I find very small countries fascinating. They are link small scale representations of the economies we usually study, to a scale that would correspond to an experiment we would want to perform. But these very small countries are not perfect replicas of the larger ones. Because of their size, they are less diversified, need more per capita overhead for governing, their capital accounts are more vulnerable, but they can play very well with tax competition.
Patrice Pieretti, Skerdilajda Zanaj and Benteng Zou, fittingly based in Luxembourg, set up a linear, small open economy where government set tax rates (and thus productivity enhancing public amenities) and household firms locate à la Hotelling around the country border. The result is that there are three possible paths, as so often in dynamic systems: the economy either collapses, explodes or finds its way towards a steady-state along a saddle path.
But do we really learn something from this exercise? The entities here are really P.O. box firms that can move from one country to the next on a whim, except that each firm takes a worker with it. What if there are moving costs? Concave production? People who stay in the country when capital leaves? I bet you would easily find multiple, stable equilibria, some with low taxes, low returns and ovecrowding, some with high taxes, high returns and high amenities. And now things become really interesting and more realistic.