Question 1: Assume that Australia is hit by the arrival of "some bad news" that will make the economy less productive starting 5 years in the future.  

(a) Analyse the effect of this news today on the real wage, unemployment, output, and prices in the short run and in the medium run using a standard dynamic stochastic general equilibrium (DSGE) model (with flexible wages and sticky prices).

(b) How would your answer change if there are flexible prices?

(c) Draw the AS/AD graph associated with this shock.

(d) Plot the impulse response function of GDP to this news, according to the model. You do not need to worry about numbers on the vertical axis; just show the general pattern as the economy moves after the shock and eventually returns to steady states.

Question 2: Assume that the central bank follows the following simplified version of the Taylor rule:

R_t^CB - r^- = n^-Y^~t    n- > 0

R_t = R_t^CB + p^-

where r^- and Y^~_t are the marginal product of capital and short-run output respectively, n^- is a parameter. R_t^CB is the short-term real interest rate controlled by the central bank, R_t is the real interest rate that the private agents face, and p^- is the risk premium.

(a) First, assume that the risk premium p^- = 0. Draw an IS-MP diagram but instead of the usual MP curve, graph the monetary policy rule. You might label this curve MPR for the simplified Taylor rule.

(b) Now consider the effect of a positive aggregate demand shock in the IS-MPR diagram. Compare and contrast the effect of this shock on the economy in the standard IS-MP diagram versus the IS-MPR diagram.  Explain the "crowding out" by using the results.

(c) Now consider the effect of an increase in risk premium from 0 to some positive value in the IS-MPR diagram. Compare and contrast the effect of this risk premium shock on the economy in the standard IS-MP diagram (without policy response to the shock) versus the IS-MPR diagram.  Is there a difference?

(d) If the central bank follows the simplified Taylor rule, how would the AD curve look like? Explain.  Now show the effect of the risk premium shock on the AS/AD diagram in the period when the shock hits. Is this consistent with what you had in the IS-MPR diagram?

Question 3: Assume that the central bank can directly observe the aggregate demand shock and follows the following monetary policy rule:

(*)          R_t - r^- = m^-(π_t - π^-) + n^-Y^~_t + z^-a^-,   m^- > 0

Note that, R_t, r^-, π, π^-, and a^- are defined as in lectures. m^-, n^- and z^- are parameters.

(a) Derive the AD curve in the case when the central bank uses the above rule. What would be sensible restrictions on parameter z^- (possibly depending on other parameters)?  If you were a central banker which value would you choose for z^- (again this can depend on other parameters)? Why?

AS schedule is represented by the following equation:

π_t = π^e_t + v^-Y^~_t + o^-

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

π^e_t = λ^-π^- + (1 - λ^-)π_t-1

The IS schedule is     

Y^~_t = a^- - b^-(R_t - r^-)

Now assume that b^- = λ^- = 0.5, m^- = v^- = z^- = 1, π^- = 2, r^- = 3 and n^- = 2. Also assume that in period 0 the economy is in its long-run equilibrium, in particular a^- = 0 and o^- = 0.

Note: When doing you calculations, round up to the second decimal place. 

(b) Assuming that in period 1 the economy is hit by the demand shock a^- = 3 lasting for one period, find the values of inflation, short-run output and the real interest rate in periods 1 and 2. Explain how the economy will adjust to its long-run equilibrium starting from period 3.  Accompany your answer with a graph.

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

(d) Briefly explain how would your answer to (b) and (c) would change qualitatively if λ^- were higher.