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Exercises before the second mid-term (II)
Caio Machado
Instituto de Econoḿıa
Pontificia Universidad Católica de Chile
Macroeconomia II, 2017
Exercise 1
The two paths to the medium-run equilibrium explored in this chapter [Chapter 9]
make two different assumptions about the formation of the level of expected
inflation. One path assumes the level of expected inflation equals lagged inflation.
The level of expected inflation changes over time. The other path assumes the level
of expected inflation is anchored to a specific value and never changes. Begin in
medium-run equilibrium where actual and expected inflation equals 2% in period t.
a. Suppose there is an increase in consumer confidence in period t+1 (and
assume that because of it consumption increases for any given level of
available income). How does the IS curve shift? Assume that the central
bank does not change the real policy rate. How will the short-run
equilibrium in period t+1 compare to the equilibrium in period t?
r
Y
IS′IS
Y ′Y
r LMA
′A
The IS shifts to the left. Equilbrium goes from A to A’.
b. Consider the period t + 2 equilibrium under the assumption that
πet+2 = πt+1 . If the central bank leaves the real policy rate unchanged,
how does actual inflation in period t+2 compare to inflation in period t+1?
Continue to period t+3. Making the same assumption about the level of
expected inflation and the real policy rate, how does actual inflation in
period t+3 compare to inflation in period t+2.
r
Y
IS′IS
Y ′Y
r LMA
′A
∆π
Y
0
PC
A
A′
Inflation at t + 2 is larger than at t + 1. If the central bank does not do
anything, at date t + 3 inflation will be larger than at t + 2 (as long as r
does not move, the economy remains at A′, with inflation accelerating).
c. Consider the period t+2 equilibrium making the assumption that
πet+2 = π. If the central bank leaves the real policy rate unchanged, how
does actual inflation in period t+2 compare to inflation in period t+1?
Continue to period t+3. Making the same assumption about the level of
expected inflation and the real policy rate, how does actual inflation in
period t+3 compare to inflation in period t+2?
r
Y
IS′IS
Y ′Y
r LMA
′A
π
Y
π
PC
A
A′
(It is the same graph as in item b, only the y-axis changed). As long the
central bank does not change r , the economy stays at A’.Thus, inflation in
t + 2 is higher than in t + 1, but the same as in t + 3.
d. Compare the inflation and output outcomes in part b to that in part c.
r
Y
IS′IS
Y ′Y
r LMA
′A
∆π
Y
0
PC
A
A′
r
Y
IS′IS
Y ′Y
r LMA
′A
π
Y
π
PC
A
A′
Output will be the same in both cases. Even though the initial increase in
inflation is the same in both cases, in the subsequent periods it keeps
accelerating when expectations are adaptative, while it stabilizes when
expectations are anchored.
e.Which scenario, part b or part c, do you think is more realistic. Discuss.
Scenario c. Noting the central bank has been keeping too low interest
rates, agents will start to look to past inflation to form their expectations.
Exercise 2
Consider the IS-LM-PC model and suppose there is an increase the price
oil. Assume that initially output is equal to potential output. Compare the
response of the economy in two cases: (i) expected inflation always equal
lagged inflation; (ii) inflation expectations are anchored at some level π. In
the medium run, the central bank adjusts interest rates to keep it as close
as possible to potential output . You may assume that initially the interest
rates are very high, so that the zero lower bound will not be binding. Write
a graph with time on the horizontal axis and the path of output and
inflation on the vertical axis, for each of the cases mentioned.
As we have seen, the increase in the price oil will increase the production
costs of firms. In reduced form, we can interpret that as in increase the in
the markup. This shifts the price setting curve down, increasing the the
natural rate of unemployment and decreasing output. Since the PC curve is
given by
π−πe = αL (Y − Yn)
This change shifts up the PC curve. Let’s write the IS-LM-PC diagram now.
r
Y
IS
r
LM ′A
′′
π
Y
π
PC ′
A
A′
PC
LMA and A
′
A′′
r
Y
IS
r
LM ′A
′′
∆π
Y
0
PC ′
A
A′
PC
LMA and A
′
A′′
(Left panel is anchored expectations, not the difference in the y-axis).
