This paper analyses an optimal monetary policy under a non-linear Phillips curve and linear GDP dynamics. A central bank controls the inflation and the GDP trends through the adjustment of the interest rate to prevent shocks and deviations from the long-run optimal targets. The optimal control path for the monetary instrument, the interest rate, is the result of a dynamic minimization problem in a continuous-time fashion. The model allows considering various economic dynamics ranging from hyperinflation to disinflation, sustained growth and recession. The outcomes provide useful monetary policy insights and reveal the dilemma between objectives faced by the monetary authority in trade-off scenarios.
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