A Solow-Swan Type Growth Model of An Economy with Two Classes

Yıl 2025, Cilt: 14 Sayı: 5, 2106 - 2122, 31.12.2025

Taylan Akgül , Zeynep Elitaş

https://doi.org/10.15869/itobiad.1694431

Öz

In this paper, a Solow-Swan type growth model is constructed for a two-class hypothetical economy with no government in order to highlight the links between group dynamics and aggregate dynamics. A hypothetical society with two classes (rich and poor) is assumed. They share the common technological knowledge but have different production functions. Rich group’s production is capital intensive and the poor group has a labor intensive one. Each group consists of homogenous agents. It is algebraically shown that even if none of the groups are in their steady state, the economy under consideration could be in its steady state as a whole. Furthermore, it is shown that initial capital distribution between groups and their relative weights affect the steady state per capita levels of output and consumption. Finally, a python simulation is added in order to calibrate the model and the effects of an increase in the saving rate on steady state per capita capital and output levels of groups and aggregate economy are shown. Unlike the standard Solow-Swan framework, implicitly based on homogenous agents, this modified model is suitable for analyzing and explaining dynamics of growth for heterogeneous economic unions/groups such as EU and OECD.

Anahtar Kelimeler

Agent-Based Modelling , Solow-Swan Growth Model , Steady State , Production Function , Income Distribution

İki Sınıflı Bir Ekonominin Solow-Swan Tipi Büyüme Modeli

Öz

Bu çalışmada, standart Solow-Swan modelinin aksine, grup dinamikleri ile toplam dinamikler arasındaki bağlantıları vurgulamak amacıyla, hükümetin bulunmadığı iki sınıflı varsayımsal bir ekonomi için Solow-Swan tipi bir büyüme modeli oluşturulmuştur. Bu modelde, zengin ve fakir olmak üzere iki sınıfın olduğu ve her iki sınıfın teknolojik bilgi düzeylerinin aynı fakat üretim fonksiyonlarının farklı olduğu varsayılmaktadır. Zengin sınıfın üretimi sermaye yoğun, fakir sınıfın üretimi ise emek yoğun olarak modellenmiştir. Her grup homojen ajanlardan oluşmaktadır. Grupların her biri durağan durumda olmasa da, ekonominin bir bütün olarak durağan durumda olabileceği cebirsel olarak gösterilmiştir. Ayrıca, gruplar arasındaki başlangıç sermaye dağılımı ve bunların göreceli ağırlıklarının, kişi başına üretim ve tüketimin durağan durum seviyelerini nasıl etkilediği de gösterilmiştir. Son olarak, modeli kalibre etmek ve tasarruf oranındaki artışın kişi başına düşen sermaye, grupların çıktı düzeyleri ve toplam ekonomi üzerindeki etkilerini göstermek amacıyla bir Python simülasyonu eklenmiştir. Bu modifiye edilmiş Solow-Swan modeli, ekonomik birliklerin büyüme dinamiklerini analiz etmek ve açıklamak için kullanılabilir. Gizil olarak homojen ajan tabanlı çerçevenin aksine bu modifiye model Avrupa Birliği veya OECD gibi heterojen kuruluşların ya da ekonomik bölgeler ve birliklerin büyüme dinamiklerini ampirik uzantılarla analiz etmek için uygundur.

Anahtar Kelimeler

Ajan Tabanlı Modelleme , Solow-Swan Büyüme Modeli , Durağan Durum , Üretim Fonksiyonu , Gelir Dağılımı

