The Benefit Rule for a Pure Public Good in the Presence of a Social Security Program

Abstract

public good whereby the sum of the marginal rates of substitution between the public good and some numeraire private good for all agents who benefit frqm the public good must be equal to the corresponding marginal rate of transformation, i.e., XMRS = MRT. This rule can be implemented in a decentralized fashion if the government has enough financing instruments available, e.g., person-specific lump sum taxes and government debt. However, whether or not the first-best benefit rule can be implemented when the government only has control over relative prices is an open issue. Pigou (1947), Diamond and Mirrlees (1971), Dasgupta and Stiglitz (1971), Atkinson and Stern (1974), Pestieau (1974), and more recently, Wildasin (1979, 1984, 1985), King (1986), and Batina (1987) have considered the effect of decentralizing the government's policy on the optimal first-best benefit rule for a public good. It is generally true that if the government cannot completely control the economy because of a lack of policy instruments, then the first-best benefit rule governing the provision of the public good must be modified as a result.