Numerical Analysis of a Monetary Overlapping Generation Model

  • Jenni X. Li
Part of the Advances in Computational Economics book series (AICE, volume 6)


In this paper, mathematical and numerical analysis are applied to a nonlinear operator equation arising from monetary economic modeling. For the nonlinear operator equation the contraction property is established, and fixed point iterations are employed to numerically solve the equation based on finite element discretization. Convergence rate and error estimates are given for the numerical schemes. In this investigation, several numerical algorithms are proposed and analyzed. These algorithms have been realized as computer programs which make extensive use of several modern computer software packages such as Matlab (for numerical computations and graphics) and Mathematica (for symbolic computations).


Equilibrium Price Money Supply Piecewise Linear Function Price Function Contraction Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Baumol, W., 1952, ‘The transactions demand for cash: An inventory theoretic approach’, Quarterly Journal of Economics 90, 545–556.CrossRefGoogle Scholar
  2. Bona, J. and S. Grossman, 1983, ‘Price and interest rate dynamics in a transaction-based model for money’, Preprint, University of Chicago, Department of Economics.Google Scholar
  3. Grossman, S. and L. Weiss, 1982, ‘A transactions-based model of the monetary transmission mechanism’, National Bureau of Economic Research Working Paper No. 973–974.Google Scholar
  4. Bewley, T., 1980, ‘The optimum quantity of money’, in John H. Kareken and Neil Wallace (Eds), Models of Monetary Economies, Federal Reserve Bank of Minneapolis, pp. 169–210.Google Scholar
  5. Bryant, J. and N. Wallace, 1979, ‘The efficiency of interest-bearing national debt’, Journal of Political Economy 87, 365–382.CrossRefGoogle Scholar
  6. Robert, C.W., 1967, ‘A reconsideration of the microfoundations of monetary policy’, Western Economic Journal 6, 1–8.Google Scholar
  7. Christiano, L.J., 1991, ‘Modeling the liquidity effect of a money shock’, Federal Reserve Bank of Minneapolis Quarterly Review 15, 3–34.Google Scholar
  8. Cochrane, J.H., 1989, ‘The return of the liquidity effect: A study of the short-run relation between money growth and interest rates’, Journal of Business and Economics Statistics 7, 75–111.Google Scholar
  9. Grandmont, J. and Y. Younes, ‘On the role of money and the existence of a monetary equilibrium’, Review of Economic Studies 39, 355–372.Google Scholar
  10. Grossman, S., 1982, ‘A transactions based model of the monetary transmission mechanism: Part II’, Working paper No. 974, National Bureau of Economic Research, Cambridge.Google Scholar
  11. Grossman, S., 1985, ‘Monetary dynamics with proportional transaction costs and fixed payment periods’, Working paper No. 1663, National Bureau of Economic Research, Cambridge.Google Scholar
  12. Hahn, F.H., 1965, ‘On some problems of proving existence of an equilibrium in a monetary economy’, in F.H. Hahn and F.R.P. Brechling (Eds), The Theory of Interest Rates, London: Macmillan, pp. 126–135.Google Scholar
  13. Hartley, P., 1980, ‘Distributional effects and the neutrality of money’, unpublished doctoral dissertation, University of Chicago.Google Scholar
  14. Jovanovic, B., 1982, ‘Inflation and welfare in the steady state’, Journal of Political Economy 90, 561–577.CrossRefGoogle Scholar
  15. Li, Jenny X., 1993, ‘Essays in mathematical economics and economic theory’, Ph.D. Dissertation, Department of Mathematics, Cornell.Google Scholar
  16. Lucas, R., 1980, ‘Equilibrium in a pure currency economy’, Economic Inquiry 28, 203–220.CrossRefGoogle Scholar
  17. Lucas, R. and N.L. Stokey, 1985, ‘Money and interest in a cash-in-advance economy’, Working paper No. 1618, National Bureau of Economic Research, Cambridge.Google Scholar
  18. McCallum, B.T., 1982, ‘The role of overlapping-generations models in monetary economics’, Working paper No. 989, National Bureau of Economic Rearch, Cambridge.Google Scholar
  19. Rotemberg, J., 1982, ‘A monetary equilibrium model with transactions costs’, mimeo.Google Scholar
  20. Sargent, T. and N. Wallace, 1982, ‘The real bills doctrine vs. The quantity theory: A reconsideration’, Journal of Political Economy 90, 1212–1237.CrossRefGoogle Scholar
  21. Shell, K. and J. Stiglitz, 1967, ‘The allocation of investment in a dynamic economy’, The Quarterly Journal of Economics 81, 592–609.CrossRefGoogle Scholar
  22. Shell, K., M. Sidrauski, and J.E. Stiglitz, 1968, ‘Capital gain, income, and saving’, The Review of Economic Studies 36(1), No. 105, 15–26.CrossRefGoogle Scholar
  23. Sidrauski, M., 1967, ‘Inflation and economic growth’, Journal of Political Economy 75, 798–810.CrossRefGoogle Scholar
  24. Tobin, J., 1956, ‘The interest-elasticity of the transactions demand for cash’, Review of Economics and Statistics 38, 241–247.CrossRefGoogle Scholar
  25. Townsend, R.M., 1980, ‘Models of money with spatially separated agents’, in John H. Kareken and Neil Wallace (Eds), Models of Monetary Economies, Federal Reserve Bank of Minneapolis, pp. 265–303.Google Scholar
  26. Townsend, R.M., 1982, Asset return anomalies: A choice-theoretic, monetary explanation’, unpublished manuscript.Google Scholar
  27. Hirsch, M.W. and C.C. Pugh, 1968, ‘Stable manifold and hyperbolic sets’, in Global Analysis (Proc. Symp. Pure Math., Vol. XIV), Berkeley, pp. 133–163.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Jenni X. Li

There are no affiliations available

Personalised recommendations