This paper examines the time inconsistency issues by means of non-coordinated fiscal authority and union. It is found that a rise in the weight assigned to inflation by the central banker depresses the social welfare. However, the social welfare can be enhanced if (i) the fiscal authority raises the weight assigned to the government spending ratio; or (ii) the union raises its concern about inflation. It is also found that there is no policy trade-off between the inflation and output stability. Moreover, in contrast to Rogoff's Proposition, we find that the inflation aversion of the central banker plays no role in the inflation or output fluctuations.