PS 6 SOLUTIONS
1. True or
False (3 points each – 18 total)
Under a fixed exchange rate regime, interest rates are fixed. Therefore, an increase in G will not
crowd out investment, and the increase in Y will be larger than under a
Under a fixed exchange rate, the central bank cannot conduct monetary
policy. It must instead allow the
money supply (and interest rates) to fluctuate in order to support the
fixed E and keep the interest parity equation in balance.
- True. A large expected depreciation in the
future will tend to increase today's exchange rate (a depreciation of the
currency.) This will boost net
exports and increase production (shift of IS to the right) until a new equilibrium
- False. As you can see in the interest parity
equation (i = i* + (Ee -
E)/E), a rise in Ee with E fixed will lead to an increase in
the level of interest rates and will decrease output (shift of the LM to
- False. If money supply increases and the
interest rate goes down, this will weaken domestic currency. (E goes up – a depreciation of the
- False. The term refers to budget and trade
2. Open Economy
IS-LM (40 points total)
pts) Yes. NX = (30 + 0.2Y*)E - 10 - 0.4Y. Therefore,
NX is increasing in E.
pts) Goods market equilibrium,
with i and E fixed:
Y = 24 + 0.4(Y - T) + 80 - 50i + G
+ (30 + 0.2Y*)E - (10 + 0.4Y)
Y = 100 - 50i + 50E
pts) The goods market
multiplier is 1.
pts) LM: 80 = Y -
pts) The interest parity
relation is: i = 0.05 + (1.95 -
pts) In equilibrium, Y =
100, i= 1, and NX= 0.
pts) This is derived from the interest rate parity condition. Your graph should have i on the
vertical axis, E on the horizontal axis, and should have curve with i and
E negatively related.
pts) The LM curve is drawn in
i-Y space – Y is on the horizontal axis, i on the vertical. The LM is an upward sloping curve, with
Y and i positively related, determined from (d).
pts) The IS relates Y and i
through a negatively sloped curve in the same plane as the LM curve
above. When E is larger, the curve
shifts more to the right.
pts) G=20 implies Y=110 -50i
+50E ; 80=Y - 20i ; i=0.05 +(1.95 - E)/E.
Solving this system, one gets E=.95, Y=102.1, i=1.11.
pts) If M = 200, then E=2.02,
pts) If Ee goes up
to 2.5, then Y=102.8, E=1.20, and i=1.14.
pts) In part (i), your graph
should look the same as under flexible exchange rates – if E changes due
to market fluctuations or due to changes in government policy, the effect
on the IS via NX is similar. For
part (j), the answer is more complicated.
When you had flexible exchange rates in the first part of this
question, your 3 endogenous variables were i, Y, and E. Now that exchange rates are fixed, your
3 endogenous variables are i, Y, and Ms . This means that you fix E = 1, Ee = 1.95, G = 20, and all the other
variables as before, and solve the system of equations. This gives you, in equilibrium: MS
= 90, Y = 110, E =1, NX = -4,
and i = 1.
3. Exchange Rates
and Expectations (4 points per
question, 12 total)
expect a devaluation to a level where E is equal to 1.09.
the country devalues, E will rise.
This will put pressure on the interest parity equation – at the
moment of devaluation (before i has had a chance to adjust), domestic
bonds look more attractive than foreign bonds. This makes foreign investors want to buy domestic bonds –
they trade foreign currency for domestic at the central bank at the new
exchange rate (1.09), driving up domestic money supply. This shifts out the LM, lowering i
until i = i* = 0.6. This drop in
interest rates will push investment up (moving along the IS curve) and
therefore output will increase.
There is also be a second order
effect on NX – the new, higher E means that NX rises. This shifts out the IS curve, puts upward pressure on interest
rates, and leads to further expansionary monetary accommodation. This has an additional boost on output.
will expect an even higher E for the future (Ee goes way
up.) This shifts out the interest
parity curve. The moment that
these expectations change, the return on foreign bonds looks more
attractive than domestic bonds – see this in the arbitrage equation. This means that investors will want to
move their currency out of the country, putting lots of pressure on the
central bank to pay out its foreign reserves to support the exchange rate. In turn, this reduces the money supply,
shifts in the LM curve, and pushes interests rates very high. Output will decrease from its levels in
Note that as long as the country is
defending its exchange rate, there is no effect on NX or the IS: NX moves when
E moves, and E is still fixed here. It
is possible to imagine a scenario where the central bank runs out of reserves
if Ee keeps rising, and
abandons its fixed E all together.
If you assumed that the conditions
in (b) and (c) were happening at the same time (instead of sequentially, as
above) then the 2 changes – the devaluation and the rise in Ee –
would be pulling output in different directions. The ultimate effect on output would depend on the magnitude of
the change in Ee.