Abstract
In this chapter we try to show that a constant return to scale (CRS) technology on reproducible factors is not, by itself, a sufficient condition for endogenous growth. The literature has always relied on the CRS hypothesis and has implicitly assumed that accumulation activity is not a choosable factor. Actually, the entire time, optimally allocated, either by the planner or by individuals, is dedicated to accumulating reproducible factors which have CRS: endogenous growth is therefore a necessary result. In other words, CRS is a sufficient condition if and only if the allocation of time is never affected by the rates of growth or by the levels of the variables.
In order to state such an implicit hypothesis, we have re-examined some representative endogenous growth models with the explicit introduction of leisure as a source of welfare for individuals. This gives an opportunity cost to “market activities” (working + studying time), turning time into a production factor and making its scarcity relevant. This analysis leads back to exogenous growth, notwithstanding CRS on reproducible factors, and confirms our argument.
Reprint from: Mario Baldassarri, Paolo De Santis, Giuseppe Moscarini, Allocation of Time, Human Capital and Endogenous Growth, RPE-Rome 1992.
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Notes
- 1.
Throughout the paper we will refer to the neoclassical model, meaning the Ramsey-Cass-Koopmans model. Please note that the numbers in square brackets refer to the Bibliography at the end of the chapter.
- 2.
By structural parameters we mean: (1) intertemporal elasticity of substitution; (2) discount rate; and (3) labour and capital share.
- 3.
Given two economies, the one with a lower stock of capital is poor.
- 4.
As long as the production function also includes non-reproducible factors, it exhibits overall increasing returns to scale. For problems concerning the existence of a set of prices supporting a general competitive equilibrium see the survey of Sala-I-Martin [10].
- 5.
We omit a similar treatment to the AK Rebelo model, although it represents a common benchmark and all other models are simple micro-foundations of its CRS technology. Actually, the introduction of leisure, and consequently of endogenous working time, obviously requires that labour be explicitly considered. In the AK model, however, all factors are reproducible and exhibit overall CRS; hence labour also has to be taken as a reproducible factor (which is stated by Rebelo himself).
- 6.
The analysis carried out on Romer’s framework is valid for any externality-based endogenous growth model, including Barro’s [3].
- 7.
With regard to Lucas’ model, here we introduced a slight modification. As a matter of fact, in Lucas’ model, human capital is considered in per-capita terms, while the other reproducible factor, physical capital, is in aggregate terms. This asymmetry is reflected in the first-order condition that equalizes the marginal benefits from studying and working; in Lucas’ model such a condition leads to equalizing the aggregate gain from the last instant of working with the individual gain from the last instant of studying. Allowing for leisure, if H t were in per-capita terms, the necessary condition on leisure would equalize the aggregate marginal benefit from leisure to the individual marginal benefit from studying Eq. (5.5). In any case our results of zero per-capita growth rates would not be affected, if we worked with per-capita human capital.
- 8.
- 9.
The same result holds for the market economy. In this case the maximization is the same as the one solved by the social planner, thanks to the production function, which is CRS, K η being considered as given by the individuals. The FOC for a maximum are all the same but for Eq. (5.30). Individuals do not derive with respect to K hence η does not appear on the right-hand side (RHS) as a coefficient, but only as an exponent. The following analysis proceeds on the same lines and the final results of zero per-capita growth rates are not altered. The technological externalities obviously will play a role, affecting the steady-state levels of per-capita values, not their rates of growth.
- 10.
In this respect, we are supported by R. Solow, who has read an earlier version of this paper.
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Baldassarri, M. (2017). Allocation of Time, Human Capital and Endogenous Growth. In: The European Roots of the Eurozone Crisis. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-58080-7_5
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