The University of Sydney
School of Economics
ECON6002
Practice Final Exam
The actual final exam will be 120 minutes (+30 minutes upload time) during the uni-
versity exam period. The exam will be open book. The practice final exam is 120
minutes (+30 minutes upload time).
Examinable Material and Expectations:
1. The final exam will cover material from the whole course, although focusing mostly on material
since the mid-semester test. Anything covered in the lectures, in the tutorials, or in the
problem sets is examinable.
2. I will provide relevant formulas such as production functions to be used in answering a question
(see questions below to see examples of what sort of material will be provided and what you
might be assumed to know).
3. You will be expected to understand the “economics” behind any equations provided.
4. In answering questions, be precise, showing all of the steps, and indicate if you are making
any assumptions along the way.
Practice Final Exam Questions:
1. Consider the role of nominal rigidities and market imperfections in explaining the effects of
monetary policy shocks.
(a) Explain whether you agree or disagree with the following statement: “Nominal rigidity
can cause monetary policy shocks to have sizeable real effects on output.” (3 points)
In the Lucas imperfect-information model the aggregate demand curve is: y = m− p and the
aggregate supply curve is: y = 1
γ−1
σ2z
σ2z+σ
2
m
(p− E[p]) where 1
γ−1 > 0 is the elasticity of labour
supply with respect to the real wage, σ2z > 0 is the variance of the good-specific taste shock,
σ2m > 0 is the variance of the aggregate demand shock.
(b) Is there a distinction between the aggregate demand curve and the good-specific demand
curve? Explain how different factors influence the good-specific demand curve in the
Lucas imperfect-information model. (3 points)
(c) Suppose that the volatility of aggregate demand shocks σ2m increases relative to the
volatility of good-specific taste shocks σ2z . How would the slope of the aggregate supply
curve change? Explain by providing an economic interpretation. (3 points)
(d) Discuss the validity of the following statement within the context of the Lucas imperfect-
information model: “Money growth, whether observed by economic agents or not, raises
the price level which consequently translates into higher output.” (3 points)
2. Consider the IS curve and New Keynesian Phillips curve:
ỹt = Et[ỹt+1] −
1
θ
rt
πt = βEt[πt+1] + κỹt + u
π
t
where uπt = ρπu
π
t−1 + e
π
t is a cost-push shock. Assume that there is no serial correlation so
that ρπ = 0. The solution for the model takes the form ỹt = aπu
π
t , πt = bπu
π
t and rt = cπu
π
t .
Suppose that monetary policy responds to expected inflation and and expected output gap
such that: rt = φπEt[πt+1] + φyEt[ỹt+1].
(a) Use the method of undetermined coefficients to solve for aπ, bπ and cπ and explain how
a positive cost-push shock affects the output gap, inflation, and the real interest rate.
(4 points)
(b) How would an increase in φπ affect the response of the real interest rate and inflation to
an unfavourable cost-push shock? (2 points)
Assume instead that monetary policy responds to current inflation and current output gap
such that: rt = φππt + φyỹt.
(c) Use the method of undetermined coefficients to solve for aπ, bπ and cπ. What is the
effect of a positive cost-push shock in this case? (4 points)
(d) How would an increase in φπ affect the response of the real interest rate and inflation to
an unfavourable cost-push shock? (2 points)
3. Consider the time-inconsistency model of monetary policy. The central bank has a loss
function that is different to the social loss function. In particular, the central bank, subject
to an aggregate supply constraint, sets inflation π in order to minimize:
LCB =
1
2
(y − y∗)2 +
1
2
a′(π − π∗)2
where π∗ is the central bank’s inflation target, y∗ is socially optimal output, and a′ > 0
reflects the central bank’s preference for stabilizing inflation. The social loss function is:
Lsociety =
1
2
(y − y∗)2 +
1
2
a(π − π∗)2
where a > 0 reflects society’s relative preference for stabilizing inflation around π∗.
Suppose that the aggregate supply curve takes the form y = yn+(π−πe) where y is aggregate
output, yn is flexible-price output, and πe is inflation expectations.
(a) What are the equilibrium levels of output, y, and inflation, π, if the central bank has
discretion, i.e., chooses policy taking expectations as given? (3 points)
(b) Using the expressions derived for y and π, compute the social loss function in terms of
yn, y∗, and the parameters of the model. What value of a′ minimizes social loss? (2
points)
Suppose instead that the economy is hit by aggregate supply shocks and that the aggregate
supply curve takes the form y = yn + (π − πe) + ε. Assume that the aggregate supply shock
is i.i.d. with mean E[ε] = 0 and variance var(ε) = σ2.
(c) Solve for the equilibrium levels of output, y, and inflation, π, if the central bank has
discretion in this case. (3 points)
(d) Using the expressions derived for y and π, compute the social loss function in terms of
yn, y∗, ε and the parameters of the model. (2 points)
(e) Explain why a hawkish central bank with a′ >>> a would introduce a trade-off between
credibility and flexibility in the presence of aggregate supply shocks. (2 points)
4. Consider an individual with perfect foresight who lives from 1 to T , and whose lifetime utility
is given by U =
∑T
t=1 β
tu(Ct), where u
′(·) > 0, u′′(·) < 0. The individuals intertemporal
budget constraint is given by:
∑T
t=1
(
1
1+r
)t
Ct ≤ A0 +
∑T
t=1
(
1
1+r
)t
Yt where A0 > 0 is initial
wealth, r is the real interest rate and Yt is the individual’s income. Assume that β(1+r) = 1.
(a) Using the first order condition of the individual’s optimization problem with respect to
consumption, show that optimal consumption each period is constant. (3 points)
Assume now that β = 1 and r = 0. Suppose also that the individual’s income is constant in
each period such that Yt = Ȳ for all t.
(b) What is the individual’s utility-maximizing level of consumption and savings in each
period? (3 points)
(c) Are savings positive or negative? Explain why. (3 points)
(d) Suppose the individual decides to leave a bequest (or gift) B for the future generation
only in the last period of life. Compute the individual’s consumption in each period in
this case. (3 points)
5. Consider the “Q” model of investment with adjustment costs. Equilibrium suggests that
capital K(t) evolves as K̇(t) = C ′(I(t))−1(q(t) − 1) (normalizing the number of firms N = 1
and assuming no depreciation), while the marginal value of capital, q(t) evolves as q̇(t) =
rq(t)−π(K(t)), where r is the real interest rate. Note that the capital adjustment cost func-
tion, C(I(t)) satisfies C(0) = 0, C ′(0) = 0, and C ′′(·) > 0 and the real profit function, π(K(t)),
satisfies π′(·) < 0. Assume the transversality condition limt→∞e−rtq(t)κ(t) = 0, where κ(t)
is the representative firm’s capital stock. Assume initially that the economy is in steady-state.
(a) Draw the phase diagram for this model, explaining the location of the saddle path. (3
points)
(b) Explain the economics behind the assumptions that C ′′(·) > 0 and π′(·) < 0. (3 points)
At time t1 aggregate output rises unexpectedly to a new level.
(c) If the sudden rise in aggregate output is permanent, explain both the short-run and
long-run dynamics of q(t) and K(t) and draw the transition path for the economy using
a phase diagram. (3 points)
(d) Assume now that this unexpected rise in aggregate output is temporary instead of per-
manent, i.e. it is expected that at some future time t2 > t1, aggregate output will return
to its original level. Explain both the short-run and long-run dynamics of q(t) and K(t)
and draw the transition path for the economy using a phase diagram. (3 points)