Consider the following AD-AS model in log-linear form:
AD:yₜ=mₜ-pₜ+mcₜ
AS:yₜ=ȳ+α(pₜ-pᵉₜ)+Vₜ
Sacrifice ratio is the percentage of real GDP that must be forgone to reduce the inflation by 1 percent Where, yₜ is the output in period t, mₜ is the money supply, pₜis the price level, is the natural level of output, pᵉₜ is expected price and a>0 is a constant.
Suppose that expectation are rational. Suppose that mₜ-m+∊ₜ, where ∊ is a random variable while m is deterministic constant.
(a) Derive the equilibrium levels of aggregate output and aggregate prices at time t for this economy.
(b) Find the expression of the expected price level under rational expectations.
(c) Find the effect of monetary policy under the assumption of rational expectations, Explain your results,