In an article in this journal, Martin McGuire [4] presented a public goods model based upon voluntary contributions and Cournot interaction. His model indicated that the aggregate provision of the public good could be either positively or negatively related to group size; the exact relationship depending upon the slope of the individual reaction functions. This conclusion was generated by examining successive equilibrium solutions to the Cournot model. There was very little attempt made to determine whether these were stable or unstable equilibria; although the reader was correctly warned that, 'when the new Cournot equilibrium is unstable, it may, for reasons of dynamic behavior, never be reached.'
The stability conditions for a discrete time adjustment model will be presented in this paper. Except for the explicit consideration of a dynamic adjustment process, the model contained in this analysis will be identical to that in Martin McGuire's presentation. An examination of the stability conditions will provide the following insights: (1) the aggregate provision of the public good is unstable for large group sizes; and (2) in many cases the stability conditions are only satisfied when the aggregate provision of the public good is positively related to group size.
The analysis will follow McGuire's format by first examining a community with identical tastes and resources, and then investigating a community with heterogeneous tastes and incomes.