We study the time consistency of optimal monetary policy in a framework akin to the one in [12, Ch. 1] but we assume away lump sum taxation--all taxes are distortionary. Our major result is that under perfect foresight (as defined in [8, 23]) optimal monetary policy is bound to be time inconsistent. The paper is closely related to the previous works of Auernheimer [2], and Kydland and Prescott [15].