Kaynakça

• Acemoglu, D. (2002). Directed technical change. The Review of Economic Studies, 69(4), 781–809. https://doi.org/10.1111/1467-937x.00226
• Acemoglu, D. & Autor, D. (2009). Lectures in labor economics. Boston, MIT.
• Acemoglu, D., & Guerrieri, V. (2008). Capital deepening and nonbalanced economic growth. Journal of Political Economy, 116(3), 467–498. https://doi.org/10.1086/589523
• Acemoglu, D., & Pischke, J. (1999). Beyond Becker: training in imperfect labour markets. The Economic Journal, 109(453), 112–142. https://doi.org/10.1111/1468-0297.00405
• Aghion, P., Akcigit, U., & Howitt, P. (2015). The Schumpeterian growth paradigm. Annual Review of Economics, 7(1), 557–575. https://doi.org/10.1146/annurev-economics-080614-115412
• Aiyagari, S. R. (1994). Uninsured idiosyncratic risk and aggregate saving. The Quarterly Journal of Economics, 109(3), 659–684. https://doi.org/10.2307/2118417
• Becker, G.S. (1993). Human Capital: A theoretical and empirical analysis with special reference to education. Chicago, University of Chicago Press.
• Barro, R. J., & Sala-i-Martin, X. (1995). Economic growth. McGraw-Hill.
• Benhabib, Jess, and Roger E.A. Farmer. (1994). Indeterminacy and increasing returns. Journal of Economic Theory, 63(1), 19–41.
• Bourguignon, F., & Morrisson, C. (1998). Inequality and development: The role of dualism. Journal of Development Economics, 57(2), 233–257. https://doi.org/10.1016/S0304-3878(98)00089-3
• Desmet, Klaus, and Esteban Rossi-Hansberg. (2014). Spatial Development.American Economic Review, 104(4), 1211–1243
• Domar, E. (1946). Capital expansion, rate of growth, and employment. Econometrica, 14(2), 137–147. https://doi:10.2307/1905364
• Glomm, G., & Ravikumar, B. (1997). Productive government expenditures and long-run growth. Journal of Economic Dynamics and Control, 21(1), 183–204. https://doi.org/10.1016/0165-1889(95)00929-9
• Grossman, G. M., & Helpman, E. (1991). Innovation and Growth in the Global Economy. MIT Press
• Harrod, Roy F. (1939). An essay in dynamic theory. The Economic Journal, 49(193), 14–33. https://doi.org/10.2307/2225181
• Kaldor, N. (1966). Marginal productivity and the macro-economic theory of distribution: Comment on Samuelson and Modigliani. The Review of Economic Studies, 33(4), 309-319.
• Krueger, D., & Perri, F. (2006). Does income inequality lead to consumption inequality? Evidence and theory. The Review of Economic Studies, 73(1), 163–193. https://doi.org/10.1111/j.1467-937X.2006.00398.x
• Lucas, R. E. (1988). On the mechanics of economic development. Journal of Monetary Economics, 22(1), 3–42. http://doi:10.1016/0304-3932(88)90168-7
• Lucas, R. E., Jr. (2001). Externalities and cities. Review of Economic Dynamics, 4(2), 245–274. https://doi.org/10.1006/redy.2000.0108
• Ngai, L. R., & Pissarides, C. A. (2007). Structural change in a multisector model of growth. American Economic Review, 97(1), 429–443. https://doi.org/10.1257/aer.97.1.429
• Pasinetti, L. L. (1981). Structural change and economic growth: A theoretical essay on the dynamics of the Wealth of Nations. Cambridge University Press.
• Romer P. M. (1986). Increasing returns and long run growth. Journal of Political Economy, 94(5). https://doi.org/10.1086/261420
• Romer P. M. (1990). Endogenous technological change. Journal of Political Economy, 98(5), 71-102. Part 2: The Problem of Development: A conference of the institute for the study of free enterprise systems. https://doi.org/10.1086/261725
• Romer P. M., & Rivera-Batiz, L. (1991). Economic integration and endogenous growth. Quarterly Journal of Economics, 106(2), 531–55. https://doi.org/10.2307/2937946
• Romer P. M. (1994). The origins of endogenous growth. The Journal of Economic Perspectives, 8(1), 3-22. https://doi.org/10.1257/jep.8.1.3
• Sargent, T. J., & Stachurski, J. (2023). A first course in quantitative economics with python, The Solow-Swan Growth Model. Retrieved from https://intro.quantecon.org/solow.html
• Solow, R. M. (1956). A contribution to the theory of economic growth. Quarterly Journal of Economics, 70(1), 65-94. https://doi.org/10.2307/1884513
• Swan, T. W. (1956). Economic growth and capital accumulation. Economic Record, 32(2), 334–361. https://doi.org/10.1111/j.1475-4932.1956.tb00434.x
• Uzawa, H. (1964). Optimal Growth in a Two-Sector Model of Capital Accumulation. The Review of Economic Studies, 31(1), 1-24.