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Transitional Dynamics in the Uzawa-Lucas Model of Endogenous Growth

  • Reiß, Markus
  • Bethmann, Dirk

We introduce an easy way of analyzing the transitional dynamics of the Uzawa-Lucas endogenous growth model. We use the value function approach to solve both the social planner?s optimization problem and the representative agent?s optimization problem in the decentralized economy. The complexity of the Hamilton-Jacobi-Bellman equation is significantly reduced to a one-dimensional initial value problem for an ordinary differential equation. This approach allows us to find the optimal controls for the non-concave Hamiltonian in the centralized economy and to detect multiple transition paths in the decentralized economy for a large external effect, which are hidden when using the maximum principle. We simulate the global transitional dynamics towards the balanced growth path. The adjustment of the model?s state variable turns out to accelerate along the transition paths. By the asymmetry of the sectors an until now unknown feature is predicted for the adjustment in the output growth rate. Its relative speed follows a hump-shaped course: Starting from a relative scarcity in physical capital, the growth rate of output decelerates first before it starts rising again.

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Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 2003,17.

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Date of creation: 2003
Date of revision:
Handle: RePEc:zbw:sfb373:200317
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  1. Rubio, Santiago J. & Casino, Begona, 2001. "Competitive versus efficient extraction of a common property resource: The groundwater case," Journal of Economic Dynamics and Control, Elsevier, vol. 25(8), pages 1117-1137, August.
  2. Mulligan, C.B. & Sala-i-Martin, X., 1992. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," Papers 651, Yale - Economic Growth Center.
  3. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
  4. Robert J. Barro, 2013. "Inflation and Economic Growth," Annals of Economics and Finance, Society for AEF, vol. 14(1), pages 121-144, May.
  5. Danyang Xie, 2002. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," GE, Growth, Math methods 0210002, EconWPA.
  6. Brunner, Martin & Strulik, Holger, 2002. "Solution of perfect foresight saddlepoint problems: a simple method and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 26(5), pages 737-753, May.
  7. P.M. Hartley & L.C.G. Rogers, 2005. "Two-Sector Stochastic Growth Models ," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 322-351, December.
  8. Casey B. Mulligan & Xavier Sala-i-Martin, 1991. "A Note on the Time-Elimination Method For Solving Recursive Dynamic Economic Models," NBER Technical Working Papers 0116, National Bureau of Economic Research, Inc.
  9. repec:cup:cbooks:9780521637329 is not listed on IDEAS
  10. Bond, Eric W. & Wang, Ping & Yip, Chong K., 1996. "A General Two-Sector Model of Endogenous Growth with Human and Physical Capital: Balanced Growth and Transitional Dynamics," Journal of Economic Theory, Elsevier, vol. 68(1), pages 149-173, January.
  11. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
  12. Caballe, Jordi & Santos, Manuel S, 1993. "On Endogenous Growth with Physical and Human Capital," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1042-67, December.
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