Theoretical Analysis on Intergenerational Equity and Optimal Economic Growth without Discount Factors

• Project/Area Number: 18K01518
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 07010:Economic theory-related
• Research Institution: Hosei University
• Principal Investigator: Sagara Nobusumi 法政大学, 経済学部, 教授 (90286005)
• Project Period (FY): 2018-04-01 – 2022-03-31
• Project Status: Completed (Fiscal Year 2021)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2021: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 再帰的効用関数 / 無限期間問題 / 最適経路 / 評価関数の微分可能性 / 非凸性 / 最適経済成長 / 再帰的効用 / 非凸生産技術 / 世代間衡平性 / 割引因子 / パレート効率性 / 貧困と富裕の階層分離

Outline of Final Research Achievements

A study on optimal growth models without discount factors involves axiomatic analysis on intergenerational equity, general equilibrium theory, optimal control theory, and nonlinear economic dynamics. Since the fields mentioned above is interrelated belong to an inter-disciplinary area, this study requires an extension of conventional theory with an original viewpoint that is beyond the simple combination of them. This difficulty reveals the fact that there remains many unsolved important problems in this study.

With this backgound in mind, I have published seven papers in a refereed journal.

Academic Significance and Societal Importance of the Research Achievements

本研究の最終目標は、新古典派の標準的仮定から離れ、非凸環境下の最適経路を分析することで【貧困と富裕の階層分離】を時間選好率以外の要因で説明することである。経済活動の水準に依存して経済主体の消費リスクへの態度が異なったり、生産技術の構造が変化する状況を考察することにより、経済主体の最適化行動の結果、複数の定常状態が出現する。また、【世代間衡平性】を考慮することは、経済動学に現れる時間選好率の影響を完全に取り除くことでもある。本研究の研究成果を通じて、完全競争下では、初期資産格差が【貧困と富裕の階層分離】の最も重要な要因であることを解明することができる。

Research Products

• [Int'l Joint Research] ウェイン州立大学(米国)
• [Int'l Joint Research] Wayne State University/Johns Hopkins University(米国)
• [Journal Article] Fuzzy Core Equivalence in Large Economies: A Role for the Infinite-Dimensional Lyapunov Theorem (2022)
  • Author(s): M. Ali Khan and Nobusumi Sagara
  • Journal Title: Communications in Economics and Mathematical Scieneces Volume: 1 Issue: 0 Pages: 1-8
  • DOI: 10.50906/cems.1.0_1
  • ISSN: 2436-3162
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Value Functions and Optimality Conditions for Nonconvex Variational Problems with an Infinite Horizon in Banach Spaces (2022)
  • Author(s): Helene Frankowska and Nobusumi Sagara
  • Journal Title: Mathematics of Operations Research Volume: 47 Issue: 1 Pages: 320-340
  • DOI: 10.1287/moor.2021.1130
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Optimality conditions for nonconvex variational problems with integral constraints in Banach spaces (2020)
  • Author(s): Nobusumi Sagara
  • Journal Title: Journal of Convex Analysis Volume: 27/2 Pages: 567-583
  • Peer Reviewed
• [Journal Article] Decomposability, convexity and continuous linear operators in L^1(\mu,E): The case for saturated measure spaces (2019)
  • Author(s): Nobusumi Sagara
  • Journal Title: Linear and Nonlinear Analysis Volume: 5 Pages: 113-119
  • Peer Reviewed
• [Journal Article] Subdifferentials of value functions in nonconvex dynamic programming for nonstationary stochastic processes (2019)
  • Author(s): Boris S. Mordukhovich and Nobusumi Sagara
  • Journal Title: Communications on Stochastic Analysis Volume: 13 Issue: 3 Pages: 1-19
  • DOI: 10.31390/cosa.13.3.05
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Recursive variational problems in nonreflexive Banach spaces with an infinite horizon: An existence result (2018)
  • Author(s): Nobusumi Sagara
  • Journal Title: Discrete and Continuous Dynamical Systems - Series S Volume: 11 Issue: 6 Pages: 1219-1232
  • DOI: 10.3934/dcdss.2018069
  • Peer Reviewed
• [Presentation] Optimality conditions for nonconvex variational problems with integral constraints in Banach spaces (2019)
  • Author(s): Nobusumi Sagara
  • Organizer: 30th European Conference on Operational Research
  • Int'l Joint Research
• [Presentation] Optimality conditions for nonconvex variational problems with integral constraints in Banach spaces (2019)
  • Author(s): Nobusumi Sagara
  • Organizer: International Congress on Industrial and Applied Mathematics
  • Int'l Joint Research
• [Presentation] Optimality conditions for nonconvex variational problems with integral constraints in Banach spaces (2019)
  • Author(s): Nobusumi Sagara
  • Organizer: International Conference on Nonlinear Analysis and Convex Analysis/International Congress on Optimization: Techniques and Applications
  • Int'l Joint Research / Invited
• [Presentation] Coalitional preferences in large economies with an infinite-dimensional commodity spaces (2018)
  • Author(s): Nobusumi Sagara
  • Organizer: The 29th International Conference on Game Theory
  • Int'l Joint Research
• [Presentation] Vector representation of preferences on σ-algebras and fair division in saturated measure spaces (2018)
  • Author(s): Nobusumi Sagara
  • Organizer: International Workshop on Nonlinear Analysis and Optimization 2018
  • Int'l Joint Research / Invited
• [Presentation] Value functions and optimality conditions for nonconvex variational problems with an infinite horizon in Banach spaces (2018)
  • Author(s): Nobusumi Sagara
  • Organizer: 非線形解析学と凸解析学の研究
  • Int'l Joint Research
• [Presentation] Value functions and optimality conditions for nonconvex variational problems with an infinite horizon in Banach spaces (2018)
  • Author(s): Nobusumi Sagara
  • Organizer: OR 2018: International Conference on Operations Research
  • Int'l Joint Research
• [Presentation] Vector representation of preferences on σ-algebras and fair division in saturated measure spaces (2018)
  • Author(s): Nobusumi Sagara
  • Organizer: RIMS 共同研究「数理経済学とその周辺」
  • Invited
• [Presentation] On some recent developments on the Lyapunov convexity theorem and the integration of multifunctions in infinite dimensions (2018)
  • Author(s): Nobusumi Sagara
  • Organizer: The 6th Asian Conference on Nonlinear Analysis and Optimization
  • Int'l Joint Research / Invited
• [Remarks]
  • URL: https://borismordukhovich.com
• [Remarks]
  • URL: http://www.borismordukhovich.com
• [Remarks]
  • URL: https://econ.jhu.edu/directory/m-ali-khan/