, 1–25.
[14] Laurence J Kotlikoff, Felix Kubler, Andrey Polbin, Jeffrey D Sachs, and Simon Scheidegger,
Making carbon taxation a generational win win, Tech. report, National Bureau of Economic
Research, 2019.
[15] Laurence J Kotlikoff, Kent Smetters, and Jan Walliser, Mitigating america’s demographic
dilemma by pre-funding social security, Journal of monetary Economics 54 (2007), no. 2,
[16] Felix Kubler, Philipp Renner, and Karl Schmedders, Computing all solutions to polynomial equations in economics, Handbook of Computational Economics, vol. 3, Elsevier, 2014,
pp. 599–652.
[17] Felix Kubler and Karl Schmedders, Tackling multiplicity of equilibria with grobner bases,
Operations research 58 (2010), no. 4-part-2, 1037–1050.
[18] Felix Kubler and Karl Schmedders, Uniqueness of steady states in models with overlapping
generations, Journal of the European Economic Association 8 (2010), no. 2-3, 635–644.
[19] Lawrence H Summers, Capital Taxation and Accumulation in a Life Cycle Growth Model,
The American Economic Review 71 (1981), no. 4, 533–544.