On integrating spatial and temporal considerations into the economic theory of clubs

Two models were constructed which provide examples of how spatial and temporal considerations might be integrated into the economic theory of clubs. The first model deals with fire suppression districts, and the second model with man-made recreational facilities such as tennis courts;The model of fire suppression districts considers the effects of detection and reporting time, queuing time, travel time, and service time on expected utility. In particular, the impact of changing district size on queuing and travel time was assessed. Equilibrium district sizes were determined for each level of cost per-person, and then a particular level of cost per-person was chosen based on the median voter theorem. A restricted form of the model which assumed risk neutrality and a linear relationship between fire damage and time was constructed, and simulations of this model were run. The simulations indicated that the expansion path was such that at higher levels of cost per-person, the absolute size of the equilibrium district declined. The simulations were also used to examine the effects of changes in population density, service time, alarm frequency, wealth, and costs;The recreational facilities model incorporates two of the same considerations as the fire suppression model, namely, queuing and travel time. However, it was recognized that while everyone has a potential need for fire suppression services, individuals differ considerably with respect to their desire for recreational facilities. Utility was defined as a function of time spent at the recreational facility, other leisure time, and all other goods. Equilibrium sized districts for each level of cost per-person were determined, and again the median voter theorem was invoked to obtain an equilibrium level of cost per-person.