We show that the main empirical findings on the impact of a sequence of
transactions on prices of financial assets can be recovered within a
surprisingly simple model with fully Bayesian market expectations. This
includes {\em i)} the square-root behavior of the expected price variation with
the total volume traded, {\em ii)} it's crossover to a linear regime for small
volumes, and {\em iii)} the impact decay back to equilibrium, after the
sequence of trades is over. The simplicity of this derivation lends further
support to its robustness and universality, and it sheds light on its origin.
In particular, it suggests that the square-root impact law originates from the
over-estimation of order flows originating from meta-orders.