Galor and Weils article provides a mechanism by which one can examine the links between fertility and growth. In order to achieve this they have combined the prevalent theories of growth and family economics to formulate their model. The former theory ties in with neo-Malthusian ideas and identifies the negative affects of population growth on the level of capital per worker, as capital will be spread out amongst increasing numbers of humans. Whilst the later suggests that changes at the household level create a reduced fertility as wealth increases. The ensuing model that they develop is based upon the basic assumption that there are two types of people, men and women. Men and women are considered identical in childhood and old age, but as adults they differ in terms of their ability to earn wages in the labor market. This difference stems from the basic physiological difference between the genders, that gives men greater strength, and so they can contribute more physical labor. This sets the initial stage for low output and high fertility.
They demonstrate that this situation is changed by a positive feedback loop that generates the demographic transition, and this is initially set in place by an initial increase in capital. There are three main steps to this process. First there is an increase in capital per worker, and due to capital being more complimentary to womens labor input than to mens, this raises the relative wage of women. This increase in womens relative wages has a direct impact on their fertility, as now the cost of having children rises more than household income, as they would gain more by participating in the labor force. The result of this lower fertility will mean that the level of capital per worker will rise, and in this way the positive feedback loop is established sustaining a rapid decline in fertility and increased output growth. In this way economic growth is negatively correlated with fertility, due to the substitution affect. Women are substituting their ability to have children, in order to participate in the labor force.
When applied to society one sees a system that is characterized by multiple steady state equilibriums, and this acceleration in the rate of growth is associated with women joining the labor force. The point being that as long as women do not participate in the labor force the rate of growth of output will decline over time. This leads to a stagnating society faced with low output and high fertility.
The key variables of Galor and Weils model involve the positive effects of capital accumulation on womens relative wages, and the negative effect of womens relative wages on fertility. For the former they saw it as a causal relationship and subsequently formulated a production function that would affect capital. They considered the later to be a simple demand model, whereby increasing the wages for women in turn raised the price of having children proportionally more than they raised the couples full income.
It is through these processes that Galor and Weil demonstrate how growth, via changes in womens relative wages, affects household decisions concerning fertility and female involvement in the labor force. The net result of these changes is increased output.