Stefano Bosi, Carmen Camacho* and David Desmarchelier

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When Mahbub ul Haq introduced human development as a compound process which included education and life expectancy, he paved the way for a new avenue of research in development economics. The introduction of the Human Development Index (HDI) in ul Haq (1) led to a new paradigm and to a modern theory of human development. However, although his works have influenced prominent economists like Amartya Sen, most growth theorists still focus on the utility of consumption.

In this paper, stemming from the common belief that educated and healthy people enjoy life differently, Stefano Bosi, Carmen Camacho and David Demarchelier consider that human capital is made of both education and health.
While the seminal notion of human capital was introduced by Adam Smith in 1776 (2) and later by Arthur Cecil Pigou in 1928 (3), the modern theory of human capital can be traced back to Schultz (4) and Becker (5). Uzawa (6) was the first to incorporate human capital as an engine of growth in a theoretical model. The emergence of a new endogenous growth literature stimulated the interest of economists in the role of human capital. Building on Rosen (7), Lucas (8) underlined that the accumulation of human capital can trigger a mechanism of perpetual growth. After Lucas, the literature developed fast, scrutinizing all factors underlining the formation of human capital: education, transmission, health, culture…

Nevertheless, the literature becomes thinner regarding the other various roles of human capital in an economy. Although sociologists report that education does affect life enjoyment, research in economics has for the most part neglected the role of human capital in welfare. Among the studies in sociology, Ross and Wu (9) find that well educated individuals have a more fulfilling job and declare they have a better control over their lives. Similarly, Finkelstein et al. (10) point out a complementarity between health and consumption demand: if chronic diseases increase by 1%, then the satisfaction a household gets from consumption falls from 10 to 25%. From an economist’s viewpoint, this empirical evidence suggests that human capital does increase the household satisfaction, and in particular, the household feeling towards consumption.

In this paper, the authors incorporate the HDI into the utility function defining a new composite good, which generalizes the consumption good. This new good mixes the standard consumption good and human capital, and as a result, it embodies the notion that human capital is crucial to appreciate consumption, and it allows the authors to study the cross effect of human capital on the satisfaction generated by consumption. Under a Cobb-Douglas technology and logarithmic preferences, the authors are able to provide the explicit trajectories for capital, consumption and HDI not only because they obtain the analytical solution to the system of differential equations, but also because they compute the initial value of labor supply in a two-step maximization, which is new in growth literature. They actually prove that the optimal initial value of labor supply belongs to the Balanced Growth Path (BGP), demonstrating that the BGP is actually optimal from the start. This means that the choice that maximizes the household felicity is to increase both consumption and human capital at the same rate. Interestingly the authors highlight a HDI crossing property: the more a household enjoys consumption, the more the household consumes and the higher the HDI in the short run. Unfortunately, there is a negative effect in the long run. Indeed, since consumption is privileged over investment in education and the generation of human capital, human capital will fall in the long run making decrease the HDI. Finally, it is also proven that the more a household enjoys consumption, the lower the economy’s growth rate.


(1) Ul Haq Mahbub (1995). Reflections on Human Development. Oxford University Press.

(2) Smith A. (1776). An Inquiry into the Nature and Causes of the Wealth of Nations. Strahan and Cadell, Londres.

(3) Pigou A.C. (1928). A Study in Public Finance. Macmillan, London.

(4) Schultz T.W. (1961). Investment in human capital. American Economic Review, 51, 1-17.

(5) Becker G.S. (1964). Human Capital: A Theoretical and Empirical Analysis, with Special Reference to Education. University of Chicago Press, Chicago.

(6) Uzawa H. (1965). Optimum technical change in an aggregative model of economic growth. International Economic Review, 6, 18-31.

(7) Lucas R.E. (1988). On the mechanics of economic development. Journal of Monetary Economics, 22, 3-42.

(8) Rosen S. (1976). A theory of life earnings. Journal of Political Economy, 84, 545-567.

(9) Ross C.E. and C.-L. Wu. (1995). The links between education and health. American Sociological Review, 60, 719-745.

(10) Finkelstein A., E.F.P. Luttmer and M. Notowidigdo (2013). What good is wealth without health? The effect of health on the marginal utility of consumption, Journal of the European Economic Association, 11, 221-258.



Original title of the article: Human capital and welfare

Published in : PSE Working Paper n°2020-04

Available at :

* PSE Member

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