Abstract
This book is essentially devoted to a presentation of microeconomic theory and multisectoral models. But, in Ch.7, we studied some contributions to mathematical economics which belong to the field of macroeconomic theory. Now it seems useful to make a brief detour, from our main subjects, and present the elements of one sector growth theory, starting from Solow (1956), who can be considered as the forerunner. In this chapter, time, denoted by t,is considered to be a continuous variable, and t = 0 conventionally means the starting instant; so we have t ∈ [0, +∞). A notation such as x(t) (t ≥ 0) means the intensity of the economic variable x at time t; this means, for instance, that when x denotes output then, in a short time interval, ∆ > t 0, the quantity produced is x(t)∆t.
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References
r many primary factors, but always taken in fixed proportions.
As compared with microeconomic models.
See the Mathematical Appendix to Ch.17.
By some beneficial invisible hand, maybe the auctioneer?
In applied work it is customary to assume g(t) = eot (0, 0).
f course, when there is no technical progress, namely, when g(t) = 1 always, this average productivity is constant.
In particular, we have assumed C(t) = ryY(t) (0, y, 1).
Namely, investment gross of depreciation.
See § 24.4.2 for the elements of optimal control theory.
For a more general case, see Arrow (1968, pp.97–114).
i.e., two distinct trajectories cannot intersect.
See, for instance, Hirsch and Smale (1974, p.171.
See also Lombardini (1996, Chs.3–6), for an original analysis of economic growth based on Schumpeterian lines. Another paper in the Schumpeterian tradition is Henkin and Polterovich (1991).
Namely, the amount which could have been devoted to consumption if there were no need to use capital in the production of the same consumption commodity. Macroeconomic models frequently lend themselves to such useful simplifications!
See the previous footnote.
The term used by Schumpeter to mean the person(s) active in estabilishing and running a (new) firm, namely, to apply new combinations of inputs. In his own words: The carrying out of new combinations we call “enterprise”; the individuals whose function is to carry them out we call “entrepreneurs”.
And also of the labour force, assuming that the labour force is a constant percentage of the total population.
A valuable survey of models of growth, where learning by doing is a cause of very rapid income growth, is Lucas (1993).
See § 7.3.
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© 2000 Springer-Verlag Berlin Heidelberg
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Nicola, P. (2000). Macroeconomic Growth Theory. In: Mainstream Mathematical Economics in the 20th Century. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04238-0_22
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DOI: https://doi.org/10.1007/978-3-662-04238-0_22
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