Datta, Soumya (2013): Convergence, cycles and complex dynamics of financing investment.

PDF
MPRA_paper_52111.pdf Download (242kB)  Preview 
Abstract
This paper demonstrates the diverse dynamical possibilities of a simple macroeconomic model of debtfinanced investmentled growth in the presence of interest rate rules. We show possibilities of convergence to steady state, growth cycles around it as well as various complex dynamics from codim 1 and codim 2 bifurcations. The effectiveness of monetary policy in the form of interest rate rules is examined under this context.
Item Type:  MPRA Paper 

Original Title:  Convergence, cycles and complex dynamics of financing investment 
English Title:  Convergence, cycles and complex dynamics of financing investment 
Language:  English 
Keywords:  Growth cycles, Hopf bifurcation, complex dynamics, Taylor rule 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62  Existence and Stability Conditions of Equilibrium C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C69  Other E  Macroeconomics and Monetary Economics > E1  General Aggregative Models > E12  Keynes ; Keynesian ; PostKeynesian E  Macroeconomics and Monetary Economics > E3  Prices, Business Fluctuations, and Cycles > E32  Business Fluctuations ; Cycles 
Item ID:  52111 
Depositing User:  Dr. Soumya Datta 
Date Deposited:  10 Dec 2013 21:30 
Last Modified:  28 Sep 2019 05:29 
References:  Abrahams, C. & Zhang, M. (2009), Credit Risk Assessment: the New Lending System for Borrowers, Lenders and Investors, John Wiley and Sons, Inc., Hoboken, New Jersey. Akerlof, G. A. & Shiller, R. J. (2010), Animal Spirits: How Human Psychology Drives the Economy, and Why It Matters for Global Capitalism, Princeton University Press, Princeton, New Jersey. Asada, T. (1995), ‘Kaldorian dynamics in an open economy’, Journal of Economics 2, 1–16. Asada, T. & Semmler, W. (1995), ‘Growth and finance: An intertemporal model’, Journal of Macroeconomics 17, 623–649. Butler, G. & Waltman, P. (1981), ‘Bifurcation from a limit cycle in a two predatorone prey ecosystem modeled on a chemostat’, Journal of Mathematical Biology 12(3). Catt, A. (1965), ‘“Credit Rationing” and Keynesian Model’, The Economic Journal 75(298), 358–372. Cushing, J. (1984), ‘Periodic Twopredator, Oneprey Interactions and the Timesharing of a Resource Niche’, SIAM Journal of Applied Mathematics 44(2), 392–410. Datta, S. (2011), Investmentled Growth Cycles: A Preliminary Reappraisal of Taylortype Monetary Policy Rules, in K. G. Dastidar, H. Mukhopadhyay & U. B. Sinha, eds, ‘Dimensions of Economic Theory and Policy: Essays for Anjan Mukherji’, Oxford University Press, New Delhi. Datta, S. (2012), Cycles and crises in a model of debtfinanced investmentled growth, working paper. *http://mpra.ub.unimuenchen.de/50200/ Dumenil, G. & Levy, D. (1999), ‘Being Keynesian in the Short Term and Classical in the Long Term: The Traverse to Classical LongTerm Equilibrium’, Manchester School 67(6), 684–716. Edneral, V. F. (2007), An Algorithm for Construction of Normal Forms, in V. G. Ganzha, E. W. Mayr & E. V. Vorozhtsov, eds, ‘CASC’, Vol. 4770 of Lecture Notes in Computer Science, Springer, pp. 134–142. Feng, W. & Hinson, J. (2005), ‘Stability and pattern in twopatch predatorprey population dynamics’, Discrete and Continuous Dynamical Systems Supplement Volume, 268–279. Fisher, I. (1932), Booms and Depressions: Some First Principles, Adelphi. Fisher, I. (1933), ‘The DebtDeflation Theory of Great Depressions’, Econometrica 1, 337–357. Flaschel, P. (2009), The Macrodynamics of Capitalism: Elements for a Synthesis of Marx, Keynes and Schumpeter, second revised and enlarged edn, Springer Verlag, Berlin Heidelberg. Gardini, L., Lupini, R. & Messia, M. (1989), ‘Hopf Bifurcation and Transition to Chaos in LotkaVolterra Equation’, Journal of Mathematical Biology 27(3), 259–272. Guckenheimer, J. & Kuznetsov, Y. A. (2007a), ‘Bautin bifurcation’, Scholarpedia 2(5), 1853. *http://www.scholarpedia.org/article/Bautin bifurcation Guckenheimer, J. & Kuznetsov, Y. A. (2007b), ‘BogdanovTakens bifurcation’, Scholarpedia 2(1), 1854. *http://www.scholarpedia.org/article/BogdanovTakens bifurcation Guckenheimer, J. & Kuznetsov, Y. A. (2007c), ‘FoldHopf bifurcation’, Scholarpedia 