EC108 Macroeconomics 1
Review Class
Jorge F. Chavez
May 8, 2014
Question 1: True or false statements
Read the following statements and say whether they are TRUE, FALSE or UNCERTAIN. Briefly
justify your answer.
(a) Aggregate demand falls when the price level rises, because higher prices cut real incomes.
(b) An increase in the price of some imported goods will show up in the GDP deflator but not
in the CPI.
(c) According to the Quantity Theory of Money, the rate of inflation must equal the rate of
growth of the nominal money supply.
(d) The IS curve could be fully vertical.
(e) The basic version of the Solow model (no population growth, no technological progress)
implies an economy where growth is not possible.
Question 2: AD-AS model1
Assume an economy that is initially operating at the natural rate of output Ȳ .
(a) Write down the short-run aggregate supply equation.
(b) Suppose that this economy is characterized by price stickiness. Other things equal, what
would happen with the equation you wrote in parte (a) if the proportion of firms that follow
a sticky-price rule increases?
(c) Use the model of AD-AS to illustrate graphically the short-run and long-run effects on price
and output of an unexpected expansionary monetary policy change.
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Based on Q2, exam 2010-2011
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EC108
Review May 2014
Question 3: Unemployment dynamics2
Consider the simplest model of unemployment dynamics. Let Ut denote the number of unemployed workers at time t, and let s and f denote the job-separation rate and the job
finding rate in this economy. Assume initially that the total size of labor force is constant
(Lt−1 = Lt = Lt+1 = L, all t).
(a) Interpret s and f in terms of probabilities.
(b) Let µt denote the unemployment rate at time t. Show that the unemployment rate in
steady-state will be a function of s and f only.
(c) Suppose s = 0.03 (or 3 percent) and f = 0.7 (or 70 percent). Initially (at time t = 0), the
unemployment rate is equal to µ0 = 0.08. Further assume that at time t = 200 (in the long
run) this economy will experience a permanent shock on f such that from period t = 200
onwards, f = 0.4. Sketch the evolution of the unemployment rate over time in a simple
graph (Hint: consider how would the path of µt would look in a graph with time in the
horizontal axis, where t goes from 0 to 1000).
(d) In macroeconomics it is always useful to express a dynamic variable (say xt ) in terms of
deviations from its value in steady state: x̃t ≡ xt − x̄. Show that the deviation of the
unemployment rate at t + 1 with respect to its steady-state value can be expressed as a
linear function of the deviation of the unemployment rate at time t, that is µ̃t+1 = γ µ̃t .
Hint: Try to express the γ parameter in terms of s and f .
(Optional) Now suppose that the labor force grows at a rate n: Lt+1 = (1 + n)Lt all t.
(e) Show that the unemployment rate in steady-state will be a function of s, f and n only.
(f) (Harder) Show that we can also write µ̃t+1 = ξ µ̃t . What is the relationship between ξ and
γ?
Question 4: Solow’s Growth Model3
Consider how unemployment would affect the Solow growth model. Suppose that output is
produced according to the following production function:
Yt = Ktα [(1 − u) Lt ]1−α
where Kt is the aggregate stock of capital, Lt is the labor force and u is the natural rate of
unemployment. The national saving rate is s, the labor force grows at a rate n and capital
depreciates at a rate δ.
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Based on Problem Sets
Based on an exercise proposed in Mankiw’s textbook
Jorge F. Chávez
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EC108
Review May 2014
(a) Express output per worker yt = Yt /Lt as a function of capital per worker kt = Kt /Lt and
the natural rate of unemployment u.
(b) Describe the steady state of this economy and find the golden-rule level of kt . What is the
saving rate that allows the economy to reach the Golden Rule?
(c) Is there any difference if we analyze output per effective worker instead of output per worker?
Why?
(d) Suppose that some change in government policy reduces the natural rate of unemployment.
Describe how this change affects output both immediately and over time. Is the steady-state
effect on output larger or smaller than the immediate effect? Explain.
Question 5: Phillips curve
Suppose that an economy has the following Phillips curve:
πt = πte − 0.5(ut − 0.06) + vt
(a) What is the natural rate of unemployment (un )?
(b) Use the Phillips curve diagram to illustrate graphically how the inflation rate π and unemployment rate u change in the short run to an unexpected expansionary monetary policy.
(c) Use the Phillips curve diagram to illustrate graphically how the inflation rate π and the
unemployment rate u change in the short run to an expected expansionary monetary
policy.
Question 6: Dynamic AD-AS Model4
Consider a dynamic AD-AS model is characterized by the following equations:
Yt = Ȳt − α (rt − ρ) + ϵt
The demand for goods and services
rt = it − Et πt+1
The Fisher equation
(
)
πt = Et−1 πt + ϕ Yt − Ȳt + vt
The Phillips curve
Et πt+1 = πt
Adaptative expectations
(
)
it = πt + ρ + θπ (πt − πt∗ ) + θY Yt − Ȳt
The Monetary-Policy rule
(a) Write down the DAD and DAS curves and characterize the long-run equilibrium.5
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Based on exercises proposed in Mankiw’s textbook
That is, say what happens in the long-run once the economy reaches an equilibrium.
Jorge F. Chávez
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EC108
Review May 2014
(b) Suppose the economy is hit by a transitory supply shock vt > 0. Explain graphically how
the economy returns to its short-run equilibrium.
(c) The sacrifice ratio is the accumulated loss in output that results when the central bank
lower its target for inflation by 1 percentage point. What is the sacrifice ratio implied by
the dynamic AD-AS model?6
Question 7: Deficit and Public Debt7
The government debt of Mediterranea stands at £12, 000, and the long term interest rate is 5
percent. The governments budget for this year is based on a proportional income tax rate of
20 percent. From the revenue the government must meet consumption spending commitments
of £1, 000 as well as interest payments on the debt. The economys production possibilities are
given by its natural rate of GDP, which is £6, 000.
(a) What is the level of GDP at which the Mediterranean government will balance its budget
this year (5 marks)?
(b) What is the structural deficit or surplus of the Mediterranean government (5 marks)?
(c) Given your answers to (a) and (b), explain what is likely to happen in the Mediterranean
economy over the next years on the assumption that the economy has an IS-LM structure
and policies remain unchanged (10 marks).
(d) How might your answer change if it turned out that Mediterranean households adhere to a
Ricardian view of government borrowing (that it is equivalent to taxation) (5 marks)?
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Hint: You have to write down an expression for the sacrifice ratio in terms of model parameters.
Exam 2009/10
Jorge F. Chávez
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