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2013, 3(1): 63-76. doi: 10.3934/naco.2013.3.63

Instability and growth due to adjustment costs

Franz Wirl 1, and  Andreas J. Novak 1,

1. 

University of Vienna, Brünnerstr. 72, 1210 Vienna, Austria, Austria

Received  September 2011 Revised  November 2012 Published  January 2013

This paper provides a new and surprising reason for growth, namely costs. More precisely, adding adjustment costs of the control to a one-dimensional, strictly concave optimal control problem does not affect the steady state(s). Then, sufficiently high adjustment costs turn an interior and saddle-point stable steady state of the original, one-state variable model into a source that can lead to unbounded growth. Given a version of the open economy Ramsey model, the initial conditions determine whether unbounded growth or impoverishment results. Related to this threshold property, the strict concave two-state variable control model allows for thresholds even if it has a unique and stable steady state.
Keywords: thresholds, adjustment costs, Growth, strict concave dynamic optimization, optimal control models..
Mathematics Subject Classification: Primary: 91B62, 91B55; Secondary: 49J15, 58E2.
Citation: Franz Wirl, Andreas J. Novak. Instability and growth due to adjustment costs. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 63-76. doi: 10.3934/naco.2013.3.63
References:
[1]

R. J. Barro and X. Sala-i-Martin, "Economic Growth," Mc Graw Hill, 1995. Google Scholar

[2]

J. Benhabib and K. Nishimura, The Hopf bifurcation and the existence and stability of closed orbits in multi-sector models of economic growth, Journal of Economic Theory, 21 (1979), 421-444. doi: 10.1016/0022-0531(79)90050-4.  Google Scholar

[3]

E. Dockner, Local stability analysis in optimal control problems with two state variables, in "Optimal Control Theory and Economic Analysis" (ed. G. Feichtinger), Amsterdam, North Holland, 2 (1985), 89-103.  Google Scholar

[4]

R. A. Easterlin, Income and happiness: towards a unified theory, Economic Journal, 111 (2001), 465-484. doi: 10.1111/1468-0297.00646.  Google Scholar

[5]

G. Feichtinger, A.J. Novak and F. Wirl, Limit cycles in intertemporal adjustment models - theory and applications, Journal of Economic Dynamics and Control, 18 (1994), 353-380. doi: 10.1016/0165-1889(94)90013-2.  Google Scholar

[6]

J. Guckenheimer and P. Holmes, "Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields," (second printing), Springer Verlag, New York, 1986. Google Scholar

[7]

F. X. Hof and F. Wirl, Wealth induced multiple equilibria in small open economy versions of the Ramsey model, Homo Oeconomicus, 25 (2008), 1-22. Google Scholar

[8]

A. Khibnik, I. Yu, A. Kuznetsov, V. V. Levitin and E. V. Nikolaev, "Interactive Local Bifurcation Analyzer, Manual," Amsterdam, CAN, 1992. Google Scholar

[9]

M. Kurz, Optimal economic growth and wealth effects, International Economic Review, 9 (1968), 348-357. doi: 10.2307/2556231.  Google Scholar

[10]

R. E. Lucas Jr., On the mechanics of economic development, Journal of Monetary Economics, 22 (1988), 3-42. doi: 10.1016/0304-3932(88)90168-7.  Google Scholar

[11]

S. Rebelo, Long run policy analysis and long-run growth, Journal of Political Economy, 99 (1991), 500-521. doi: 10.1086/261764.  Google Scholar

[12]

P. Romer, Increasing returns and long-run growth, Journal of Political Economy, 94 (1986), 1002-1037. doi: 10.1086/261420.  Google Scholar

[13]

P. Romer, Endogenous technical change, Journal of Political Economy, 98 (1990), 71-101. doi: 10.1086/261725.  Google Scholar

[14]

F. Wirl and G. Feichtinger, History dependence in concave economies, Journal of Economic Behavior and Organization, 57 (2005), 390-407. doi: 10.1016/j.jebo.2005.04.009.  Google Scholar

[15]

F. Wirl, A. J. Novak and F. X. Hof, Happiness due to consumption and its increases, wealth and status, Studies in Nonlinear Dynamics and Econometrics, 12 (2008). Google Scholar

show all references

References:
[1]

R. J. Barro and X. Sala-i-Martin, "Economic Growth," Mc Graw Hill, 1995. Google Scholar

[2]

J. Benhabib and K. Nishimura, The Hopf bifurcation and the existence and stability of closed orbits in multi-sector models of economic growth, Journal of Economic Theory, 21 (1979), 421-444. doi: 10.1016/0022-0531(79)90050-4.  Google Scholar

[3]

E. Dockner, Local stability analysis in optimal control problems with two state variables, in "Optimal Control Theory and Economic Analysis" (ed. G. Feichtinger), Amsterdam, North Holland, 2 (1985), 89-103.  Google Scholar

[4]

R. A. Easterlin, Income and happiness: towards a unified theory, Economic Journal, 111 (2001), 465-484. doi: 10.1111/1468-0297.00646.  Google Scholar

[5]

G. Feichtinger, A.J. Novak and F. Wirl, Limit cycles in intertemporal adjustment models - theory and applications, Journal of Economic Dynamics and Control, 18 (1994), 353-380. doi: 10.1016/0165-1889(94)90013-2.  Google Scholar

[6]

J. Guckenheimer and P. Holmes, "Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields," (second printing), Springer Verlag, New York, 1986. Google Scholar

[7]

F. X. Hof and F. Wirl, Wealth induced multiple equilibria in small open economy versions of the Ramsey model, Homo Oeconomicus, 25 (2008), 1-22. Google Scholar

[8]

A. Khibnik, I. Yu, A. Kuznetsov, V. V. Levitin and E. V. Nikolaev, "Interactive Local Bifurcation Analyzer, Manual," Amsterdam, CAN, 1992. Google Scholar

[9]

M. Kurz, Optimal economic growth and wealth effects, International Economic Review, 9 (1968), 348-357. doi: 10.2307/2556231.  Google Scholar

[10]

R. E. Lucas Jr., On the mechanics of economic development, Journal of Monetary Economics, 22 (1988), 3-42. doi: 10.1016/0304-3932(88)90168-7.  Google Scholar

[11]

S. Rebelo, Long run policy analysis and long-run growth, Journal of Political Economy, 99 (1991), 500-521. doi: 10.1086/261764.  Google Scholar

[12]

P. Romer, Increasing returns and long-run growth, Journal of Political Economy, 94 (1986), 1002-1037. doi: 10.1086/261420.  Google Scholar

[13]

P. Romer, Endogenous technical change, Journal of Political Economy, 98 (1990), 71-101. doi: 10.1086/261725.  Google Scholar

[14]

F. Wirl and G. Feichtinger, History dependence in concave economies, Journal of Economic Behavior and Organization, 57 (2005), 390-407. doi: 10.1016/j.jebo.2005.04.009.  Google Scholar

[15]

F. Wirl, A. J. Novak and F. X. Hof, Happiness due to consumption and its increases, wealth and status, Studies in Nonlinear Dynamics and Econometrics, 12 (2008). Google Scholar

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