2(10), 1855. *http://www.scholarpedia.org/article/FoldHopf bifurcation Harrod, R. (1939), ‘An Essay in Dynamic Theory’, Economic Journal 49, 14–33. Hodgman, D. R. (1960), ‘Credit risk and credit rationing’, The Quarterly Journal of Economics 74(2), 258–278. Hofbauer, J. & So, J.H. (1994), ‘Multiple Limit Cycles for Three Dimensional LotkaVolterra Equations’, Applied Mathematical Letters 7(6), 65–70. Hsu, S.B., Hwang, T.W. & Kuang, Y. (2001), ‘Rich dynamics of a ratiodependent oneprey twopredators model’, Journal of Mathematical Biology 43(5), 377–396. Jaffee, D. & Stiglitz, J. E. (1990), Credit Rationing, in B. Friedman & F. Hahn, eds, ‘Handbook of Monetary Economics’, Vol. II, Elsevier Science Publishers B.V., chapter 16. Kalapodas, E. & Thomson, M. E. (2006), ‘Credit risk assessment: a challenge for financial institutions’, IMA Journal of Management Mathematics 17(1), 25–46. Kalecki, M. (1937), ‘The Principle of Increasing Risk’, Economica pp. 440–447. Koch, A. L. (1974), ‘Competitive coexistence of two predators utilizing the same prey under constant environmental conditions’, Journal of Theoretical Biology 44(2), 387–395. Korobeinikov, A. & Wake, G. (1999), ‘Global Properties of the Threedimensional Predatorprey LotkaVolterra Systems’, Journal of Applied Mathematics and Decision Sciences 3(2), 155–162. Kregel, J. (2008), Minsky’s Cushions of Safety Systemic Risk and the Crisis in the U.S. Subprime Mortgage Market, Economics public policy brief archive, The Levy Economics Institute. Kuznetsov, Y. A. (1997), Elements of Applied Bifurcation Theory, Vol. 112 of Applied Mathematical Sciences, second edn, SpringerVerlag, New York. Kuznetsov, Y. A. (2006), ‘Saddlenode bifurcation’, Scholarpedia 1(10), 1859. *http://www.scholarpedia.org/article/Saddlenode bifurcation LeonLedesma, M. & Thirlwall, A. (2000), ‘Is the natural rate of growth exogenous?’, Banca Nazionale del Lavoro Quarterly Review 53(215), 433–445. LeonLedesma, M. & Thirlwall, A. (2002), ‘The endogeneity of the natural rate of growth’, Cambridge Journal of Economics 26, 441–459. LeonLedesma, M. & Thirlwall, A. (2007), Is the natural rate of growth exogenous?, in P. Arestis, M. Baddeley & J. McCombie, eds, ‘Economic Growth: New Directions in Theory and Policy’, Edward Elgar Publishing Limited, Cheltenham, UK. Loladze, I., Kuang, Y., Elser, J. J. & Fagan, W. F. (2004), ‘Competition and stoichemetry: coexistence of two predators on one prey’, Theoretical Population Biology 65(1), 1–15. Minsky, H. P. (1975), John Maynard Keynes, Columbia University Press, New York. Minsky, H. P. (1982), Inflation, Recession and Economic Policy, M.E. Sharpe Inc., New York. Minsky, H. P. (1986), Stabilizing the Unstable Economy, Yale University Press, New Haven. Minsky, H. P. (1994), Financial Instability Hypothesis, in P. Arestis & M. Sawyer, eds, ‘Elgar Companion to Radical Political Economy’, Edward Elgar Publishing Limited, Vermont, USA, pp. 153–158. Reinhart, C. M. & Rogoff, K. S. (2009), This Time is Different: Eight Centuries of Financial Folly, Princeton University Press, Princeton, New Jersey. Shiller, R. J. (2008), The Subprime Solution: How Today’s Global Financial Crisis Happened, and What To Do About It, Princeton University Press, Princeton, New Jersey. Smith, H. L. (1982), ‘The interaction of steady state and Hopf bifurcations in a twopredatoroneprey competition model’, SIAM Journal on Applied Mathematics 42(1), 27–43. Stiglitz, J. E. & Weiss, A. (1981), ‘Credit Rationing in Markets with Imperfect Information’, American Economic Review 71(3), 393–410. Stiglitz, J. E. & Weiss, A. (1983), ‘Incentive effects of terminations: Applications to the credit and labor markets’, American Economic Review 73, 912–927. Stiglitz, J. E. & Weiss, A. (1992), ‘Asymmetric Information in Credit Markets and its implications for Macroeconomics’, Oxford Economic Papers 44(4), 694–724. Zeeman, E. & Zeeman, M. (2002), ‘From Local to Global Behavior in Competitive LotkaVolterra Systems’, Transactions of the American Mathematical Society 355(2), 713–734. Zeeman, M. (1993), ‘Hopf Bifurcations in competitive threedimensional LotkaVolterra sys tems’, Dynamics and Stability of Systems 8(3), 189–216. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/52111 