A Note on the Cost-Benefit Ratio in Self-Enforcing Agreements

Since the analysis of a self-enforcing agreement by Barrett (1994) it has been clear that the ratio between the slopes of the marginal cost and marginal benefit functions is conclusive for stability of self-enforcing agreements. For example Finus and Rundshagen (1998) stated: 'it turns out that all qualitative results depend only on this ratio' as it determines the non-orthogonal free-riding response along Nash reaction functions. This note shows that this 'pure' connection between the cost-benefit ratio and non-orthogonal free-riding response occurs due to the 'anonymous contributions' property of public goods, and in such cases the cost-benefit ratio effect holds regardless the functional form of objectives, the formulation of congestion or the degree of impureness of the public good. Therefore we expect to see the cost-benefit ratio still be the conclusive component also in self-enforcing agreements based on more general functional forms than seen hitherto in the literature.