Final answer:
The rapid increase in average world income coincided with the Industrial Revolution, which drastically shifted economies from agriculture to manufacturing, leading to growth in population and per capita income but also to global inequality.
Step-by-step explanation:
The period when average world income began to increase rapidly was during the Industrial Revolution. This significant phase in history modernized the world and marked a transformation from agrarian economies to manufacturing powerhouses. Between 1800 and 2000, there was a significant surge in the world's population, which grew sixfold, alongside a tenfold increase in per capita income. The Industrial Revolution, which took place from the late 18th to early 19th centuries, had a significant impact on the world's economy. It marked a transition from handmade and cottage industry production to machine-based manufacturing in factories.
This shift led to increased productivity, trade, and economic growth, resulting in a rapid increase in average world income.Countries such as Japan, South Korea, and China have exemplified this growth in the recent half-century. The shift towards manufacturing, increased worker productivity, and the development of market institutions contributed massively to what economists call modern economic growth. However, the Industrial Revolution also generated increasing inequality among nations, with developed economies accelerating much faster than those in regions such as Africa or Asia.