Capital Deepening
Begin with capital deepening as a nation approaches its “Steady State” level of capital per worker. There is an increase in capital per worker from K/N1 to K/N2.

Rise in the Relative Wages of Females
With the accumulation of capital, there is a greater demand for mental labor relative to physical labor. This reduces the relative advantage of males in labor markets and the relative demand for female workers increases as does the ratio of female wages to male wages.

Rise in the Labor Force Participation Rate of Females
When the ratio of female to male wages reaches a cretain threshold value, women find it profitable to work outside the home and the labor force participation rate of women begins to rise.

The Effect on Fertility
The increase in the relative wages of women leads to increased participation in the labor force by women. This results in a higher opportunity cost for children since children compete with employment for a mother’s time. Women have fewer children and the population growth rate falls.

A Fall in the Population Growth Rate
A fall in the population growth rate results in a higher “Steady State” capital-labor ratio. This allows room for more capital deepening which will lead to a further increase in the relative wages of women. That will increase female labor force participation rates and reduce fertility and so it goes. This may explain the collapse in fertility in Western Europe and Japan.