نگاهی به انتخاب کار و اوقات فراغت، انباشت سرمایه انسانی و رشد درون زا

The growth model of Lucas [Lucas Jr., R.E., 1988. On the mechanics of economic development. Journal of Monetary Economics 22 (1), 3–42] is enriched with people having the opportunity to optimally allocate a fraction of their time to non-productive activities (‘leisure’). It is found that the chosen amount of leisure reduces the steady-state rate of growth of per capita output. This implies that the association between income and welfare may not be as strong as it is usually assumed to be. The optimal allocation of time among activities depends on some of the parameters and the marginal product of physical capital per capita.

A standard assumption in growth models is that people devote inelastically their whole time endowment to some productive activity: individuals do not have the option to optimally allocate total time between employment and leisure (Romer, 1990, Aghion and Howitt, 1992 and Jones and Manuelli, 1997). Thus, while it is always assumed that people try to maximize their discounted lifetime utility, the latter depends only on the level of consumption. This contrasts with standard analysis of labor supply where people value both income and ‘leisure’ or ‘free time’. The omission of leisure from the representative agent’s utility function provides considerable analytical simplification. However, if consumption is the sole argument in the maximization of utility, then higher levels of income–or higher rates of income growth–are necessarily associated with increased welfare. This may not be the case if people value elements besides income in their welfare calculations. Hence, one might ask whether the inclusion of some of these elements can provide a more complete perspective for discussing issues regarding growth and welfare. In any case, since in this model the growth effect of the stock of human capital depends on how many units are offered to the market, it is of great interest to analyze a setting in which the number of hours worked is endogenously chosen. The present paper explores the effect of including leisure as an argument in consumers’ optimization problem. The focus is on a steady state where labor supply is constant. Thus, no distinction is made among various components of labor supply such as work effort and labor force participation. Two versions of the model of Lucas (1988) are examined. In both versions, the economy reaches a steady state with positive growth. However, in the first version, human capital has only an internal effect that is taken into account by optimizing individuals. As a result, the optimal equilibrium is identical to the competitive one. In the second version, the average level of human capital creates an external effect (positive externality) in the production of human capital that private agents disregard in their optimizing calculations. This leads the market economy to a suboptimal rate of growth. The model with no externalities is described in the next section. Section 3 presents the Pareto optimal solution provided by a social planner who maximizes the present value of the representative agent’s infinite flow of instantaneous utilities. In Section 4 the aforementioned external effect is added to the production function. Then the optimal equilibrium is presented first, and the competitive equilibrium follows. Section 5 presents some conclusions and questions for further research.

In this paper leisure is introduced as a choice variable in people’s utility function. In all versions of the model examined, the inclusion of leisure reduces the growth rate of the economy in comparison to the standard case. It thus appears that people are willing to accept a lower rate of growth of income in exchange for ‘free time’. In other words, a higher rate of income growth is not necessarily optimal in terms of welfare. Probably, a more inclusive measure that would take into account more than the level and rate of growth of per capita income (or consumption) might be a more reliable guide to welfare comparisons among countries and across time. This work studies only the steady-state features of the economy. An interesting path for further research would be to study whether equilibrium is unique and stable as well as the transitional dynamics of the model. Existing work has shown that for a wide range of parameter values, both versions (with or without the external effect) of the original model admit multiple optimal and competitive equilibria (Caballé and Santos, 1993, Chamley, 1993, Xie, 1994 and Ladron-de-Guevara et al., 1997). Further, a significant volume of work examines the stability of equilibrium in one-sector and two-sector growth models. Examples include Romer (1986), Benhabib and Farmer (1994), Boldrin and Rustichini (1994), Bond et al. (1996), Cazzavillan (1996), Greiner and Semmler (1996), King and Rebelo (1993), Mino (1996), Mulligan and Sala-i-Martin (1993) and Pelloni and Waldmann (1998). It would then be fruitful to see whether the existence of multiple equilibria can help in explaining the observed differences in growth performance among countries, as well as whether the different equilibrium positions can be Pareto ranked and the rate of substitution between income and free time is changing in any systematic way.