Lewis wanted to model development in an economy with a large agricultural sector and a small "modern" sector (e.g., manufacturing). His model was subsequently formalized by John Fei and Gus Ranis, who ended up at Yale. Ranis also made the first formal empirical application, looking at Japan, which around 1960 was still a heavily agrarian developing economy. Below we develop this framework to apply to China. First, let's remind ourselves of our basic growth model, so that we have it always in the back of our mind.
One-Sector Model: Robert Solow, Nobel Laureate - our Cobb-Douglas version
Two-Sector Model: W. Arthur Lewis, Nobel Laureate
The two-sector model is an extension of the standard growth model with which we've worked.
To help understand its structure, think of the starting point as a subsistence economy in which everyone is in agriculture, living a hand-to-mouth existence. For non-agricultural output to increase, then, there has to be a surplus of resources above subsistence, so that not all activity has to focus on agriculture.
For clarity, think of an economy where all manufacturing and commerce is located in a city.
In reality, during the last millennium agricultural by-employment was the norm. Farmers (and their wives) were also weavers or basket weavers or carpenters or raised silkworms. In the US they were shoemakers or clockmakers, while women canned food and sewed garments Indeed, in many places a "putting out" system developed, where a merchant would supply materials to households specialized in various stages of production, who were dispersed about the countryside. This was a viable alternative to gathering laborers at a central workplace, especially as it facilitated switching back and forth from farm tasks to manufacturing as the daily agricultural cycle varied. Of course, it also required high levels of inventory of goods in process, and controlling quality could also be problematic. Furthermore, organizing the delivery and picking up of goods was hard But until recent decades such "protoindustry" was often the dominant organizational form for the production of many goods.
But in order to free up labor for such activities, agricultural productivity has to rise. From a starting point where the entire population is farming full-time, let's say that better implements are invented - a metal-tipped hoe - which allow a field hand to do more work per hour. Then that worker can spend the time that is freed up on other, non-agricultural tasks. Indeed, he or she can even move to the city, to formal industry. Higher productivity allows labor to be pulled out of agriculture, with food flowing to the city as well as labor. It's even better if land productivity rises - more food per hectare - because then some of the land can be devoted to cotton or other non-food crops (mulberry for silkworms to eat; fiber crops for rope & twine; grain for animal feed), which serve as inputs to industry.
Below are a series of queries, to get you to think through the model.
Modified Two-Sector Model