On the Existence of an Equilibrium in Models of Local Public Good Use by Cities to Attract the Creative Class

We analyze a stylized model of competition between two cities that use a local public good(LPG) to attract members of the creative class. The creative class consists of artists and engineersand we study the behavior of a representative artist and an engineer. The level of the LPG in eachcity is determined by majority voting of the two representative creative class members. If bothrepresentative members choose to live in the same city then the LPG provision is the average ofthe preferred quantities of the two members. In this setting, we perform three tasks. First, weascertain the preferred quantity of the LPG for the representative artist and the engineer. Second,assuming that the representative artist and the engineer accurately predict the outcome of living ina particular city, we describe a scenario in which there is no equilibrium in our model. Finally, weshow that if the representative artist and the engineer treat the LPG provision levels in each city asexogenous then an equilibrium does exist in the model