Suppose there is a continuum of people who have an ideal government policy 2' distributed uniformly between zero and one. The people need a government to enact a policy - and they can either choose a single government or split into two regions (L and R) - each with their own policy 9. Each government has a per person cost of C to operate. We are not considering the case of more than 2 governments. See the figure below for a graphical representation. {1 \" Centralized 1 Region L Region R l) Decentralized I Now the utility of a person with preferences 1' is u', {lr_t % J. ) It". under the central solution. This is because their utility decreases with the absolute distance between g=0.5 and their person preference 1'. Their utility under decentralization is