The Effect of Production Complementarities on Public Good Provision

The following paper examines the individuals’ choice of the ‘local’ public good provision in the network structure framework. To be more precise, the work evaluates what effect the presence of production complementarities has on the individual and aggregate public good provision. The CES (constant elasticity of substitution) production function is used. The utility function of agents depends on both the effort exerted by the agent oneself and the effort level exerted by one’s neighbours. This function was chosen due to trackability which accounts for the variation of the complementarity degree. In this paper the threshold indicating the nature of the game (strategic complements or strategic substitutes) and the condition guaranteeing valid maximization results are determined. The Complete Network case is characterised in detail. Further part of the analysis focuses on the symmetric equilibrium in the regular network, the existence and uniqueness of this equilibrium are analysed. The effects of the increase in the network density on the individual and aggregate effort levels and the utility of agents are evaluated for this case. The description of several network structure examples (circular model and ‘star’ model) are presented. The redistribution of equilibrium efforts occurs if the network density is increased in an irregular network. The final section of the paper proposes a centrality measure which attempts to tie the equilibrium of the game with the network structure. Key words: public good provision, production complementarity, networks, existence and uniqueness of equilibrium, network density, centrality measure