Optimal Monetary Policy under Rational Inattention and a Cost Channel

This paper examines how monetary authorities should balance inflation and output stabilization when firms face rational inattention and working capital requirements. In our environment, monetary expansion both stimulates aggregate demand and lowers marginal costs, yet rational inattention endogenously determines the net transmission: limited information capacity strictly governs the policy sensitivity of the price level. We identify an endogenous regime-switching property in optimal policy: as information capacity improves, the focus shifts from price to output stability, a transition strictly accelerated by the cost channel. For natural rate shocks, this implies a shift from aggressive to restrained policy responses. For markup shocks, the cost channel generates a supply-side subsidy that makes an accommodative policy optimal in high-information environments, overturning the conventional "lean against the wind" prescription. Furthermore, we establish that financial frictions amplify welfare losses from natural rate disturbances but can endogenously mitigate the costs of markup shocks. We analytically and numerically confirm the robustness of these mechanisms under elastic attention, generalized signal structures, and persistent shocks.