Optimal Life-Cycle Education Decisions of Atomistic Individuals

  • Bernhard Skritek
  • Jesus Crespo Cuaresma
  • Arkadii V. Kryazhimskii
  • Klaus PrettnerEmail author
  • Alexia Prskawetz
  • Elena Rovenskaya


We analyze the optimal life-cycle education decision of a single atomistic individual and show that the standard result of part-time education and part-time work throughout the life-cycle holds only under very special and unrealistic assumptions. Once these assumptions are relaxed, different education strategies become optimal. These range from switching back and forth between work and education (educational leave) to full-time education at the beginning of life and full-time work when older (classical schooling). The resulting strategies for investing in education are better aligned with the observable pattern of educational investments over the life cycle. The particular path chosen by individuals then depends on other aspects, e.g., on the individual’s lifetime horizon or on nonlinearities in human capital accumulation with respect to time invested in education.


Human capital Optimal lifetime education Economic growth Aging Optimal control Singular control 

JEL Codes

C60 O41 I20 



We would like to thank the editor who handled our submission, Alberto Bucci, as well as an anonymous referee and Uwe Sunde for valuable comments and suggestions.

Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.


  1. Acemoglu, D. (2009). Introduction to Modern Economic Growth. Princeton University Press.Google Scholar
  2. Aseev, S. and Veliov, V. (2014). Needle variations in infinite-horizon optimal control. Variational and Optimal Control Problems on Unbounded Domains, G. Wolansky, A. J. Zaslavski (Eds). Contemporary Mathematics, 619: 1–17.Google Scholar
  3. Barro, R. J. (1991). Economic growth in a cross section of countries. The Quarterly Journal of Economics, 106(2): 407–443.CrossRefGoogle Scholar
  4. Bella, G., Mattana, P., and Venturi, B. (2017). Shilnikov chaos in the Lucas model of endogenous growth. Journal of Economic Theory, 172: 451–477.CrossRefGoogle Scholar
  5. Ben-Porath, Y. (1967). The Production of Human Capital and the Life Cycle of Earnings. Journal of Political Economy, 75(4): 352–365.CrossRefGoogle Scholar
  6. Blinder, A. S. and Weiss, Y. (1976). Human capital and labor supply: A synthesis. Journal of Political Economy, 84(3): 449–472.CrossRefGoogle Scholar
  7. Bucci, A. (2008). Population growth in a model of economic growth with human capital accumulation and horizontal R&D. Journal of Macroeconomics, 30(3): 1124–1147.CrossRefGoogle Scholar
  8. Cervellati, M., and Sunde, U. (2013). Life expectancy, schooling, and lifetime labor supply: Theory and evidence revisited. Econometrica, 81: 2055–2086.CrossRefGoogle Scholar
  9. Cohen, D. and Soto, M. (2007). Growth and human capital: good data, good results. Journal of Economic Growth, 12: 51–76.CrossRefGoogle Scholar
  10. Cuaresma, J. C., Lutz, W., and Sanderson, W. (2014). Is the demographic dividend an education dividend? Demography, 51(1): 299.CrossRefGoogle Scholar
  11. Dalgaard, C. and Kreiner, C. (2001). Is declining productivity inevitable? Journal of Economic Growth, 6(3): 187–203.CrossRefGoogle Scholar
  12. de la Fuente, A. and Domenéch, R. (2006). Human capital in growth regressions: How much difference does data quality make? Journal of the European Economic Association, 4(1): 1–36.CrossRefGoogle Scholar
  13. Edle von Gaessler, A. and Ziesemer, T. (2016). Optimal education in times of ageing: The dependency ratio in the Uzawa-Lucas growth model. The Journal of the Economics of Ageing, 7: 125–142.CrossRefGoogle Scholar
  14. Encyclopædia Britannica (2018). Monopoly and competition. [Accessed on 12/05/2018].
  15. Farmer, J. D. and Foley, D. (2009). The economy needs agent-based modeling. Nature, 460: 685–686.CrossRefGoogle Scholar
  16. Ghez, G. and Becker, G. S. (1975). A theory of the allocation of time and goods over the life cycle. In The Allocation of Time and Goods over the Life Cycle, pages 1–45. NBER.Google Scholar
