Protein responses to extracellular cues are governed by gene transcription, mRNA degradation and translation, and protein degradation. In order to understand how these time-dependent processes cooperate to generate dynamic responses, we analyzed the response of human mammary cells to the epidermal growth factor (EGF). Integrating time-dependent transcript and protein data into a mathematical model, we inferred for several proteins their pre-and post-stimulus translation and degradation coefficients and found that they exhibit complex, time-dependent variation. Specifically, we identified strategies of protein production and degradation acting in concert to generate rapid, transient protein bursts in response to EGF. Remarkably, for some proteins, for which the response necessitates rapidly decreased abundance, cells exhibit a transient increase in the corresponding degradation coefficient. Our model and analysis allow inference of the kinetics of mRNA translation and protein degradation, without perturbing cells, and open a way to understanding the fundamental processes governing time-dependent protein abundance profiles.