• Previously unknown capital growth paths discovered
  • Type of capital driving growth differs depending on economic structure
  • Finding can be applied to the planning of efficient agricultural assistance

(28 November 2012) A scientist at International Program in Agricultural Development Studies (IPADS), the English-language postgraduate program within Graduate School of Agricultural and Life Sciences, The University of Tokyo, has discovered the first-order approximated growth paths of capital in the neoclassical economic growth model.

In an article published in the 20 November issue of international journal PLOS ONE, Assistant Professor Taro Takahashi derived the previously unknown paths and demonstrated that, depending on the inherent properties of the economy, the type of capital that drives economic growth is different, a finding useful in the planning of international agricultural assistance.

The basis of Dr Takahashi's research is the theory of economic growth, a subdiscipline of economics that tries to explain the process of economic growth mathematically. Extensively used by governments and central banks to derive optimal fiscal, financial, and other economic policies, the theory is being investigated by two schools of researchers: the neoclassical school that assumes the origin of technological innovation resides outside of the economy, and the endogenous growth school that assumes inner-driven technological innovation.

Of the two, the neoclassical school established an economic model with two types of capital in the 1990s (Mankiw et al, Quarterly Journal of Economics 107: 407-437), whereby unlike its predecessors, physical capital and human capital were explicitly distinguished. To date, this model has been applied to all corners of the world economy and cited by more than 1,500 articles. The majority of these subsequent works test the theory by comparing the model-predicted growth path of national income (national income expressed as a function of elapsed time) against its historically observed counterpart.

On the other hand, the growth paths of physical and human capital (the amount of each capital possessed by an economy expressed as a function of elapsed time) in the neoclassical growth model have previously been unknown because of the complex forms of time-differential equations for capitals (equations expressing the change in capital accumulation at any given time) that are required to derive them. This means that while the absolute value of national income could be predicted from the model, the absolute values of capitals could not, and consequently no policy implication could be derived as to which type of capital should be enhanced in order to achieve economic growth more efficiently.

In the new research, Dr Takahashi applied Tailor-series expansion, a common method of approximation for mathematical functions, to time-differential equations for capitals and converted them to a system of linear differential equations. Since the solutions for this system were already known, this conversion led to the derivation of the growth paths of capitals, albeit in the approximated form. In addition, Dr Takahashi found that the type of capital that contributes more effectively to economic growth depends on the inherent properties of the economy.

These findings can be applied to policy debates and assist determination of optimal growth strategies, particularly the optimal form of capital injection that suits the economy’s geographical setting, population dynamics, and the speed of technological development. Such information will also be valuable for the design of efficient foreign aid packages that minimise the cost borne by donor countries.

For more details

Takahashi T (2012), Capital growth paths of the neoclassical growth model. PLOS ONE, 7(11): e49484.
Article DOI: 10.1371/journal.pone.0049484
Article URL: http://dx.doi.org/10.1371/journal.pone.0049484


Dr Taro Takahashi
Department of Global Agricultural Sciences
Graduate School of Agricultural and Life Sciences
The University of Tokyo
Email: ataro@mail.ecc.u-tokyo.ac.jp