Prueba 2 2019 - 01

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Pontificia Universidad Católica de Chile
Facultad de Ciencias Económicas y Administrativas
May 22, 2019
Midterm exam 2
Macroeconomía II
Instructions
1. The duration of this test is 2 hours.
2. Do not write the answer of two questions on the same sheet (of course, different
items of the same question can be on the same sheet). You can use both sides of each sheet
to answer. You have more space than needed to answer everything, but if you need more
sheets to answer ask the TAs.
3. Answers can be written in English or in Spanish.
Page 1
1 True or False (25 points)
Answer if the underlined statements below are True or False. You must justify your answers.
1. The United States is currently in the middle of a trade war with China. In the context
of that trade war, the US has decided to increase in 25% the import tariffs to 50.000
million imports from China. When asked about the consequences of such policy, a well
known analyst said: “If we assume everything else constant, with no doubt, one of the
consequences of that policy is that there will be a reduction in the US net exports.” (5
points)
2. Still looking at the context of the trade war from the US point of view (assuming that there
are only two countries, China and the US, and the US is the local economy), and assuming
that external savings SE are strictly larger than zero, another analyst comments: “We
expect an appreciation of the equilibrium real exchange rate in the US, as a consequence of
the increase in import tariffs.” (5 points)
3. Every month, the Central Bank of Chile conducts a expectations survey. In the edition
of May 2019, the analysts projected a nominal exchange rate of 650 pesos for a horizon of
one year. Given that the nominal exchange rate is currently 670, the analysts must expect
that the spread between domestic and foreign nominal interest rates (it − i∗t ) will go up. (5
points)
4. The Cagan’s model tells us that the price level is determined by the current and lagged
money supply, weighted by the distance in time. That is, as we move further away in time,
the lagged money supply is less important. (5 points)
5. Recently, the Central Bank of Argentina promised to keep the money supply constant. This
measure is a response to the high inflation in the country (55% in the last year), and the
central bank has honored its promise since its announcement. In a opinion piece, an analyst
comments: “This anti-inflationary measure can be rationalized or understood if we analyze
it through the lens of the Cagan’s model.” (5 points)
Page 2
2 Seignioriage (25 points)
Consider an economy with a single final good and perfect foresight. The seignioriage revenue in
real terms in a given period is given by
S = ∆M
P
,
where ∆M is the increase in the money supply and P is the price of the good. The demand for
money is given by M/P = Y e−αi, where i is the nominal interest rate, Y is output and α > 0.
Using the Fisher equation, we can write M/P = Y e−α(r+π), where r is the real interest rate and
π is the inflation rate. Suppose that in the long run the interest rate and output are constant
(i.e., ∆i = 0 and ∆Y = 0).
1. Find the inflation rate that maximizes S in the long run. (9 points)
2. Explain in words why the government is unable to raise the segnioriage revenue indefinitely.
(9 points)
3. Now suppose α = 0. Is there a inflation rate that maximizes segnioriage? Justify. (7 points)
3 IS-LM (25 points)
Consider an economy in which the aggregate consumption function is:
C = α0 + α1(Y − T )
Aggregate investment is:
I = β0 − β1i
Denote government spending by G. The money demand (in real units) is given by:
(
M
P
)d
= l0Y − l1i
Assume the parameters are such that α0 > 0, 0 < α1 < 1, β0 > 0, β1 > 0, l0 > 0, l1 > 0. In the
equations above Y represents output, T represents taxes and i is the nominal interest rate.
1. Given the equations above, find the equilibrium output as a function of i, G, T and param-
eters. In other words, find the IS curve. (5 points)
Page 3
2. Which policy would lead to a lower shift in the IS curve: a fall in taxes of 100 million
dollars or an increase in government spending of 100 million dollars? Provide an economic
interpretation. (3 points)
3. Suppose the central bank fixes the money supply, denoted by M
P
. Find the equilibrium
interest rate in the money market as a function of Y , M
P
and parameters. In other words,
find the LM curve. (5 points)
4. From the IS and LM curves derived in the previous items, show that equilibrium output in
this economy is:
Y = 11− α1 + φ(β1, l0, l1)
(
α0 − α1T + β0 +
β1
l1
(
M
P
)
+G
)
You must find the function φ(β1, l0, l1). (5 points)
5. Now we also consider the case in which central bank fixes the nominal interest rate (instead
of the money supply), setting i = i. We want to compare two cases: (i) the central bank
fixes the money supply; (ii) the central bank fixes the nominal interest rate. Suppose there
is an increase in government spending of 100 million dollars. In which case will output
increase more? Show it mathematically and provide an economic interpretation (if you
want, you may use a graph to help you with the intuition). (7 points)
4 IS-LM (25 points)
Suppose some economists documented the following stylized facts for the Brazilian economy:
• Monetary policy is very weak. That is, to achieve a given increase in output, the Brazilian
Central Bank needs to lower interest rates much more than central banks in other countries.
• Fiscal policy is not powerful (reduction in taxes or increases in government spending have
a small effect on output, compared to other countries).
• Interest rates in Brazil are much higher than in similar countries.
Some economists argue that each of those 3 facts can be partially explained by the fact there is a
huge development bank in Brazil (called BNDES). BNDES lends at interest rates way below the
the market interest rate (for some selected firms).
To shed some light on the impact of BNDES on the Brazilian economy, consider the following
extension of the IS-LM model. Assume the central bank fixes the nominal interest rate. Suppose
Page 4
that a fraction 1− λ of firms in the economy borrow at the nominal policy interest rate i, and a
fraction λ borrows at a rate (1−s) · i from BNDES, where s ∈ (0, 1) denotes the BNDES subsidy.
Each firm has a linear investment function on output Y and on the interest rate they borrow, so
that the aggregate investment is equal to:
I = b0 + (1− λ) [b1Y − b2i] + λ [b1Y − b2(1− s)i]
The consumption function is standard: C = c0 + c1(Y − T ), where T are taxes. Assume b0 > 0,
c0 > 0, and 0 < b1 + c1 < 1. Assume interest rates are always far above zero, so that you can
ignore the zero lower bound in your answers below. Denote government spending by G.
1. Suppose that initially λ = 0 (no BNDES). Consider the following shock: λ becomes positive,
taking some value λ ∈ (0, 1) (the development bank is introduced). How will that affect
output in the short run? Represent your answer in the IS-LM graph (you must represent
any possible shift and/or change in the slope of the IS curve correctly). (6 points)
2. Suppose now that right after the introduction of BNDES (which increases λ from zero to a
positive level), the central bank reacts, using monetary policy to ensure output will remain
at its previous level. Represent the equilibrium before and after the introduction of BNDES
in the IS-LM diagram, taking into account the central bank’s reaction. Assuming the central
bank behaves like that, does your answer support the claim that the BNDES contributes
to high interest rates in Brazil? (6 points)
In the remaining items we consider two economies: economy A has λ = 0, while economy B has
λ = λ > 0. In all other dimensions they are identical.
3. Suppose government spending increases one unit in both economies. How much does output
increase in each economy? Write your answer as a function of parameters. Does your answer
support the claim that the BNDES contributesto a not powerful fiscal policy in Brazil? (6
points)
4. Suppose both economies have a negative consumption shock: c0 falls one unit. The central
bank of each economy avoids a fall in output after this shock by using monetary policy.
How much the central bank had to lower interest rates in each economy? Write your answer
as a function of parameters. Does your answer support the claim that monetary policy is
less powerful because of the existence of BNDES? (7 points)
Page 5
	True or False (25 points)
	Seignioriage (25 points)
	IS-LM (25 points)
	IS-LM (25 points)