  17. Haley, W. J. (1976). Estimation of the earnings profile from optimal human capital accumulation. Econometrica, 44: 1223–1238.CrossRefGoogle Scholar
  18. Funke, M. and Strulik, H. (2000). On endogenous growth with physical capital, human capital and product variety. European Economic Review, 44: 491–515.CrossRefGoogle Scholar
  19. Hanushek, E. A. and Woessmann, L. (2012). Do better schools lead to more growth? Cognitive skills, economic outcomes, and causation. Journal of Economic Growth, 17: 267–321.CrossRefGoogle Scholar
  20. Hanushek, E. A. and Woessmann, L. (2015). The Knowledge Capital of Nations: Education and the Economics of Growth. The MIT Press.CrossRefGoogle Scholar
  21. Hazan, M. (2009). Longevity and lifetime labor supply: Evidence and implications. Econometrica, 77: 1829–1863.CrossRefGoogle Scholar
  22. Hazan, M. and Zoaby, H. (2006). Does Longevity Cause Growth? A Theoretical Critique. Journal of Economic Growth, 11: 363–376.CrossRefGoogle Scholar
  23. Kirman, A. P. (1992). Whom or What does the Representative Individual Represent? Journal of Economic Perspectives, 6: 117–136.CrossRefGoogle Scholar
  24. Lee, R. and Mason, A. (2010). Fertility, human capital, and economic growth over the demographic transition. European Journal of Population, 26(2): 159–182.CrossRefGoogle Scholar
  25. Lucas, R. (1988). On the mechanics of economic development. Journal of Monetary Economics, 22(1): 3–42.CrossRefGoogle Scholar
  26. Lutz, W., Cuaresma, J. C., and Sanderson, W. (2008). The demography of educational attainment and economic growth. Science, 319(5866): 1047–1048.CrossRefGoogle Scholar
  27. Mason, A., Lee, R., and Xue Jiang, J. (2016). Demographic dividends, human capital, and saving. The Journal of the Economics of Ageing, 7: 106–122.CrossRefGoogle Scholar
  28. Prettner, K. (2014). The non-monotonous impact of population growth on economic prosperity. Economics Letters, 124: 93–95.CrossRefGoogle Scholar
  29. Prettner, K. and Strulik, H. (2016). Technology, Trade, and Growth: The Role of Education. Macroeconomic Dynamics, 20(5): 1381–1394.CrossRefGoogle Scholar
  30. Romer, P. (1990). Endogenous technological change. Journal of Political Economy, 98(5): 71–102.CrossRefGoogle Scholar
  31. Ryder, H. E., Stafford, F. P., and Stephan, P. E. (1976). Labor, leisure and training over the life cycle. International Economic Review, 17(3): 651–74.CrossRefGoogle Scholar
  32. Sala-i-Martin, X. (1997). I just ran two million regressions. American Economic Review, 87(2): 178–183.Google Scholar
  33. Sala-i-Martin, X. S., Doppelhofer, G., and Miller, R. (2004). Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach. American Economic Review, 94(4):813–835.CrossRefGoogle Scholar
  34. Strulik, H. (2005). The role of human capital and population growth in R&D-based models of economic growth. Review of International Economics, 13(No. 1):129–145.Google Scholar
  35. Strulik, H., Prettner, K., and Prskawetz, A. (2013). The past and future of knowledge-based growth. Journal of Economic Growth, 18: 411–437.CrossRefGoogle Scholar
  36. Strulik, H. and Werner, K. (2016). 50 is the new 30 – long-run trends of schooling and retirement explained by human aging. Journal of Economic Growth, 21: 165–187.CrossRefGoogle Scholar
  37. Uzawa, H. (1965). Optimum technological change in an aggregative model of economic growth. International Economic Review, 6(1): 18–31.CrossRefGoogle Scholar
  38. Venti, S. and Wise, D. A. (2015). The long reach of education: Early retirement. The Journal of the Economics of Ageing, 6: 133–148.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Bernhard Skritek
    • 1
  • Jesus Crespo Cuaresma
    • 2
  • Arkadii V. Kryazhimskii
    • 3
  • Klaus Prettner
    • 4
    Email author
  • Alexia Prskawetz
    • 1
  • Elena Rovenskaya
    • 3
  1. 1.Institute of Statistics and Mathematical Methods in EconomicsVienna University of TechnologyViennaAustria
  2. 2.Department of EconomicsVienna University of Economics and BusinessViennaAustria
  3. 3.International Institute of Applied Systems Analysis (IIASA)LaxenburgAustria
  4. 4.Institute of EconomicsUniversity of HohenheimStuttgartGermany

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