Generalized functions in the qualitative study of heterogeneous populations. Issue 3 (3rd July 2019)

• Record Type: Journal Article
• Authors: Hritonenko, Natali; Yatsenko, Yuri; Boranbayev, Askar
• Is Part Of: Mathematical population studies. Volume 26:Issue 3(2019)
• Page Start: 146
• Page End: 162
• Publication Date: 2019-07-03
• Subjects: Optimal control -- age-structured population models -- generalized functions -- age-distributed investment -- capital vintage -- technological change; C61, E22, O11, O32, Q55; Demography -- Mathematical models -- Periodicals; Demography -- Mathematics -- Periodicals; 304.60724
• DOI: 10.1080/08898480.2018.1553395
• Languages: English
• ISSNs: 0889-8480

Abstract

ABSTRACT: Solutions from non-smooth functional spaces, including generalized functions and measures, often appear in optimal control theory but are avoided in applications. They are however useful in finding the optimal distribution of investments into new and old capital equipment under improving technology. The corresponding economic problem involves optimal control in a linear Lotka-McKendrik model of age-structured population. Optimal solutions do not exist in normal functional classes and, so, generalized functions are used to construct the solutions. The optimal age-distributions of capital and investment include the Dirac function and are interpreted as instantaneous investment in equipment of certain age. A numerical simulation completes the presentation of the dynamics.