i just need some help for an assignment, any help would be greatly appreciated. thanks

Assume that the central bank follows the following monetary policy (Taylor) rule:

(*) ???????? ???????? − ????̅= ????̅(???????? − ????̅) + ????̅????̃ ???? , ????̅ > 0, ????̅ > 0

The interest rate facing the markets is ???????? = ????????^???????? + f (bar), where f (bar) is financial friction.

AS schedule is represented by the following equation: ???????? = ???????? ???? + ????̅????̃ ???? + ????̅

Inflation expectations are a mixture of backward looking expectations and expectations anchored to the inflation target:

???????? ???? = ????̅????̅ + (1 − ????̅) ????????−1

The IS schedule is ????̃ ???? = ????̅ − ????̅(???????? − ????̅)

(a) Derive the AD curve in the case when the central bank uses the above rule (*). Derive the AS curve.

Assume that n (bar) = m(bar)= 1, **λ(bar)**= 0.2, b(bar)= v(bar)= 1, inlaltion(bar) = 3 and r(bar)= 3. Also assume that in period 0 the economy is in its long-run equilibrium, in particular, a (bar)= 0, o(bar)= 0 and f(bar)= 0.

Note: When doing your calculations in (b)-(c), round up to the third decimal place.

(b) Assume that in period 1 the economy is hit by the demand shock a(bar)= −2 lasting for two periods and there is also financial friction f(bar)= 1 lasting for two periods. Find the values of inflation, short-run output and real interest rate facing the markets in periods 1, 2 and 3. Explain how the economy will adjust to its long-run equilibrium starting from period 4. Accompany you answer with a well-labelled graph.

(c) Now assume that in addition to the demand shock and financial friction from part (b) lasting for two periods, the economy is also hit by the supply shock o(bar)= 2 lasting for 1 period. Find the values of inflation, short-run output and real interest rate facing the markets in periods 1, 2 and 3. Explain how the economy will adjust to its long-run equilibrium starting from period 4. Accompany your answer with a well-labelled graph.

(d) Briefly explain how would your answers to (b) and (c) would change qualitatively if **λ (bar) **were higher.

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