Before revision: This article describes a simple model of market microstructure which explains a concave price impact . In the proposed model , the local relationship between the order flow and the fundamental price (i.e. the local price impact) is linear,  which makes the model dynamically consistent.
After revision: This article provides a simple explanation of the asymptotic concavity of the price impact of a meta-order via the microstructural properties of the market. This explanation is made more precise by a model in which the local relationship between the order flow and the fundamental price (i.e. the local price impact) is linear, which makes the model dynamically consistent.