In fluid mechanics, resolvent analysis is commonly used to predict second-order flow statistics from measured mean fields. Here, we focus on a different objective: understanding how statistically steady flows respond to external forcing. To do so, we introduce a transfer function called the mean resolvent operator. Its definition is rooted in linear response theory from statistical physics, where the same concept is known as susceptibility. The mean resolvent operator predicts the ensemble-averaged linear response to forcing and, as such, it provides the best linear time-invariant approximation of the underlying unsteady flow dynamics. Since this operator is effectively infinite-dimensional, its input-output analysis must rely on time-stepping methods. We accordingly develop an adjoint-free approach based on projecting the forcing input onto a low-dimensional subspace. The method is applied to periodic and stochastic jet flows, enabling partial validation against adjoint-based approaches when available. The results highlight major shortcomings of the standard mean-flow resolvent for predicting flow receptivity and open the door to mean resolvent analysis of more complex chaotic flows.