Taking the objective inflation strategy as a frame of reference, it is usual to discuss what is most convenient for a society in terms of the degree of hardness or aggressiveness of a monetary authority to defend its inflation target, and the credibility it has among the economic agents. In this document we use a Neo-Keynesian Stochastic Dynamic General Equilibrium (DSGE) model both with rational and adaptive expectations to analyze this question and we also quantify the effects of these two types of authorities on social welfare using an utility function. Our results suggest that the problem that can be derived from a soft authority is to risk the loss of credibility in its (supposed) effort to reach a certain inflation target. In addition, we present and use a solution of our model simple enough to allow other simulations related to this class of models to be implemented in a spreadsheet.