A note on the neo Keynesian Phillips curves with long term growth



This note details the computation of the Phillips curves for prices and wages when there is long term growth on real variables.
With respect to the case without growth, the slope and discount factor include a corrective term. The uniqueness of the solution of a neo-Keynesian model shall then require that the long term growth is smaller than the real interest rate, a condition which should be verified with most calibrations or estimations and is necessary for the intertemporal objective of the firm or household to be defined.
This result has been previously established in the DSGE literature, but is sometimes forgotten by economists who derive neo-Keynesian models with long term growth.


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