This paper presents an efficient method of calculating the continuous-time transition path of a heterogeneous-agent economy in steady state in response to a perturbation path (aka MIT shock path) affecting a price or another variable. In other words, it is a continuous-time counterpart of (Auclert et al. 2021). The goal is to introduce a method that satisfies the following criteria to the extent possible: efficiency, simplicity (e.g., no analytical derivative is needed) and general applicability. The method has three main building block: Dirac’s Delta function for Impulses, fast matrix exponentiation methods for forward response path, and a simple linearisation theorem to capture the anticipation effects backwards.