Summary: We provide an economically sound micro-foundation to linear price impact models, by deriving them as the equilibrium of a suitable agent-based system. In particular, we retrieve the so-called propagator model as the high-frequency limit of a generalized Kyle model, in which the assumption of a terminal time at which fundamental information is revealed is dropped. This allows to describe a stationary market populated by asymmetrically-informed rational agents. We investigate the stationary equilibrium of the model, and show that the setup is compatible with universal price diffusion at small times, and non-universal mean-reversion at time scales at which fluctuations in fundamentals decay. Our model suggests that at high frequency one should observe a quasi-permanent impact component, driven by slow fluctuations of fundamentals, and a faster transient one, whose timescale should be set by the persistence of the order flow.