This book focuses on the Frobenius theorem regarding a nonlinear simultaneous system. The Frobenius theorem is well known as a condition for a linear simultaneous system’s having a nonnegative solution. Generally, however, the condition of a simultaneous system, including a non-linear system’s having a nonnegative solution, is hardly discussed at all. This book, therefore, extends the conventional Frobenius theorem for nonlinear simultaneous systems for economic analysis.  Almost all static optimization problems in economics involve nonlinear programing. Theoretical models in economics are described in the form of a simultaneous system resulting from the rational optimization behavior of households and enterprises. On the other hand, rational optimization behavior of households and enterprises is, mathematically speaking, expressed as nonlinear programing. For this reason it is important to understand the meaning of nonlinear programing. Because this book includes explanations of the relations among various restrictions in a nonlinear programing systematically and clearly, this book is suitable for students in graduate school programs in economics.

This book is a work that focuses on the forest environmental tax. Forest resources have played a major role in preventing global warming by absorbing carbon dioxide and supplying oxygen. However, global economic growth has adversely affected the global environment and has exacerbated global warming due to excessive consumption of forest resources. The functions or "services" of forests are diverse, but the interest of the citizenry in forest cultivation is scarce since forests are public goods. Concurrently, Japanese forestry, which has played an important role in forest conservation, is steadily declining, and it is no longer possible for private forest operators to maintain the forest environment. Therefore, in order to realize sustainable economic growth, it is necessary to formulate policies for the conservation of appropriate forest environments. Forest conservation is an especially important policy issue for Japan, where two-thirds of the country is forested. In Japan, a forest environmental tax is being introduced as a forest conservation policy. As of 2021, the forest environmental tax has already been introduced in about two-thirds of the prefectures and soon will be introduced as a national tax. In this book, the significance and issues of the forest environmental tax will be sorted out, and the status of the introduction of the forest environmental tax in Japan will be compared with that of other countries. In addition, there is additional material regarding the water source conservation fund in Toyota City, Aichi Prefecture, a system similar to the forest environmental tax.

This monograph presents potential remedies for some of the current environmental issues in developed countries in a theoretical or empirical manner with the interdisciplinary approaches of economics, statistics, and engineering. The book illustrates effective economic and environmental policies for environmental challenges and factors where corrective policies to date may have failed. The importance of this essential book has is related to the transition in the major concerns of the people or governments in developed countries shifting from economic growth to the stability of life and environmental preservation as their economies have matured. The environmental issues dealt with here include forest environment tax introduced as part of local taxes, air pollution reduction policies for mobile emission sources, introduction of renewable energies and power fuel cell technology, the mechanism of city agglomeration and dispersion, and measurement of environmental sustainability. In analytical methods, some research employs theoretical approaches such as the mathematical economic model or nonlinear dynamic model. Other analyses are implemented with empirical or statistical tools such as the long-run general equilibrium model, the input-output model, and the dynamic optimization model, among others.