Endogenous Growth
The model assumes that as per capita income rises, the rate of growth of GDP also rises. This is because a greater part of income is saved and thus the rate of capital formation increases. Higher per capita income also implies greater human capital and a more receptivity to technological advance. Many of these ideas are embodied in the endogenous growth literature.

Demographic Transitions
It is assumed that up to a certain threshold level of per capita income, households will respond to improved living conditions by having more children (due to earlier marriage and healthier mothers). Also higher per capita incomes mean better nutrition and medical care for children thus reducing the death rate. But beyond a certain level of per capita income, Y/P(2), children become an economic burden and fertility falls. At the same time, it becomes difficult to reduce already low mortality rates. The result is a falling population growth rate.

Multiple Equilibria
The growth rate of per capita GDP can be found by subtracting the growth rate of population from the growth rate of GDP. Hence, per capita income remains the same (there is an equilibrium) when the growth rate of GDP is equal to the growth rate of the population. In this model equilibrium occurs at two different levels of per capita GDP, at a low level , Y/P(1), and at a high level, Y/P(2). Both are equilibria; but only Y/P(1) is dynamically stable.

Low Level Equilibrium Trap
Let us suppose we are initially at a low-level equilibrium, Y/P(1). If through the discovery of new land or a technological advance, per capita income temporarily increases to Y/P(x), the result will be both an increase in the growth rate of GDP and an increase in the growth rate of the population. But the growth rate of population will exceed the growth rate of GDP and GDP per capita will fall until it reaches its old equilibrium level. That is called “The Low-Level Equilibrium Trap”.

Takeoff Into Self-Sustaining Growth
If the external force applied to per capita income pushes it to Y/P(z), the growth rate of GDP will exceed the growth rate of population. This will set off a period of self-sustaining growth in GDP per capita as the gap between the growth rate of GDP and the growth rate of population gets ever wider. This is often referred to as a “takeoff” just as an airplane takes off.

Role of Population Policy
Population policies, such as increasing the awareness and acceptability of family planning, raising the legal age of marriage or increasing the status of women, can shift downward the population growth rate curve making it easier to escape the “Low-level Equilibrium Trap” and reach the “Takeoff” level of per capita income.