In this paper we study the Nash equilibrium in a smooth public goods economy, described as a non-cooperative game, where the set of players is a mixed measure space of consumers. We assume a finite number of private goods. We show that under certain conditions there exists a unique Nash equilibrium in the economy, where the public goods are produced with a linear technology. Moreover, we discuss the difference in market power between an atomless sector and an atom with the same utility function, and an atom with its split atomless sector, both in a pure exchange economy and a public goods economy.
