Gender Income gap: why women earn less than men?

It is widely known that women earn less than men for the same job. Academic research, it is also extensive enough to support the notion that any income difference between men and women ,can be explained by different factors and variables ,each one of them related to one another such as education, family obligations, social backgrounds. But there is one key variable which count deeply in any prospective analysis for future on the job performance, and expected productivity: men can compromise themselves with the labor force more actively than women, because very much of the burden of raising a family( to have a child, initial years of mother attention) looks like a women task, at least those nine months that nature impose upon them to sustain unborn child life. It follows that in such a case, employers discount that expected on the job productivity difference against women(lower for women )usually paying at most one third (30%)less than men .The theoretical support for that decision is in the Marginal productivity theory, which states that expected return for hiring a productive factor must be equal to its cost ,leaving all others variables constant.
No matter the economic justification, the first question arising is :Is it fair for women being paid less, just because the expected productivity is lower when there is a period of time she is out of labor force ?; after all, she might recover that productivity losses by extra working hours. The problem still to solve, is that it is hard to find perfect matching between the worker abilities who is out with the worker abilities who is in, and even though there are head hunters agencies to do the job of finding the best worker alternative, it imply additional cost for firms, such that women must paid that cost with lower wages. In the men ´s case, they paid that cost with variable wages.-
Thus the real issue for women fair wage, is on the greater flexibility of women jobs. This means that they can work at home, which with technological support currently available is quite sure is the way jobs are going to be designed in the future. Alternatively, they can have part time jobs, flexible enough to make sure productivity levels are not severely affected while they are absent . It is all about more flexible labor market.-
Unfortunately , labor market flexibility discussion, has been focused exclusively from the wages levels point of view, specially the wage earned by men. Women wages ,and women labor condition ,seems to be aside of the matter. How can be explain that bias ?.
In European countries, women labor force participation is well above 60 %, So it is in the United States. Advanced countries seems to have become equally inspired, concerning jobs opportunities. In some Latin America countries, women are still considered for domestic activities and the labor force participation is below 50%.These differences, also count as an explaining factor for the bias in the labor market .Women are a minority with a weak capacity of organization and representation, which make them more vulnerable. The measure of that weakness is the income gap .