Abstract
This chapter focuses on technological progress and its relationship with population growth. Although we begin with the Malthusian theory, it is important to note that Malthus did not understand the importance of technological progress in society at the time. Kremer (Q J Econ 108:681–716, 1993) and other economists have stressed that it is possible to observe a close relationship between population growth and production technology, and Boserup (The conditions of agricultural progress. Aldine Publishing Company, Chicago, 1965) has pointed out that Malthus ignored the positive consequences of population growth in the long run. We define technological progress in an economic sense and emphasize that such progress has become an engine of economic growth for the modern economy. The important question to be posed is, “Does the size of population affect technological progress?” The answer is that a large population will generate many ideas that could bring about rapid technological progress. In addition, technological progress eases the constraints triggered by population growth by increasing the production of economic resources. Furthermore, we discuss the scale effect which means that a larger population would generate a rapid growth of population by mediating technological progress. Next, in developed countries, declining fertility rates have been widely observed and identified as causing population declines in the future. This phenomenon has raised an important point to discuss concerning the relationship between technological progress and population. Lastly, we conclude that the relationship between population size and technological progress encompasses complicated mutually exclusive effects. Specifically, technological progress leads to economic prosperity, which results in reduced fertility and population growth, while population size has a positive effect on technological progress. In the appendices of this chapter, we summarize the Kremer’s theoretical model and provide a simple survey of endogenous growth theory including population dynamics.
Keywords
 Population Growth
 Total Factor Productivity
 Scale Effect
 Economic Resource
 Technological Progress
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Notes
 1.
Kremer referred from McEvedy and Jones (1978) and so on.
 2.
In the case of regression that excludes the most recent data, the adjusted determinant coefficient rises from 0.914 to 0.938, and the coefficient of POP changes from 0.0524 to 0.0621.
 3.
The original data of National Institute of Population and Social Security Research “Population Statistics” are from Kito (2000).
 4.
Collins et al. (2013) pointed out that even if population growth rate has been positively associated with population size, the relationship has been deteriorating at the stage where the total population of the world has over 30 million people. The era in which the amount of population is over 30 million is after the Second World War and also the period in which large disparity began to occur among world nations.
 5.
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Appendices
Appendix 1: Kremer’s Theoretical Model
Various theoretical interpretations concerning the relationship between population and technological progress have been argued about since Malthus (1798). In this appendix, we summarize three such models and show the assumptions for an analysis on the relationship between population and technological progress induced from each model.^{Footnote 5}

(1)
Malthusian Model
The Malthusian model conducts a scenario whereby land is in short supply relative to other production factors from increasing population and decreasing output per capita to a resulting steadystate level. We can define the production function as Eq. (1.3) such that \(Y\) is output, \(P\) is population, and \(T\) is amount of land.
$$Y = AP^{\alpha } T^{1  \alpha }$$(1.3)
In the case where the amount of land is normalized to unity and \(y\) is the constant output per capita at steady state, we have Eq. (1.4), which shows the relationship between output per capita and population at the steady state.
For the condition α < 1, a direct relationship between population and technology is obtained from Eq. (1.4). As for this direct relationship, (Kuznets 1960) and Simon (1977) discussed that as much as the amount of population increased, there were so many potential innovators, such that technological progress was stimulated. Eliminating the condition that the output per capita converges to a constant steadystate level in the Malthusian model, assuming the relationship between population and technological progress \(\frac{{\dot{A}}}{A} = gP\), where \(g\) is a parameter, we get Eq. (1.5).
If this is the case and Kuznets (1960) and others’ assumptions are correct, then we can find a direct relationship between the scale and the growth rate of population from Eq. (1.5).
Proposition 1
From Eq. (1.5), there is a direct relationship between the scale and the growth rate of population.

