Brander-Taylor model and variations

This is the original Brander-Taylor Easter Island model. Brander and Taylor (1998) describes the model as the following: "The paper presents a general equilibrium model of renewable resource and population dynamics related to the Lotka-Volterra predator-prey model, with man as the predator and the resource base as the prey. We apply the model to the rise and fall of Easter Island, showing that plausible parameter values generate a 'feast  and famine" pattern of cyclical adjustment in population and resource stocks.

This model describes the Pezzey-Anderies extension to the Brander-Taylor Easter Island model. In addition to the parameters in the Brandor-Taylor model, Pezzey and Anderies have introduced $tax$ and $h_m$. Pezzey and Anderies (2003) gives the following overview: "We extend the Brander–Taylor model of population and resource development in an isolated society by adding a resource subsistence requirement to people's preferences.

This is a two-sector growth model that couples the dynamics of human demographics and a renewable resource base. The two sectors are agricultural and manufacturing sectors. To capture both the positive (Malthusian) and negative (modern growth) type relationships between population growth and output, it is important to model the shifting composition of output from agricultural to manufacturing as growth occurs.

This model explores the long-term dynamic interaction between the exploitation of natural resources and population growth. This is a variant of Brander and Taylor (1998). The reference article, D'Alessandro (2007), gives the following description of the model. "Two new assumptions are introduced: i) the disaggregation of the ecological complex into two different resources; ii) irreversibility —namely, an inexorable tendency to exhaustion when the renewable resource stock is below a certain threshold".

Most models of Malthusian population dynamics specify logistic growth to a carrying capacity, but the historical record of agrarian societies strongly suggests that repeated cycles of overshoot and collapse (so-called "Malthusian crises") are endogenous to population dynamics (see Nefedov, 2013 for details and citations). In this model, Nefedov (2013) explicitly models harvest surplus production as the carrying capacity of an agricultural population. When population pressure drives the agricultural surplus to zero, a devastating famine occurs, which kills a large proportion of the population. This "Malthusian crisis" then enables renewed population growth in repeated cycles -- producing dampened oscillations. The eventual equilibrium is conceived of as a very rare case, as historical factors (economic, social, and political change) exogenous to the model are expected to repeatedly provoke recurring growth-collapse dynamics.