Modeling Malthusian Dynamics in Pre-Industrial Societies

The discussion about the Malthusian character of pre-industrial economies that has arisen in the recent years extensively uses simple mathematical models. This article analyzes some of these models to determine their conformity with Malthusian postulates. The author suggests two models that are more adequate for the description of the Malthusian patterns. Until recently, most economic historians were inclined to think that the medieval economies in Eurasia had a Malthusian nature (Allen 2008: 951). However, following the publication of Lee and Anderson's work (Lee and Anderson 2002), many came to dispute this opinion. A discussion has arisen about how the available data confirm the Malthusian relationship between demographic dynamics and consumption (i.e., real wages). This discussion has largely involved simple mathematical models of the Malthusian economy. In 1980, Lee published the first and most popular of these models. This model describes the relationship between the real wage, wt (consumption), and labor resources, Nt (population), using the following equation: