Равновесные расположения центров благ по городу
We consider a situation in which the municipal government has to open n cultural centres in a city. The task is to subdivide efficiently the city into n districts D i and open a center at the geometric median m(D i ) of each district. We assume that the density ρ of the population in the city is constant ρ = 1. If each inhabitant of district D i living at point x follows the prescriptions and visits the centre m(D i ), his profit is λ i /area(D i )−d(x,m(D i )) where area(D i ) is the area of D i that coincides with its population and λ i is a positive weight representing the utility of the center. We show that the government can subdivide the city into a prescribed number of districts so that the optimal strategy of each inhabitant is to visit the center of his own district.