Assume that the central bank follows the following monetary policy

(Taylor) rule: (*) = 0.5 ( ) + 0.5 ,

Note that -real interest rate , MPK , inflation , inflation target and short run output

The 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 = ( )

Assume that = 0.5, = = 1, = 2 , and = 2 .

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

(Please show steps in your derivation).

Re-write the AS curve using the formula for inflation expectations. Make sure you write down the AD and AS with the parameter values substituted.

Now assume that in period 0 the economy is in its long-run equilibrium, in particular = 0 and = 0. Note:

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

(b) Assuming that in period 1 the economy is hit by the demand shock = 1 lasting for two periods. Find the values of inflation, short-run output and the ex-post real interest rate in periods 1, 2 and 3.

Explain how the economy will adjust to its long-run equilibrium starting from period 3. Accompany you answer with a well-labelled graph.

(c) Now assume that in period 1 in addition to the demand shock, the economy is also hit by a favourable supply shock = 1 lasting for 1 period. Find the values of inflation, short-run output and the ex-post real interest rate in periods 1, 2 and 3. Explain how the economy will adjust to its long-run equilibrium starting from period 3. Accompany you answer with a well-labelled graph.

(d) Explain in words how your answer to (b) and (c) would change if were lower

Hint: Using AS and AD relations, express short-run output and inflation as functions of the past inflation and shocks.