In the following model, (e) is inflation (expected inflation), () is output (potential), and m is the rate of growth of the money supply:

= ()+

=1+(1)1

1=(1)

,, are all positive. is less than one.

1. Find the characteristic equation and comment briefly on its possible properties. (30)
2. Does this model show a long-run trade-off between inflation and unemployment? Explain your answer in terms of the model's coefficients. (10)