This study examines how the size of government and government transaction policies affect the long-run relationship between inflation and unemployment in a search-theoretic framework with explicit microfoundations. Government agents, subject to the same matching technology and other constraints as private agents, are sellers and buyers in the goods market and behave exogenously regarding terms of trade. I show that public agents' transaction policies can change the private agents' incentives, the set of equilibria, and the slope of the Phillips curve. If their terms of trade resemble those of private agents, government agents ameliorate trade frictions for households and firms, thus inducing firms to hire workers. Higher inflation, and thus lower real money balances, discourage firms from hiring workers because a decrease in profits ensues. Thus, higher inflation accompanied by a larger government might induce a lower unemployment rate. If there are multiple equilibria, a sufficiently large government might eliminate the equilibrium accompanied by a high unemployment rate. However, a larger size of government induces a higher unemployment rate if a government agent makes a take-it-or-leave-it offer to a firm and a household. Then, the effect of government moves in the opposite direction.