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 engineers and we study the behavior of a representative artist and an engineer. The level of the LPG in each city is determined by majority voting of the two representative creative class members. If both representative members choose to live in the same city then the LPG provision is the average of the preferred quantities of the two members. In this setting, we perform three tasks. First, we ascertain 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 in a particular city, we describe a scenario in which there is no equilibrium in our model. Finally, we show that if the representative artist and the engineer treat the LPG provision levels in each city as exogenous then an equilibrium does exist in the model.