Optimal investment with vintage capital: Equilibrium distributions

Silvia Faggian, Fausto Gozzi and Peter Kort

Journal of Mathematical Economics, 2021, vol. 96, issue C

Abstract: The paper concerns the study of equilibrium points, or steady states, of economic systems arising in modeling optimal investment with vintage capital, namely, systems where all key variables (capitals, investments, prices) are indexed not only by time but also by age. Capital accumulation is hence described as a partial differential equation (briefly, PDE), and equilibrium points are in fact equilibrium distributions in the variable of ages. A general method is developed to compute and study equilibrium points of a wide range of infinite dimensional, infinite horizon, optimal control problems. We apply the method to optimal investment with vintage capital, for a variety of data, deriving existence and uniqueness of equilibrium distribution, as well as analytic formulas for optimal controls and trajectories in the long run. The examples suggest that the same method can be applied to other economic problems displaying heterogeneity. This shows how effective the theoretical machinery of optimal control in infinite dimension is in computing explicitly equilibrium distributions. To this extent, the results of this work constitute a first crucial step towards a thorough understanding of the behavior of optimal paths in the long run.

Keywords: Equilibrium points; Optimal investment; Vintage capital; Age-structured systems; Optimal control in infinite dimension; Maximum Principle (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Working Paper: Optimal investment with vintage capital: equilibrium distributions (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:96:y:2021:i:c:s0304406821000793

DOI: 10.1016/j.jmateco.2021.102516

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