Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-19T10:22:12.409Z Has data issue: false hasContentIssue false


Published online by Cambridge University Press:  03 August 2016

Hiroaki Sasaki*
Kyoto University
Keisuke Hoshida
Kyoto University
Address correspondence to: Hiroaki Sasaki, Graduate School of Economics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, JAPAN; e-mail:


This study investigates the rates of technological progress, total output growth, and per capita output growth when population growth is negative using a semiendogenous research and development (R&D) growth model. The analysis shows that within a finite time horizon, the employment share of the final goods sector reaches unity and that of the R&D sector reaches zero; accordingly, the rate of technological progress tends toward zero. In this case, the growth rate of per capita output asymptotically approaches a positive value.

Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


We would like to thank Kouichi Futagami, Kazuhiro Yuki, Keita Kamei, and Yusuke Amano for their useful comments and helpful suggestions on earlier versions of this paper. We also thank the editor of this journal. The first author is grateful to KAKENHI (25380295) for financial support. The usual disclaimer applies.



Abdih, Y. and Joutz, F. (2006) Relating the knowledge production function to total factor productivity: An endogenous growth puzzle. IMF Staff Papers 53 (2), 242271.Google Scholar
Arnold, L.G. (2006) The dynamics of the Jones R&D growth model. Review of Economic Dynamics 9 (1), 143152.Google Scholar
Christiaans, T. (2011) Semi-endogenous growth when population is decreasing. Economics Bulletin 31 (3), 26672673.Google Scholar
Dinopoulos, E. and Thompson, P. (1998) Schumpeterian growth without scale effects. Journal of Economic Growth 3 (4), 313335.Google Scholar
Dinopoulos, E. and Thompson, P. (1999) Scale effects in Schumpeterian models of economic growth. Journal of Evolutionary Economics 9 (2), 157185.Google Scholar
Ferrara, M. (2011) An AK Solow model with a non-positive rate of population growth. Applied Mathematical Sciences 5 (25), 12411244.Google Scholar
Futagami, K. and Hori, T. (2010) Technological progress and population growth: Do we have too few children? Japanese Economic Review 61 (1), 6484.CrossRefGoogle Scholar
Futagami, K. and Nakajima, T. (2001) Population aging and economic growth. Journal of Macroeconomics 23 (1), 3144.CrossRefGoogle Scholar
Gruescu, S. (2007) Population Ageing and Economic Growth: Education Policy and Family in a Model of Endogenous Growth. Heidelberg, Germany: Physica-Verlag.Google Scholar
Jones, C.I. (1995) R&D-based models of economic growth. Journal of Political Economy 103 (4), 759784.CrossRefGoogle Scholar
Lucas, R.E. (1988) On the mechanics of economic development. Journal of Monetary Economics 22 (1), 342.Google Scholar
Madsen, J.B. (2008) Semi-endogenous versus Schumpeterian growth models: Testing the knowledge production function using international data. Journal of Economic Growth 13 (1), 126.CrossRefGoogle Scholar
OECD (2013) Economic Outlook. Paris: OECD.Google Scholar
Peretto, P. (1998) Technological change and population growth. Journal of Economic Growth 3 (4), 283311.Google Scholar
Prettner, K. (2013) Population aging and endogenous economic growth. Journal of Population Economics 26 (2), 811834.Google Scholar
Prettner, K. and Prskawetz, A. (2010) Demographic change in models of endogenous economic growth: A survey. Central European Journal of Operations Research 18 (4), 593608.CrossRefGoogle Scholar
Romer, P. (1986) Increasing returns and long-run growth. Journal of Political Economy 94 (5), 10021037.Google Scholar
Romer, P.M. (1990) Endogenous technological change. Journal of Political Economy 98 (5), 71102.Google Scholar
Sasaki, H. (2011) Population growth and North–South uneven development. Oxford Economic Papers 63 (2), 307330.Google Scholar
Sasaki, H. (2015) International trade and industrialization with negative population growth. Macro-economic Dynamics 19 (8), 16471658.Google Scholar
Solow, R. (1956) A contribution to the theory of economic growth. Quarterly Journal of Economics 70 (1), 6594.CrossRefGoogle Scholar
Strulik, H., Prettner, K., and Prskawetz, A. (2013) The past and future of knowledge-based growth. Journal of Economic Growth 18 (4), 411437.Google Scholar
United Nations (2013) World Population Prospects: The 2012 Revision. New York: United Nations.Google Scholar
World Bank (2013) World Development Indicators. Washington, DC: World Bank.Google Scholar
Young, A. (1998) Growth without scale effects. Journal of Political Economy 106 (1), 4163.Google Scholar