## Malthusian regime: The Basic Structure of the Model

In the Modern Growth regime, technology and output per capita increase rapidly, while population growth is moderate.

The rest of this paper is organized as follows. In Section 2, we formalize the assumptions about the determinants of fertility and relative wages presented above, and incorporate them into an overlapping generations model. Section 3 derives the dynamical system implied by the model, and analyzes the evolution of the economy along transitions to the steady state. Section 4 concludes by discussing possible extensions of the model.

The Basic Structure of the Model

Consider a small, open, overlapping-generations economy that operates in a perfectly competitive world where international capital movements are unrestricted and economic activity extends over infinite discrete time. In every period the economy produces a single homogeneous good that can be used for either consumption or investment. The good is produced using physical capital, efficiency units of labor, and land.

In every period the three factors of production are supplied in competitive factor markets. The supply of capital and labor are endogenously determined while the supply of land is exogenous and fixed over time. The stock of physical capital in every period is given by the sum of the economy’s aggregate saving and international borrowing, net of the aggregate value of land purchases. The number of efficiency units of labor is determined by households5 decisions in the preceding period regarding the number and level of human capital of their children.

Production of Final Output

Production occurs within a period according to a constant-returns-to-scale neoclassical production technology that is subject to endogenous technological progress. The output produced at time t, Yu is

where Kt: Ht, and X are the quantities of capital, efficiency units of labor, and land, employed in production at time t, a € (0,1) and f3 G (0,1) are parameters which are fixed over time, and Bt> 0, represents the endogenously determined technological level at time t. The production function is therefore strictly increasing and concave, satisfying the neoclassical boundary conditions which assure the existence of an interior solution to the producer’s profit-maximization problem.

Producers operate in a perfectly competitive environment. Given the wage rate per efficiency unit of labor, the interest rate on capital, and the rent on land, producers determine the level of employment of labor, capital, and land so as to maximize profits. Suppose that world interest rate is constant at a level r > 0. Since the small economy permits unrestricted international lending and borrowing, its interest rate will also be r. The amount of capital employed in production at time t is therefore a function of BtyHt, X, r, a and (5. Substituting the level of capital into the production function yields: payday loan relief

where the state of technology at time t is represented by the technological parameter, At = = [(^/г)^/(1″^)Б/1/(1_^)]1/(1”а).