3. Accelerating Economic Growth in Industrial Societies: The Process of Expansive Reproduction

Stavenhagen (1982) defines an agricultural society as one in which the majority of the population lives in rural communities and thus where an agriculture-based economy prevails. In an agricultural society, economic activities mainly cover agricultural production, where farmland and farmers are the most important resources of the economy. In addition to this definition, we define a “pure agricultural society” as one in which the economy is based entirely upon agriculture before the Industrial Revolution.

The economic growth rate generally shows the rate of change in pGDP as a percentage; if we assume the discrete time interval (t₀ < t₁ < t₂), we mean the increase in the rate compared with a base time period, or \( \frac{ pGD{P}_2- pGD{P}_1}{ pGD{P}_1} \). Thus, the economic growth rate represents the relative increase in the size of economic growth, but it does not necessarily reflect the absolute size of economic growth. For instance, a country with a pGDP of $40,000 that has a growth rate of 2 % has an increase of $800, while a country with a pGDP of $400 that has a growth rate of 10 % would have a $40 increase. Herein, the concept of “economic growth speed” (the speed at which the economy grows) is used, which accurately reflects the absolute increase in economic growth. In other words, herein, the acceleration of economic growth is defined as the accelerating speed of economic growth for all t. Extending this continuously, when the first derivative with respect to time increases (convex function), we say that it shows acceleration.

Economic growth does not have a direct causal relationship with time. Because of this, we cannot express economic growth trends as a function of time. However, to facilitate understanding, if we assume a continuous time–output function, the cases are relevant in which the first-order derivative > 0, the second-order derivative < 0 (decelerating growth), the first-order derivative > 0, the second-order derivative = 0 (uniform growth), the first-order derivative > 0, and the second-order derivative > 0 (accelerating growth).

There is a fundamental difference between the economic growth pattern of an industrial society and that of an agricultural society, namely “simple reproduction” in agricultural societies (Kim et al. 2010) and “expansive reproduction” in industrial societies (this will be further discussed in Sect. 3.3).

The term “sudden stop” was inspired by the following adage among bankers: “It is not speed that kills, it is the sudden stop” (Dornbusch et al. 1995).

In referring to this, Kaldor (1961) notes that the “rate of profit on capital” is greater than is the “pure” long-term interest rate in developed capitalist societies. Further, Brown and Weber (1953) show that profits per capita increased greatly when the UK underwent its Industrial Revolution in the period 1870–1914. Thus, it is impossible to find a pattern of economic growth that is specific to industrial societies via the same process of the investment and accumulation of capital that is present in agricultural societies.

k is the ratio of capital input per unit of labor input (K/L), where K is capital input and L is labor input.