Suppose someone invents an inexpensive and reliable way in which parents can choose the gender of their offspring. From the economic standpoint, this represents an increase in quality—you get a child of your preferred gender instead of a fifty-fifty chance—at no significant increase in cost. Increased quality at constant cost corresponds to decreased cost at constant quality; you are now getting more for your money. Lowering the cost of something increases the quantity demanded.
Do you conclude that, as a result of the new invention, the birth rate goes up? If not, why not? Are children Giffen goods?
Hint: I am fond of the sort of mathematical puzzle which consists of a proof of something obviously false, for example that two equals one; the puzzle is finding the mistake in the proof.