Mid-Term Exam # 3
Economics 514
Macroeconomic Analysis
Friday, December 11th , 2009
Write your answers on this white exam. Do not write your answers on
the blue book! Do not hand in your blue book!
For the purpose of easier algebra, examine Questions 1-3 under the assumption that t the
log of potential output in the economy is y  ln Y P  0 . If YP = 1, then y  0 , so this
simplifying assumption could be seen as a normalization.
1. Adaptive Expectations The demand for goods in an economy is a negative
function of the interest rate. yt   t  gt  rt where the term αt represents
fluctuations in optimism and pessimism while gt is government spending.
Fluctuations in optimisim and pessimism follow a random walk in which
t  t 1   t . Monetary policy follows the Taylor principle rt   t . The level of
output produced by firms is given by yt   t  gtW  . In this economy, wage
contracts are signed for two periods in advance with half the wage contracts
signed today and half signed two periods ago. gtW  .5   t 1  .5   t  2 . Assume that
in all periods prior to period 0, αt = 0 and in period 0 and afterwards αt = ε0 = .08.
Also assume that  1   2  0 .]
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A.
Assume that government spending, gt = 0, for all periods. Solve for the
dynamics of output and inflation in period 0, 1, 2, and 3. Solve for the steady state
level of inflation and output.
Period 0
1
2
3
SS
πt
yt
B.
Assume that government spending can respond to demand shocks.
Assume that we can set gt = At ∙ ε0 =At ∙ .08. For each period, solve for the At
which sets output equal to zero in every period, 0, 1, 2, and 3. Solve for inflation
in those periods.
Period 0
1
2
3
0
0
0
0
πt
yt
At
2
C.
Assume that government spending can respond to demand shocks only
with a lag, so that g0 = g1 = 0 but g2 = A2∙ .08, and g3 = A3∙ .08 where A2 and A3
are the answers that were solved for in part B. Solve for the level of output and
inflation under this policy.
Period 0
1
2
πt
yt
gt
3
3
D.
Draw a picture of the dynamics of the AS-AD curve for outcomes in part
A, B. and C.
Part A.
Part B.
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Part C.
2. Rational Expectations In an economy, the demand for goods is a negative
function of the real interest rate. yt   t  rt . The monetary policy reaction
function is of the form rt   t  h  yt where the central bank raises the real interest
rate when inflation or output rise. Consider two possible values for the sensitivity
of monetary policy to output, h = 0 or h = 1.
A.
Draw the AD curve under the two assumptions for h. In which case is it
steeper.
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B.
Output is above potential output, when inflation is above the growth rate
of real wages. yt   t  gtW  . Also assume that workers have rational
expectations g tW =Et-1[πt]. Assume that demand shifts follow a random walk,
t  t 1   t . Also assume that wage growth is set according to rational
expectations You can solve for output and inflation as function of yesterday’s
yt  A   t 1  B   t
demand level and today’s technology shock.
. Solve for A, B,
 t  C   t 1  D   t
C, and D for h = 0 and h = 1.
A
B
C
h =0
h=1
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D
C.
For which setting of h, is the value of B largest. Explain why. Draw a
version of the AS-AD showing the effect of a shock in period t on the output gap
on period t.
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b. For which setting of h, is the value of A largest. Explain why. Draw a
version of the AS-AD showing the effect of a shock in period t on the
output gap on period t+1.
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3. Rational Expectations Assume demand shocks are zero and monetary policy
shocks are zero. The economy is driven only by cost push shocks, νt. Cost push
shocks have a predictable, nt and unpredictable, ωt, component. Monetary policy
can respond to the predictable component and to current inflation. The economy
will be described by the equations
IS ) yt  rt
MPR ) rt  mt   t mt    nt
AS ) yt   t  gtW 
Wage) gtW  Et 1  t   t
Cost Push)  t  nt  t
A.
Et 1  nt   nt Et 1 t   0
Solve for the level of κ that will set expected inflation equal to zero.
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B.
form
Using a specification of κ, we can solve for output and inflation in the
yt  A  nt  B  t
 t  C  nt  D  t
Solve for A, B,C, and D when κ = 0 and when κ is equal to that solved for in part
A.
A
B
C
κ=0
κ from part A.
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D
4. The Deficit and National Savings. Consider an economy in which a household
lives for two periods (t = 0 and 1). The net interest rate between periods is 0, so
1+r = 1. The household starts with no financial wealth and consumes in period 0
and period 1. The household has an income profile Y0 = 50 and Y1 = 150. The
dynamics of household bank balances are given by
B0  Y0  TAX 0  C0
C1  Y1  TAX 1  B0
The government has no expenditure but may set taxes at either a positive or a
negative level. If taxes are negative, they will make a payment to the household.
At time 0, the government has zero outstanding debt (i.e. DEBT-1 = 0). The
dynamics of government debt follow the equation DEBTt = DEBTt-1 – TAX.
In period 0, the government has two possible policies. Policy A is to have zero
taxes, TAX0 = 0 and Policy B is to make a transfer payment to households, TAX0 =
-50. Define National Savings in period 0 as NS0 = B0 – DEBT0.
a. Assume that the government runs a generational balance budget so when the
household dies, the government must have zero debt at the end of period 1,
DEBT1 = 0. Assume that the household is a permanent income consumer.
Solve for national savings under both policies. Assume that the household
faces borrowing constraints so B0  0 . Solve for national savings under both
policies.
NS0
Permanent
Income
Consumers
TAX0 = 0
TAX0 = -50
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Borrowing
Constraints
b. Assume the government does not need a generational balance budget and sets
TAX1 = 0. Solve for national saving if the household are permanent income
consumers.
NS0
Permanent
Income
Consumers
TAX0 = 0
TAX0 = -50
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