Since it is known that in the continuous-time optimal growth model, the optimal solution is never a cycle when there is only one type of capital good, it was generally an open question in 1978 whether the continuous-time model optimal solution could be a cycle. This paper settled the issue by proving the existence of limit cycles in a three-sector economic model consisting of Cobb-Douglas production functions with more than one type of capital good. The paper uses the fact that limit cycles diverge when the stationary solution changes from a saddle point to fully unstable. It is regarded as the most important pioneering paper in the field of nonlinear economic dynamics.

The paper analyzes the behavior of the optimal solution in a discrete-time optimal growth model where the production function is S-shaped with a fugitive harvest portion. The paper proves that there exists a certain critical point in the capital stock, and that convergence to a positive steady-state solution is optimal from an initial capital stock larger than that point, and convergence to zero from a lower initial capital stock as capital is eaten up. Since the production function is not a concave function, the Euler equations and the transversality condition do not guarantee optimality, it was necessary to analyze the behavior of the optimal solution in a new way. In the end, the method used in this paper, which succeeded in completely analyzing the behavior of the optimal solution, contributed greatly to the subsequent development of nonlinear economic dynamics. As a pioneering paper, it has been cited in many papers.”

This paper proves that the sign of the cross derivative of the utility function determines whether the solution of the discrete-time optimal model takes a monotonic or oscillating path. The sign of the cross-differentiation is determined solely by the magnitude of the factor intensities between the sectors in the case of a two-sector model with a linear utility function. This paper is capable of making economic sense of situations in which complex phenomena such as chaos arise, and together with papers 1 and 2 above, it is regarded as the most important pioneering paper in nonlinear economic dynamics.

This paper is an example of a two-sector infinite horizon model in which the production function of each sector is a Leontiev function, and it is the first to obtain sufficient conditions under which the optimal solution is chaotic, using the well-known utility function and production function examples. Moreover no matter how close the discount factor is to 1, the optimal solution can be chaotic by changing other parameters.

“Period Three implies Chaos,” a well-known paper by Li and Yorke, has focused on period three solutions in relation to chaos. This paper proves that in an optimal growth model, if the optimal solution is a periodic solution with period three, then the upper bound of the discount factor is . While in the paper 4 above we showed that the optimal solution can be chaotic for any discount factor, this paper is an important paper that proves that the value of the discount factor is limited if one assumes the existence of periodic solutions with a particular period.

The introduction of expectations and externalities of economic agents into the infinite period dynamic model drew attention to the indeterminacy of equilibrium, meaning that there are an infinite number of equilibrium paths from the same initial point. Until then, the indeterminacy of equilibrium required that the production function was increasing returns to scale. This paper proved that even under a constant returns to scale production function in a two-sector model, equilibrium is indeterminate under certain conditions regarding the capital intensity between sectors when there are externalities, and had a major impact on the direction of subsequent research on indeterminacy.

The endogenous growth theory by Lucas and Romer has been in the limelight since the late 1980s. This model is a development of the 1965 Uzawa model. This paper with proves the indeterminacy of the equilibrium growth path of the endogenous growth model without assuming increasing returns in the production function. The condition is expressed using capital intensity. Along with paper 6 above, this paper is regarded as the most important paper on indeterminacy.

This is a two-country international trade model that maximizes utility over an infinite period of time and analyzes dynamic equilibrium paths. It proves that when each country’s industry consists of two sectors and the production function has an externality, the equilibrium is indeterministic under certain conditions on capital intensity. It is regarded as the first paper to prove equilibrium indeterminacy in a two-country dynamic model of international trade.

This paper proves that the per capita income distribution converges to a unique stationary distribution in an optimal growth model under uncertainty. The paper gives a significantly simpler proof than previous methods and weakens assumptions made in previous literature, such as the concavity of the production function, the boundedness of the distribution of productivity shocks, and the Inada condition at 0. The paper is regarded as a breakthrough in the field of optimal problems under uncertainty.

According to the United Nations World Happiness Report, the level of happiness in Japan is not very high, and “”freedom of choice in life”” tends to be low. Since the 1970s, one of the important themes in the study of happiness has been that “”happiness is not necessarily correlated with income level””. We analyzed 20,000 Japanese subjects by asking them various questions in a questionnaire, using income, education, health, personal relationships, and self-determination as explanatory variables. The results showed that “”self-determination”” had a stronger influence than “”income”” and “”education”” as determinants of happiness, following “”health”” and “”relationships””. In Japanese society, where freedom of life choice is considered low, it is noteworthy that people with high levels of self-determination have higher levels of happiness.

In this study, by utilizing data from two surveys conducted in 2016 and 2020, we examined whether or not the changes in the number of hours of science and mathematics classes over the past 50 years have had an impact on R&D activities since becoming a researcher. Specifically, we analyzed the relationship between the number of class hours for science and mathematics in junior high school, which changed every 10 years, and the R&D output after becoming an R&D engineer, such as the number of patent applications, the number of patent renewals, the number of presentations at academic conferences, and the number of papers published in academic journals. Comparing the results of the previous survey with those of the current survey, we found that there was a change in the number of patents between generations that could not be explained by differences in age, and that this change was correlated with the number of hours spent in science and mathematics classes in junior high school.