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Optimal Control of Investments in Old and New Capital Under Improving Technology

Natali Hritonenko (), Nobuyuki Kato () and Yuri Yatsenko ()
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Natali Hritonenko: Prairie View A&M University
Nobuyuki Kato: Kanazawa University

Journal of Optimization Theory and Applications, 2017, vol. 172, issue 1, No 15, 247-266

Abstract: Abstract An optimal control problem for nonlinear integral equations of special kind is analyzed. It considers a firm’s investment into age-dependent capital under improving technology and limited substitutability among capital of different ages. We prove the existence of solutions and analyze their structure. It is shown that the initially bang-bang optimal investment switches to an interior one and eventually converges to a steady-state trajectory that represents balanced economic growth. The obtained analytic outcomes contribute to better understanding of investment policies under technological change.

Keywords: Nonlinear optimal control; Existence theorem; Technological change; Constant elasticity of substitution; Bang-bang solution; Balanced growth; 91B62; 49J22; 49K22; 45M05; 37N40 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10957-016-1022-y

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