Population growth,soil fertility,and agricultural intensification

This paper presents a renewable resource model of soil fertility with a nonconvexity in the net benefit function. In this setting, recurring cycles of cropping and fallow can be the optimal soil management strategy. The model is used to illuminate the Boserup discussion of agricultural development, in which population growth leads to agricultural intensification, defined as an increase in cropping frequency. Previous formal models of the Boserup hypothesis focus on the land-labor ratio rather than cropping frequency and have not directly incorporated soil fertility dynamics. These models assume a convex production technology and are not optimistic about the prospect for agricultural development without technological progress. This paper explicitly models soil fertility dynamics and demonstrates that nonconvexities in the production technology are an important feature of the use of long fallow periods for soil management. As population grows, and the demand for food increases, the importance of the nonconvexity diminishes and more frequent cropping becomes economical. Given a nonconvexity in the production technology, it is possible, though not necessary, that average labor productivity increases with agricultural intensification. Thus, it is possible to reconcile the greater labor requirement of intensive farming with an increase in average labor productivity. In addition, Boserup argued that a larger and denser population facilitates the development of economic and social infrastructure which improve agricultural productivity.