Instability and growth due to adjustment costs

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

Instability and growth due to adjustment costs

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

Received September 2011 Revised November 2012 Published January 2013

Abstract
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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).
[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. doi: 10.1016/0022-0531(79)90050-4.
[3]	E. Dockner, Local stability analysis in optimal control problems with two state variables,, in, 2 (1985), 89.
[4]	R. A. Easterlin, Income and happiness: towards a unified theory,, Economic Journal, 111 (2001), 465. doi: 10.1111/1468-0297.00646.
[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. doi: 10.1016/0165-1889(94)90013-2.
[6]	J. Guckenheimer and P. Holmes, "Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields,", (second printing), (1986).
[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.
[8]	A. Khibnik, I. Yu, A. Kuznetsov, V. V. Levitin and E. V. Nikolaev, "Interactive Local Bifurcation Analyzer, Manual,", Amsterdam, (1992).
[9]	M. Kurz, Optimal economic growth and wealth effects,, International Economic Review, 9 (1968), 348. doi: 10.2307/2556231.
[10]	R. E. Lucas Jr., On the mechanics of economic development,, Journal of Monetary Economics, 22 (1988), 3. doi: 10.1016/0304-3932(88)90168-7.
[11]	S. Rebelo, Long run policy analysis and long-run growth,, Journal of Political Economy, 99 (1991), 500. doi: 10.1086/261764.
[12]	P. Romer, Increasing returns and long-run growth,, Journal of Political Economy, 94 (1986), 1002. doi: 10.1086/261420.
[13]	P. Romer, Endogenous technical change,, Journal of Political Economy, 98 (1990), 71. doi: 10.1086/261725.
[14]	F. Wirl and G. Feichtinger, History dependence in concave economies,, Journal of Economic Behavior and Organization, 57 (2005), 390. doi: 10.1016/j.jebo.2005.04.009.
[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).

show all references

References:

[1]	R. J. Barro and X. Sala-i-Martin, "Economic Growth,", Mc Graw Hill, (1995).
[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. doi: 10.1016/0022-0531(79)90050-4.
[3]	E. Dockner, Local stability analysis in optimal control problems with two state variables,, in, 2 (1985), 89.
[4]	R. A. Easterlin, Income and happiness: towards a unified theory,, Economic Journal, 111 (2001), 465. doi: 10.1111/1468-0297.00646.
[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. doi: 10.1016/0165-1889(94)90013-2.
[6]	J. Guckenheimer and P. Holmes, "Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields,", (second printing), (1986).
[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.
[8]	A. Khibnik, I. Yu, A. Kuznetsov, V. V. Levitin and E. V. Nikolaev, "Interactive Local Bifurcation Analyzer, Manual,", Amsterdam, (1992).
[9]	M. Kurz, Optimal economic growth and wealth effects,, International Economic Review, 9 (1968), 348. doi: 10.2307/2556231.
[10]	R. E. Lucas Jr., On the mechanics of economic development,, Journal of Monetary Economics, 22 (1988), 3. doi: 10.1016/0304-3932(88)90168-7.
[11]	S. Rebelo, Long run policy analysis and long-run growth,, Journal of Political Economy, 99 (1991), 500. doi: 10.1086/261764.
[12]	P. Romer, Increasing returns and long-run growth,, Journal of Political Economy, 94 (1986), 1002. doi: 10.1086/261420.
[13]	P. Romer, Endogenous technical change,, Journal of Political Economy, 98 (1990), 71. doi: 10.1086/261725.
[14]	F. Wirl and G. Feichtinger, History dependence in concave economies,, Journal of Economic Behavior and Organization, 57 (2005), 390. doi: 10.1016/j.jebo.2005.04.009.
[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).

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