(2)
Population Relationships with Technology and Output
Although the direct relationship between population and technological progress conducts a direct relationship between population and output, per capita income is relatively low in the developing countries with large population in the real world. This fact casts doubt on the direct relationship between population and technological progress. Then, assuming that parameter g is the function of output per capita, i.e.,
$$g = ky^{\delta } ,k,\quad \delta > 0$$we have Eq. (1.6).
$$\frac{{\dot{A}}}{A} = ky\delta P = kA^{\delta } P^{\delta (\alpha  1) + 1}$$(1.6)
From Eq. (1.6), when δ is the less than \(\frac{1}{1  \alpha }\), the larger population causes the more rapid growth of technological progress. However, when δ is larger than \(\frac{1}{1  \alpha }\), the above conclusion is reversed. Therefore, the relationship between population and technological progress is dependent on those values of parameters.
On the other hand, the growth rate of technological progress is the function of the technological level itself; Eq. (1.7) is given by
When \(\varphi = 1\), the growth rate of technological progress has a direct relationship with population P. In addition, the relationship between output per capita at a steadystate level and the scale or the growth rate of population is shown by Eq. (1.8), which is calculated from Eq. (1.7) using Eq. (1.5).
Proposition 2
When \(\varphi = 1\) in Eq. (1.7), there is a direct relationship between the scale of population and the growth rate of technological progress.

(3)
Relationship between Population Growth and Technology
Kuznets (1960) discussed that more population brought about more intellectual interactions, and this promoted the specialty and efficiency of the human capital such that the growth rate of technological progress was increased. Similar to Kuznets (1960), Aghion and Howitt (1992), Grossman and Helpman (1991), and others argued that the population increase with an expansion of the economical scale encouraged outputs of R&D and spurred technological progress as a result. On the contrary, they also pointed out that the large population situation caused duplications of technology, which led to inefficiency in its development.
Barro and SalaiMartin (2003), Jones (1995), and others presumed Eq. (1.9), which is more generalized than Eq. (1.7).
Furthermore, defining the growth rate of population as \(\frac{{\dot{P}}}{P} = n\), Eq. (1.10) is obtained.
From Eq. (1.10), we have \(\frac{\partial }{\partial t}\left( {\frac{{\dot{A}}}{A}} \right) = (\varphi  1)(gP^{\phi } A^{\varphi  1} )^{2}\). When \(\varphi > 1\), then the growth rate of technological progress would rise rapidly with increasing level of technology. However, such situations have not been observed in developed nations through postwar periods, so Barro and SalaiMartin (1992) imposed the condition \(\varphi \le 1\). In this case, the growth rate of technological progress has a direct relationship with that of population.
Proposition 3
From Eq. (1.10), there is a direct relationship between the growth rate of technological progress and that of population.
Appendix 2: Endogenous Growth and Population Literature
Demography, which was founded by Malthus (1798), had an estranged relationship with economics in the long term, as economics had considered population as a simple exogenous variable. Hence, there was a large gap between the two academic disciplines for a long time. More concretely, population had been handled as a given condition, and it was not a subject of analysis in either the optimum growth model by Ramsey (1928) or the neoclassical growth model by Solow (Solow 1956).
However, the study about fertility by Becker (1965) and the optimum population growth rate by Samuelson (1976) have since established a new relationship between demography and economics, and economics has commenced analysis regarding population dynamics. However, the relationship between economic growth and population or that between economic growth and technological progress was not one of interdependence, but rather population and technological progress were considered as exogenous variables.
These relationships have changed greatly with the emergence of endogenous economic growth theories by Romer (1986) and Lucas (1988), which treated technological progress itself as an endogenous variable of economic growth. Furthermore, Becker and Barro (1988) presented a model wherein fertility and economic growth were determined simultaneously. Population and technological progress, which had been treated as exogenous variables of economic growth, were to be analyzed as endogenous variables from these studies. Yet, problems remained concerning the relationship between population and technological progress. In studies of economic growth to date, it has been rare to analyze the relationship between them. Thus, studies exploring the relationship between population and technological progress have continued from the Malthusian era, as shown by the analysis of this chapter. Indeed, the purpose of this book is exploring this exact relationship between population and technological progress (Fig. 1.5).
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Kato, H. (2016). Population Growth and Technological Progress—From a Historical View. In: An Empirical Analysis of Population and Technological Progress. SpringerBriefs in Population Studies(). Springer, Tokyo. https://doi.org/10.1007/9784431549598_1
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