This research paper presents a new theoretical explanation for Zipf's law (power law) in the distribution of firm sales and individual incomes.
Existing theoretical models have a problem in that the time required for firms to become giants or individuals to become super-rich is excessively long compared to what is observed in empirical data. Additionally, while existing models predict that Zipf's law holds primarily for older firms and individuals, actual data shows that Zipf's law is also observed in the size distributions of younger firms and individuals, creating a contradiction.
This study focuses on the heavy-tailed nature of the growth rate distribution for firm sales and individual incomes. This characteristic reveals that the growth dynamics of sales and incomes are characterized by rapid growth over short periods. In other words, giant firms and the super-rich emerge not from long-term gradual growth, but as a result of rapid growth in short periods in the past.
This new explanation resolves the contradictions between traditional theoretical models and empirical data. Zipf's law reflects the characteristics of growth dynamics common to both firm sales and individual incomes, demonstrating that rapid growth is the essential mechanism for the formation of Zipf's law.
The article suggests that Zipf's law is not merely a statistical regularity, but a universal law that reflects the fundamental characteristics of the growth process of economic agents.