SUMMARYConvexity constraints create problems in the theory of public goods that need not arise in the theory of private goods. This paper discusses these problems, which have not been fully recognized in the standard literature. The dimensionality of public goods becomes critical. A distinction must be made betweenconsumption units, that enter as arguments in utility functions, andproduction units, which enter production functions, and which are directly purchased by the demanders. Standard convexity properties defined on consumption units need not imply convexity properties on production units, given standard properties of utility and production functions. The ambiguities are clarified by reference to the orthodox literature in public goods theory.