Computational Mathematics and Mathematical PhysicsComputational Mathematics and Mathematical PhysicsЖурнал вычислительной математики и математической физики0044-46693034-5332The Russian Academy of Sciences13430010.31857/S0044466923030043DYFCWGOptimal controlОПТИМАЛЬНОЕ УПРАВЛЕНИЕUnknownEconomic Growth Models with Heterogeneous DiscountingМодели экономического роста с неоднородным дисконтированиемBorissovK. Yu.БорисовК. Ю.kirill@eu.spb.ruPakhninM. A.ПахнинМ. А.mpakhnin@eu.spb.ruEuropean University at Saint PetersburgЕУСПбInstitute for Problems of Regional Economics, Russian Academy of SciencesИПРЭ РАН0103202363335537910102023Copyright ©; 2023, К.Ю. Борисов, М.А. ПахнинCopyright ©; 2023, К.Ю. Борисов, М.А. Пахнин2023К.Ю. Борисов, М.А. ПахнинК.Ю. Борисов, М.А. Пахнинhttps://journals.rcsi.science/0044-4669/article/view/134300

A survey of theoretical economic growth models with agents having different subjective discount factors is proposed. The structure of equilibrium paths in such models, their dynamics and convergence to stationary equilibria, and the relationship with Pareto optimal paths are described. Models with socially determined discount factors in which time preferences are formed endogenously are discussed, and the basic difficulties associated with social choice in the case of heterogeneous discount factors are examined. The models presented in the paper shed light on internal mechanisms of a market economy that lead to the division of society into the rich and the poor.

Предлагается обзор теоретических моделей экономического роста, в которых потребители различаются по своим субъективным коэффициентам дисконтирования. Описывается устройство равновесных траекторий в таких моделях, их динамика и сходимость к стационарным равновесиям, а также взаимосвязь с оптимальными по Парето траекториями. Обсуждаются модели с социально обусловленными коэффициентами дисконтирования, в которых межвременные предпочтения формируются эндогенно, а также рассматриваются основные трудности, связанные с общественным выбором в условиях неоднородных коэффициентов дисконтирования. Представленные в статье модели проливают свет на внутренние механизмы рыночной экономики, которые приводят к делению общества на богатых и бедных. Библ. 45.

economic growthinequalityheterogeneous agentsdiscountingvotinggeneral equilibriumэкономический ростнеравенствонеоднородные агентыдисконтированиеголосованиеобщее равновесие.Ramsey F.P. A Mathematical Theory of Saving // Economic Journal. 1928. V. 38. P. 543–559.Cass D. Optimum Growth in an Aggregative Model of Capital Accumulation // Review of Economic Studies. 1965. V. 32. P. 233–240.Koopmans T.C. On the Concept of Optimal Economic Growth. In: Study Week on the Econometric Approach to Development Planning. Amsterdam: North-Holland, 1965. 38 p.Rae J. Statement of Some New Principles of Political Economy. Boston: Hilliard, Gray, and Co, 1834.Fisher I. The Rate of Interest. New York: Macmillan, 1907.Rader T. The Economics of Feudalism. New York: Gordon and Breach, 1971.Rader T. Theory of General Economic Equilibrium. New York: Academic Press, 1972.Becker R.A. On the Long-run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households // Quarterly J. of Economics. 1980. V. 95. I. 2. P. 375–382.Bewley T.F. An Integration of Equilibrium Theory and Turnpike Theory // J. of Mathematical Economics. 1982. V. 10. P. 233–267.Becker R.A. Equilibrium Dynamics with Many Agents. In: Mitra T., Dana R.-A., Le Van C., Nishimura K., editors, Handbook on Optimal Growth 1. Discrete Time. Heidelberg: Springer, 2006. P. 385–442.Борисов К.Ю., Пахнин М.А. О некоторых подходах к моделированию деления общества на бедных и богатых // Ж. новой экономической ассоциации. 2018. Т. 4. № 40. С. 32–59.Борисов К.Ю., Пахнин М.А. Общественное благосостояние в моделях экономического роста с неоднородными потребителями // Вестник СПбГУ: Экономика. 2019. Т. 35. № 2. С. 173–196.Wang M., Rieger M.O., Hens T. How Time Preferences Differ: Evidence from 53 Countries // J. of Economic Psychology. 2016. V. 52. P. 115–135.Falk A., Becker A., Dohmen T., Enke B., Huffman D., Sunde U. Global Evidence on Economic Preferences // Quarterly J. of Economics. 2018. V. 133. I. 4. P. 1645–1692.Hübner M., Vannoorenberghe G. Patience and Long-run Growth // Economics Letters. 2015. V. 137. P. 163–167.Kamihigashi T. A Simple Proof of the Necessity of the Transversality Condition // Economic Theory. 2002. V. 20. I. 2. P. 427–433.Duran J., Le Van C. Simple Proof of Existence of Equilibrium in a One-Sector Growth Model with Bounded or Unbounded Returns From Below // Macroeconomic Dynamics. 2003. V. 7. P. 317–332.Becker R.A., Boyd III J.H., Foias C.A. The Existence of Ramsey Equilibrium // Econometrica. 1991. V. 59. P. 441–460.Becker R.A., Foias C.A. Characterization of Ramsey Equilibrium // J. of Economic Theory. 1987. V. 41. P. 173–184.Becker R.A., Tsyganov E.N. Ramsey Equilibrium in a Two-Sector Model with Heterogeneous Households // J. of Economic Theory. 2002. V. 105. P. 188–225.Sorger G. On the Structure of Ramsey Equilibrium: Cycles, Indeterminacy, and Sunspots // Economic Theory. 1994. V. 4. P. 745–764.Sorger G. Chaotic Ramsey Equilibrium // International J. of Bifurcation and Chaos. 1995. V. 5. P. 373–380.Mitra T., Sorger G. On Ramsey’s Conjecture // J. of Economic Theory. 2013. V. 148. I. 5. P. 1953–1976.Borissov K., Dubey R.S. A Characterization of Ramsey Equilibrium in a Model with Limited Borrowing // J. of Mathematical Economics. 2015. V. 56. P. 67–78.Becker R.A., Borissov K., Dubey R.S. Ramsey Equilibrium with Liberal Borrowing // J. of Mathematical Economics. 2015. V. 61. P. 296–304.Borissov K., Dubey R.S. Growth with Many Agents and Wages Paid ex ante // Economic Modelling. 2020. V. 89. P. 101–107.Le Van C., Vailakis Y. Existence of a Competitive Equilibrium in a One Sector Growth Model with Heterogeneous Agents and Irreversible Investment // Economic Theory. 2003. V. 22. I. 4. P. 743–771.Becker R.A., Mitra T. Efficient Ramsey Equilibria // Macroeconomic Dynamics. 2012. V. 16, I. S1, P. 18–32.Borissov K. Growth and Distribution in a Model with Endogenous Time Preferences and Borrowing Constraints // Mathematical Social Sciences. 2013. V. 66. P. 117–128.Borissov K., Lambrecht S. Growth and Distribution in an AK-model with Endogenous Impatience // Economic Theory. 2009. V. 39. I. 1. P. 93–112.Борисов К.Ю., Подкорытова О.А. О влиянии неравенства в распределении доходов на темпы экономического роста // Вестник СПбГУ: Экономика. 2006. Т. 1. С. 155–168.Pakhnin M. Collective Choice with Heterogeneous Time Preferences // J. of Economic Surveys. 2022. P. 1–32.Boylan R.T., McKelvey R.D. Voting over Economic Plans // American Economic Review. 1995. V. 85. I. 4. P. 860–871.Boylan R.T., Ledyard J., McKelvey R.D. Political Competition in a Model of Economic Growth: Some Theoretical Results // Economic Theory. 1996. V. 7. P. 191–205.Jackson M.O., Yariv L. Collective Dynamic Choice: The Necessity of Time Inconsistency // American Economic Journal: Microeconomics. 2015. V. 7. I. 4. P. 150–178.Beck N. Social Choice and Economic Growth // Public Choice. 1978. V. 33. I. 2. P. 33–48.Borissov K., Pakhnin M., Puppe C. On Discounting and Voting in a Simple Growth Model // European Economic Review. 2017. V. 94. P. 185–204.Borissov K., Pakhnin M. Economic Growth and Property Rights on Natural Resources // Economic Theory. 2018. V. 65. I. 2. P. 423–482.Borissov K., Hanna J., Lambrecht S. Public Goods, Voting, and Growth // J. of Public Economic Theory. 2019. V. 21. I. 6. P. 1221–1265.Mankiw N.G. The Savers-Spenders Theory of Fiscal Policy // American Economic Review. 2000. V. 90. I. 2. P. 120–125.Palivos T. Optimal Monetary Policy with Heterogeneous Agents: A Case for Inflation // Oxford Economic Papers. 2005. V. 57. I. 1. P. 34–50.Smetters K. Ricardian Equivalence: Long-run Leviathan // J. of Public Economics. 1999. V. 73. I. 3. P. 395–421.Тарасенко М.В., Трусов Н.В., Шананин А.А. Математическое моделирование экономического положения домашних хозяйств в России // Ж. вычисл. матем. и матем. физ. 2021. Т. 61. № 6. С. 1034–1056.Shananin A.A., Tarasenko M.V., Trusov N.V. Consumer Loan Demand Modeling // Communications in Computer and Information Science. 2021. V. 1476. P. 417–428.Glätzle-Rützler D., Lergetporer P., Sutter M. Collective Intertemporal Decisions and Heterogeneity in Groups // Games and Economic Behavior. 2021. V. 130. P. 131–147.