A three-piece set for understanding the money circulation

In this article, we introduce a three-piece set for grabbing the money circulation. The three-piece set is the circular flow diagram, a definition of nominal GDP, and the quantity equation (Fisher's equation of exchange). These items are independent in the modern economics. We integrate them for the money circulation. As a conclusion, we obtain M=G+I=S+T and V=Y/(G+I).

The contents of this article are as follows.

• Description of the 3-piece set.
• Integration of the 3-piece set.
• Two money flows.
• A money circulation from nominal GDP.

Quantitative Understanding of the Trickle-Down Hypothesis

Quantitative Understanding of the Trickle-Down Hypothesis (Amazon Kindle)

We obtained quantitative result that is the exact opposite of the trickle-down hypothesis.

For studying trickle-down, we performed an estimation of the circulation of the money flow only between business and households. Business is divided into small, middle, and large companies, and households are divided into low-, middle-, and high-income earners. In this estimation, we obtained numbers of small and middle companies that a high-income earner needs for trickle-down. Free parameters of our estimation are the income ratio and the number ratio of the low-, middle-, and high-income earners in a large company.

Football Tactics 8 Analysis of Open Tracking Data

The theme on this book is an elementary analysis of football tracking data. Analysis programs made by the author are opened.

The open tracking data analyzed in this book is observed in a mini-game format (8 vs. 8, a half coat, 30 minutes half). The author is grateful to Dr. Mutschler and to the committee of The International Conference on Distributed Event-Based Systems held in 2013.

In chapter 3, described is an elementary analysis. Several steps are necessary to apply analysis results for coaches' decisions. An attempt for such steps is three indexes for detecting off-the-ball movements in chapter 4. In chapter 5, the author described restrictions of the Voronoi diagrams in the football analysis. The Voronoi diagrams in the football games show consistent personal areas, at a glance. However, one must understand assumptions that the Voronoi diagrams include in the football analysis.