On the Provision of Public Goods in Dynamic Contracts: Lack of Commitment

We study a model of efficient risk sharing between two agents, A and B, who enjoy a non-durable common good. Only agent B can provide the common good whereas agent A can merely contribute indirectly by making transfers to the provider, agent B. We consider self-enforcing equilibria in the absence of commitment. We characterize the Pareto frontier of the subgame perfect equilibrium payoffs. The main results are: First, the consumption of the public good is significantly more stable than are the private consumptions. Second, in the absence of aggregate uncertainty, agents' consumptions are invariant to distribution of income in most cases. In the remaining cases, private consumptions and continuation values covary positively with respective incomes. Third, if some first best allocation is sustainable, the long-term equilibrium converges to the first best allocation. Otherwise, agents' utilities oscillate over a finite set of values. We find that an increase in the provider's deviation lifetime utility shifts the frontier of the set of subgame perfect equilibrium payoffs to exclude the lowest values of the provider (hence the highest values of the other). A decrease in the provider's deviation lifetime utility shifts the frontier of the set to include lower values for the provider (hence higher values for the other)