Originally posted by ranjan sinha
That is why this measure would have the exactly opposite effect. The proportion of baby girls would asymptotically go up to a certain percentage above 50% which can be worked out. I leave it for the smarter guys.
Let's assume for simplicity that all babies to be born are born in lockstep on the first day of the year. Let's assume we start with 400 couples and no children, and each viable couple is required to have a child, and let's assume no additional couples come to town.
Year 1: We expect 400/2 = 200 girls and 400/2 = 200 boys to be born.
This leaves us with an expected ratio of 200:200 and 200 remaining viable couples.
Year 2: We expect 200/2 = 100 new girls and 200/2 = 100 new boys to be born.
This leaves us with an expected ratio of 300:300 and 100 remaining viable couples.
Year 3: We expect 100/2 = 50 new girls and 100/2 = 50 new boys to be born.
This leaves us with an expected ratio of 350:350 and 50 remaining viable couples.
And so on throughout the years until no viable couples remain.
It should be clear that at each iteration, the expected ratio of boys to girls is always 1:1. It should also be clear that the assumptions are for simplicity only and could be relaxed without affecting the essence of the above analysis.