Macroeconomics 2023 - Clabe Problem set 6
Pietro De Cesare 0001075052
EX.1
a) Balanced Trade: A situation in international trade where the value of a country's exports
equals the value of its imports over a certain period, indicating a net trade balance of zero.
b) Nominal Exchange Rate: The rate at which one currency can be exchanged for another,
usually quoted in terms of how much foreign currency can be bought with a unit of domestic
currency.
Real Exchange Rate: Adjusts the nominal exchange rate by the relative prices of domestic
and foreign goods, reflecting the purchasing power of a country's currency in terms of goods
and services.
c) Small Open Economy: An economy that participates in international trade and finance but
is small enough that its policies do not affect world prices or income, often assuming perfect
capital mobility and fixed exchange rates.
d) Purchasing Power Parity (PPP) Theory: An economic theory that compares different
countries' currencies through a "basket of goods" approach, suggesting that exchange rates
should adjust to equalize the price of identical goods and services in different countries.
e) Fixed Exchange Rate: A regime where the government or central bank sets and maintains
the official exchange rate of its currency relative to another currency or a basket of
currencies.
Floating Exchange Rate: A regime where the value of a currency is determined by market
forces without direct government or central bank intervention.
f) Interest Rate Spread: The difference between two interest rates, often referring to the gap
between borrowing and lending rates in financial institutions or the difference between
interest rates of different maturities or credit qualities.
EX.2
a) Perfect capital mobility implies r = r∗ = 1
so I = 4 − 2 ∗ 1 = 2
In the long run output is at its natural level
so C = 0.6 (10 − 5) = 3
Sprivate = Y − T − C = 10 − 5 − 3 = 2
Spublic = T − G = 5 − 5 = 0
In equilibrium Y = C + I + G + NX, or Sprivate + Spublic − I = NX(ε), that is
2 + 0 − 2 = 10 − 5ε -> ε = 2 and NX = 0 balance trade
b) With G = 7
Sprivate = 2
Spublic = −2 so
Sprivate + Spublic − I = NX(ε) that is 2 − 2 − 2 = 10 − 5ε -> ε = 2.4 and NX = −2 (trade
deficit)
EX. 3:
a) For a small open economy with perfect capital mobility, r = r∗ = 5. From P = P∗ = 1, it
follows that ε = eP/P*
The IS∗ curve is Y = C + I + G + NX, so
Y = 0.6(Y −50) + 200−20 ∗ 5 + 50 + 100 − 0.1e = 1/(1-0.6) (220 − 0.1e) = 550 −1/4 e
The LM∗ curve is M/P = L(r∗, Y ),
that is 100 = Y − 10 ∗ 5, which implies Y = 150
Plug into IS∗, 150 = 550 −1/4 e
e = 1, 600 and NX = 100 − 0.1 ∗ 1, 600 = − 60
b)
With G = 100,
the IS∗ curve is Y = 0.6(Y −50) + 200−20 ∗ 5 + 100 + 100 − 0.1e =1/ (1−0.6) *(270−0.1e) =
675−1/4e
In the short run prices and r∗ are not affected by the domestic fiscal policy.
The LM∗ curve Y = 150
From the IS∗ curve 150 = 675−1/4e
e = 2,100 and NX = 100−0.1∗2, 100 = −110
The short run effects of ∆G = 50 are ∆Y = 0, ∆e = 500 and ∆NX = −50
EX 4:
a) IS∗ curve is Y = 0.6(Y −50) + 200 −10 ∗ 2 + 50 + 100 − 0.1e =1/(1−0.6)*(300−0.1e) = 750
– 1⁄4 e
The LM∗ curve is 200 = Y −100 ∗ 2 -> Y = 400
Plug it in the IS∗ curve
400 = 750 −1/4 e
e = 1,400 and NX = 100 − 0.1 ∗ 1, 400 = − 40 (trade deficit)
b)
With M = 300, the LM∗ curve is 300 = Y −100 ∗ 2 -> Y = 500
Plug it in the IS∗ curve, we get 500 = 750 −1/4 e
e = 1, 000 and NX = 100 − 0.1 ∗ 1, 000 = 0 (balanced trade)
The short run effects of ∆M = 100 are ∆Y = 100, ∆e = −400 and ∆NX = 40
EX 5:
a)
Y = 400, M = 200, G = 100
The IS∗ curve Y = 0.6(Y − 50) + 200 − 10 ∗ 2 + 100 + 100 − 0.1 ∗ 1, 400 = 1/(1−0.6) *210 =
525
Plug it into the LM∗ curve
M = 525 − 100 ∗ 2 = 325. So ∆G = 50, ∆Y = 125 and ∆M = 125
b) In a small open economy with fixed exchange rates, a monetary policy expansion does not
alter output or the money supply in the short term. The central bank's efforts to increase
money supply are counteracted by its interventions to maintain the exchange rate, leading to
the reabsorption of any new liquidity and rendering the policy ineffective.
EX.6
a) When a fragile economy faces a shock, it can lead to a heightened risk premium, causing
capital to flee and the currency to depreciate. This triggers a hike in interest rates, curtails
investment, potentially spikes inflation due to costlier imports, and lowers income, further
fueling the cycle of depreciation and sovereign default risk. Central banks might respond by
tightening monetary policy to defend the currency, but this contraction during a downturn is
inherently pro-cyclical.
b) High inflation rates make it difficult to counter negative shocks with expansionary
monetary policy due to inflation fears. However, many EMEs currently possess more
transparent and independent central banks, often with inflation targeting and lower inflation
rates, providing more space for expansionary responses to the COVID-19 crisis.
c) The public debt-to-GDP ratio grows at the rate of interest minus GDP growth rate (r-g). If
this rate is positive, maintaining public debt sustainability necessitates a primary surplus.
With the U.S. public debt high and mostly foreign-held, a primary surplus could help keep
the debt on a sustainable path, avoiding increased country risk and global destabilization.
d) By achieving a primary surplus post-pandemic, the U.S. would stabilize its public debt and
maintain low interest rates, benefiting EMEs with a low global interest rate environment.
Conversely, rising U.S. rates could lead to currency depreciation in EMEs, increased capital
outflow risks, and potential financial crises.