GORMAN AND MUSGRAVE ARE DUAL An Antipodean Theorem On Public Goods

The theory of public goods would be greatly simplified if it were possible to determine the optimal amount of public goods independently of the distribution of private goods among individuals. Richard Musgrave (1958, 1969) has vigorously argued for treating the allocation and distribution functions of government as distinct. But as Paul Samuelson (1955, 1969) has demonstrated, in general equlibrium different Pareto optima corresponding to different distributions of utility will typically require different quantities of public goods. Therefore an ‘allocation branch’ of the government cannot independently determine a Pareto optimal amount of public goods unless it is informed in advance by the ‘distribution branch’ about the distribution of private goods that would simultaneously be instituted. There is a well-known special case in which allocation and distribution can for practical purposes be treated separately. This is the case of ‘quasi-linear utility’ where preferences of each individual, i, can be represented by a utility function of the form: