Optimal monetary policy has traditionally assigned greater importance to stabilizing prices in sectors with stickier prices, based on multi-sector models assuming full information or exogenous information frictions. This paper challenges the prevailing policy prescription by introducing rational inattention with endogenous information acquisition. Interestingly, the optimal policy assigns a smaller weight to sectors with stickier prices when the cost of information acquisition is sufficiently high. This counterintuitive result arises from the endogenous relationship between firms' attention and nominal rigidities: firms in sectors with more flexible prices pay less attention to macroeconomic conditions. We provide empirical evidence supporting this mechanism.