[The non-existence of an inflation-output trade-off under the rational expectations hypothesis as the cause of the steady state situation. Overtaking attempt]

This article tries to prove the existence of an inflation-output (unemployment) trade-off, at least in the long-run, under a context of the rational expectations hypothesis REH, which makes it possible to overcome the Lucasian steady state situation. This existence of trade-off is due to the importance of saving and the accumulation of capital over time, as well as to unexpected economic policies by the agents, which is essential for economic growth. To achieve this objective, we will expose the unrealistic aspect of REH which avoids any inflation-output (unemployment) trade-off in the short-run and the long-run, and consequently it leads the economy to an infinite steady state situation. Our work undertakes a personal philosophical and mathematical approach, which finds its origins in the pioneering works of economic growth theory, namely those of Harrod, Domar and Solow. We have tried to propose a solution for overcoming the steady state à la Lucas.