Optimal conservativeness in the Rogoff (1985) model : A graphical and closed-form solution

In Rogoff (1985) it is shown that society can make itself better off by appointing a central banker who places an additional weight on in ation rate stabilization relative to employment stabilization. Using an envelope theorem, Rogoff shows that this additional weight must be positive and finite. In this paper, we first use a graphical method to derive narrower boundaries for this extra weight. Then a closed-form solution is given, using Ferrari's method for solving a biquadratic equation. Finally, the comparative static properties of the optimal weight are determined by means of the graphical representation