Power laws and home
Great questions in demographics and geography: "What's the country with the biggest drop-off in population between its first city and its second city?" It would be interesting to see this graphed for a large number of countries. There's a power law to the size of cities in many or most places, to be sure. But it would be worthwhile to investigate whether the countries with flatter relationships between their 1st- and 2nd-tier cities perform better, economically, than places where all the action is found in one place.
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From a development standpoint, this is a really important question: Can more be gained by putting all of a country's eggs in one basket and leaving some places behind? Or is that such a morally unacceptable choice that no country should choose to do it, even if that comes with a net deadweight loss to society as a whole. And the same questions that make sense for a country make sense for a state, too -- should a state like Iowa just put everything into making Des Moines and Cedar Rapids grow as much as possible? Or would the returns be higher to invest in growth in Jefferson and Oskaloosa and Clinton, too?