摘要: We analyze the dynamics of a simple growth model in which production occurs with delay while new capital is installed (time-to-build). The time-to-build technology shown to yield system functional (delay) differential equations unique steady state. demonstrate that state, though typically saddle, may exhibit Hopf cycles on measurable set parameter space. Furthermore, optimal path state oscillatory. A counter-example claim intrinsically oscillatory central technical apparatus mathematics equations.
参考文章(8)
Jess Benhabib, Kazuo Nishimura, The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth Journal of Economic Theory. ,vol. 21, pp. 421- 444 ,(1979) , 10.1016/0022-0531(79)90050-4
JOSEPH M. MAHAFFY, KATHRYN M. JOINER, PAUL J. ZAK, A GEOMETRIC ANALYSIS OF STABILITY REGIONS FOR A LINEAR DIFFERENTIAL EQUATION WITH TWO DELAYS International Journal of Bifurcation and Chaos. ,vol. 05, pp. 779- 796 ,(1995) , 10.1142/S0218127495000570
Michael C Mackey, Commodity price fluctuations: Price dependent delays and nonlinearities as explanatory factors Journal of Economic Theory. ,vol. 48, pp. 497- 509 ,(1989) , 10.1016/0022-0531(89)90039-2
Nathaniel Chafee, A bifurcation problem for a functional differential equation of finitely retarded type Journal of Mathematical Analysis and Applications. ,vol. 35, pp. 312- 348 ,(1971) , 10.1016/0022-247X(71)90221-6
Finn E. Kydland, Edward C. Prescott, TIME TO BUILD AND AGGREGATE FLUCTUATIONS Econometrica. ,vol. 50, pp. 1345- 1370 ,(1982) , 10.2307/1913386
Ragnar Frisch, Harold Holme, The Characteristic Solutions of a Mixed Difference and Differential Equation Occuring in Economic Dynamics Econometrica. ,vol. 3, pp. 225- ,(1935) , 10.2307/1907258
Aldo Rustichini, Hopf bifurcation for functional differential equations of mixed type Journal of Dynamics and Differential Equations. ,vol. 1, pp. 145- 177 ,(1989) , 10.1007/BF01047829
Yannis M. Ioannides, Bart Taub, On dynamics with time-to-build investment technology and non-time-separable leisure☆ Journal of Economic Dynamics and Control. ,vol. 16, pp. 225- 241 ,(1992) , 10.1016/0165-1889(92)90032-A