Because the productivity term, q, enters symmetrically in equations 1 and 2, it does not appear in equation 3. That is, the inflation rate in this model is unaffected by the growth rate of productivity or any change in the growth rate. Equation 3 can be solved for the value of the NAIRU (U*), by setting p = pe and solving for U.
The resulting expression, given in equation 4, is the level of the unemployment rate consistent with any steady rate of inflation, once inflation expectations have converged to this steady rate. In this specification, there is no distinction between short-run and long-run NAIRUs. Equation 1’ presents the key modification of this simple model that caused an acceleration in productivity to have an effect on inflation.