This paper describes the optimal level of government purchases in the presence of unemployment. The theoretical framework is a general-equilibrium matching model in which government purchases are valuable. When the unemployment gap is zero, the conventional Samuelson formula is valid. Otherwise,...

This paper extends Samuelson's theory of optimal government purchases by considering the contribution of government purchases to macroeconomic stabilization. We consider a matching model in which unemployment can be too high or too low. We derive a sufficient-statistics formula for optimal...

This paper describes the optimal level of government purchases in the presence of unemployment. The theoretical framework is a general-equilibrium matching model in which government purchases are valuable. When the unemployment gap is zero, the conventional Samuelson formula is valid. Otherwise,...