Population Fallacy

In a far far land, there was a long war. Many men died in that war, and when it was over, there were not enough men to marry all the women in the kingdom. The king wanted to balance between men and women, so he issued an order that any woman who gives birth to a girl, will stop having children after that. Whereas, if the woman delivers a male child, she is permitted to go for another try. His theory was that there would be several families with one girl and one or no boys, but there would also be families with several boys and only one girl, and so after a few years the number of males in the kingdom would increase. What was wrong with the king's plan and why won't it work?

Answer:

Assuming that the birth rate between boys and girls is 1:1, At first, half the women would give birth to boys, and half would give birth to girls. Then, only one half would be able to continue having children, so half of them will have boys, and half will have girls, and so on...As you can see, the number of boys and girls remains the same.