This paper investigates the time inconsistency issues by considering a bargaining process between a union and a central banker. It is found that an increase in the weight assigned to inflation by the central banker may improve or worsen the social welfare. However, the social welfare is certainly enhanced if (i) the union raises its concern about inflation; or (ii) the bargaining power of the central banker increases. It is also found that there is no policy trade-off between the inflation and output stability. Moreover, we find that the inflation aversion of the central banker plays no role in the inflation or output fluctuations.