The puzzling behavior of inflation in the Great Recession and its aftermath has increased the need to better understand the constraints that firms face when setting prices. Using new data and theory, I demonstrate that each firm's choice of how much information to acquire to set prices determines aggregate price dynamics through the patterns of pricing at the micro level, and through the large heterogeneity in pricing policies across firms. Viewed through this lens, the behavior of prices in recent years becomes less puzzling, as firms endogenously adjust their information acquisition strategies. In support of this mechanism, I present micro evidence that firms price goods using plans that are sticky, coarse, and volatile. A theory of information-constrained price setting generates such policies endogenously, and quantitatively matches the discreteness, duration, volatility, and heterogeneity of policies in the data. Policies track the state noisily, resulting in sluggish adjustment to shocks. A higher volatility of shocks does not reduce monetary non-neutrality and generates slight inflation, while progress in the technology to acquire information results in deflation.