This paper attempts to build a narrative on the developments of macroeconomics in the postwar period through the debates about the so called “natural rate of unemployment”. The definitions of the concept in the seminal papers of Milton Friedman (1968a) and Edmund Phelps (1967, 1968) and its origins in their previous works will be presented - as well as the political-economic context of the U.S., in the late 1960’s. Emphasis will be given to the further development and stabilization of the concept by Robert Lucas, especially to his interaction with Edmund Phelps. This paper will argue that Lucas’s research on the topic was personally and theoretically connected to the research of Phelps, who was his true interlocutor in the subject, in spite of Lucas’s recurring references to Friedman. The theoretical connection with Phelps would be established through the general equilibrium approach to the tradeoff between inflation and unemployment, while their personal interaction can be verified through their vivid correspondence. Lucas (1972a, b) would eventually use the general equilibrium framework with rational.