Journal of Optimization Theory and Applications

, Volume 108, Issue 1, pp 175-203

First online:

Optimal Dynamics of Innovation in Models of Economic Growth

  • A. M. TarasyevAffiliated withInternational Institute for Applied Systems AnalysisInstitute of Mathematics and Mechanics
  • , C. WatanabeAffiliated withTokyo Institute of Technology

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A nonlinear model of economic growth which involves production, technology stock, and their rates as the main variables is considered. Two trends (growth and decline) in the interaction between the production and R&D investment are examined in the balanced dynamics. The optimal control problem of R&D investment is studied for the balanced dynamics and the utility function with the discounted consumption. The Pontryagin optimality principle is applied for designing the optimal nonlinear dynamics. An existence and uniqueness result is proved for an equilibrium of the saddle type and the convergence property of the optimal trajectories is shown. Quasioptimal feedbacks of the rational type for balancing the dynamical system are proposed. The growth properties of the production rate, R&D, and technology intensities are examined on the generated trajectories.

dynamic optimality principle economic growth control synthesis equilibrium of the saddle type asymptotic econometric characteristics