Inflation increases in both cases after the shock and then, when the central
bank adjusts the interest rate if falls in the left panel and remains constant
in the right panel. Output goes back to potential in both cases.
Time
Time
π
Y
π
Yn
Y ′n
Adaptative expectations
Anchored expectations
Same curve for both
Exercise 3
Brazil’s policy real interest rate are very high. Many economists argue that
part of that is caused by the fact that there is a development bank in Brazil
(called BNDES) lending at interest rates way below the the market interest
rate (for some selected firms). They argue that it makes monetary policy
less powerful, forcing the central bank to increase the interest rate a lot to
reduce inflation. The following simple extension of the IS-LM-PC model is
proposed to check if that intuition survives a more formal treatment and to
try to understand better the mechanisms behind this kind of argument.
Suppose that a fraction 1 −λ of firms in the economy borrow at the policy
rate plus the risk premium (r + x), and a fraction λ borrows at
(1 − s)(r + x) from the BNDES, where s denotes the BNDES subsidy. Each
firm has a linear investment function on Y and on the interest rate they
borrow, so that the aggregate investment is equal to:
I = b0 + (1 −λ) [b1Y − b2(r + x)] +λ [b1Y − b2(1 − s)(r + x)]
The consumption function is standard: C = c0 + c1(Y − T ), with the usual
assumption that b1 + c1 < 1. Also, inflation expectations are anchored at π.
1. Suppose that initially λ= 0 (no BNDES) and output is equal to
potential. At date t λ becomes positive (the development bank is
introduced). How will that affect the equilibrium in the short and medium
run?
First thing we need to understand is how this will affect the IS curve.
Equilibrium in the goods market imply
Y = c0 + c1(Y − T ) + b0 + (1 −λ) [b1Y − b2(r + x)] +λ [b1Y − b2(1 − s)(r + x)] + G
Y = 11 − c1 − b1
[c0 − c1T + b0 − b2 (1 −λs)(r + x) + G ]
r = 1b2 (1 −λs)
[−(1 − c1 − b1)Y + c0 − c1T + b0 + G ] − x
Note that
dr
dY = −
1 − c1 − b1
b2 (1 −λs)
Thus, as λ increases, the IS curve becomes more inclined and also shifts up.
r
Y
IS
IS′
LM
A
π
Y
π
PC
A and A′′
A′
A′′ LM ′
A′
Graphically, the equilibrium goes from point A to A’ in the short run, and to
A” in the medium run. The real policy rate is indeed higher with higher λ.
2. Now suppose that the government decides to increase λbut at the same
time increase taxes, so that the short run equilibrium remains the same.
What happens in the medium run?
r
Y
ISλ=0ISλ>0
LMA
π
Y
π
PC
A and A′
The policy rate does not change.
3. Now consider the case with λ= 0 and the case where the government
increases λ and increases taxes as in item 2. Suppose there is an increase in
c0 and compare the medium run equilibrium in both cases. Does it make
sense to say that monetary policy became less powerful because of the
subsidized credit?
Using r = 1b2(1−λs) [−(1 − c1 − b1)Y + c0 − c1T + b0 + G] − x , one can see that when
λ > 0, the shift in the IS is larger, for a given change in c0. The graph below shows the
change in equilibrium:
r
Y
ISλ=0ISλ>0
LMA
π
Y
π
PC
A,B and C
IS ′λ>0
IS ′λ=0
B
C
Note that interest rates are higher at point C (medium run equilibrium after the shock
when λ > 0), than at point B (the medium run equilibrium after the shock when λ= 0).
Monetary policy needs to react more strongly with λ > 0, so it makes sense to say it
became less powerful.