This paper addresses the study of the controllability and stability of the equilibrium in economic models which relate the unemployment level to the government expenditure. The interesting cases when the government expenditure is either bounded or a linear function of the national income are specifically considered. The relationships between both variables, namely, unemployment growth level and government expenditure is obtained by considering a Keynesian static model for the national income as well as a differential unemployment-inflation model of Phillips type. Both models are used to derive a new combined one by eliminating the common variable “taxes” which is driven by the investment and government expenditure.