In the following model, () is inflation (expected inflation), () is log of output (output trend), and is the rate of growth of the money supply:

=()+

=1+(1)1

=(1)

, , are all positive. is less than one.

(a) Briefly explain each equation.

(b) Find the equilibrium for inflation and output.

(c) Find the characteristic equation and comment briefly on its possible properties.

(d) Does this model show a long-run trade-off between inflation and output? Explain your answer in terms of the model's coefficients.