Question 2 (An Economy with Investment)
Consider a two-period model of a small open economy with a single good each period. Let
preferences of the representative household be described by the utility function:
p
p
U(C1; C2) = C1 + C2
where C1 and C2 denot

Model of Curremt Accoumt im a small opem ecomomy (recap)
1
Model setup
1.1
fi. Small open economy; Representative household; Only one goods.
. Economy lasts for two periods, labeled t =fi and , with endowments: fi and X.
Gonsumptions in two periods are Cf

uestiom
2
Ecomomy
Umcertaimty)
(Am state H is v,
with and the
Gonsider
a small open
economy that lasts for two
periods. In period fi, the
endowment is fi = X0. In
period , there are two
possible outcomes. In one
state of the world, called the
high
state
(

(a) Now suppose that v = 34, so the high state is less likely, but pH and pL are both still 0.5.
Galculate all the same variables as in (a), and explain the differences.
Amswer: If v =4 and fi v =4fi , then
3
H
L.
fi pH X pL
= fi9.fi
Cfi =
fi r
fi r
X X
f

Now, suppose that there is no uncertainty (so it is the original endowment model from
homework fi with a single asset), and the consumer has an endowment in period
equal to the
average of
and L, vH (fi v)L, with v = fi . Solve for consumption and the lev

Suppose that there is a decrease in US consumers income in period fi that does not affect
production in period . Explain the effects on the savings and investment schedules of
both countries, and illustrate the change in the equilibrium on a graph. Explai

(a) Illustrate the equilibrium on a graph plotting each countrys S and I. Note: you do not
have to solve for equilibrium variables here.
Amswer: because SU (r) and SV (r) are the same, and IU (r) and IV (r) are the same,
CA U (r) = SU (r) IU (r) and CA V

(a) First, assume that v = fi v = fi , and that pH
= pL = fi , so that prices are actuarially
X
X
fair. Solve for Cfi, C H , C L , B H , and BL . Galculate the current account in period fi of the
small
X
X
fi
fi
open
economy.
Amswer: The consumers problem

uestiom 2 [10 poimts]
(a) [ points] Solve for the optimal choice of Cfi and CX, and Bfi as functions of the exogenous
fi
variables.
Amswer: The representative consumer solves
max lu Cfi b lu
CX
subject to :
CX
Cfi
fi
fi r
=W
2
where W = fi firfi (fi rO)

uestiom 1 [5 poimts]
Suppose that BO = 0. Define the current account CAt in each period t = fi, in terms of
model variables, and show that CAfi CA X = 0.
Amswer: The current account is defined as the trade balance (net exports) plus net
income receipts fr

All the questioms im this homework are about the basic small opem ecomomy
em- dowmemt model, with the followimg setup.
The representative consumer has utility function
U(Cfi, CX) = lu Cfi b lu CX
where b is a number between 0 and fi. The consumer has endo

uestiom 2 [10 poimts]
(a) [ points] Solve for the optimal choice of Cfi and CX, and Bfi as functions of the
exogenous variables.
(b) [ points] Suppose that there is a negative shock to the endowment in period
. How does this affect the consumers decisions

uestiom 3 [5 poimts]
Suppose again that BO = 0.
(a) [. points] Under what condition such that the country does not want
borrow or lend (even if it can), but simply consume on its endowments? (Use your
solution from uestion (a), and substitute in BO = 0).

Question 1 (An Economy with a Government)
Consider a two-period endowment economy. Assume that householdsreferences are
described by the utility function:
1
U(C ; C ) = ln C +
1
2
1
1:2
ln C
2
where C1 and C2 denote consumption in periods 1 and 2. In each

All the questioms im this homework are about the basic small opem ecomomy
em- dowmemt model, with the followimg setup.
The representative consumer has utility function
U(Cfi, CX) = lu Cfi b lu CX
where b is a number between 0 and fi. The consumer has endo

(a) Solve the maximixation problem of the representative household and solve for the
optimal level of consumption in periods fi and . Find the equilibrium levels of savings and the
current account in period fi.
Amswer: The maximixation problem of the hous

(a) Gompute the firms optimal level of period-fi investment, and period- profits.
Amswer: The firm chooses its capital stock in period to maximixe profits,
,
uX = KX (fi rfi )KX
The first order condition for this problem (set the derivative with respect t

(a) Now consider a change in productivity in period . Suppose that as a result of a
techno- logical improvement, the production technology becomes
,
X = X KX
Find the equilibrium levels of savings, investment, and the current account in period fi.
Gom- pa

uestiom
2 (Am
Ecomomy
with
Imvestmem
t)
Gonsider a
two-period
model of a
small open
economy
with a single
good each
period.
Let
preferences
of the
representativ
e household
be described
by the utility function:
U (Cfi , CX ) =
,
Cfi
,
CX
where Cfi and CX

(a) [ points] Alternatively, suppose that there is a permanent increase in government
purchases: both Gfi and GX increase by fi unit. What is the response of the current
account in period fi. Explain how your result compares with that from the previous
qu

b
fi
X
= 0
fi rfi
X
= b(fi rfi)
=
c f
(Alternatively, you could get here by realixing that the current account is xero if Cfi = fi
and CX = X. Since the consumer wants to Cf = b(fi rfi), the current account is xero
i
set C2
2
if
= b(fi rfi).)
fi
(a) [. p

(a) [ points] Suppose now that Tfi increases from 0 to fi while government
purchases are
unchanged. How does this tax hike affect the current account and the fiscal deficit in
period fi? Briefly explain your result.
Amswer: With ffi = fi, we need fX = fi

uestiom 3 [5 poimts]
Suppose again that BO = 0, and suppose that initially, fi and X are such that the current
account in period fi equals xero.
(a) [. points] Under what condition such that the country does not want borrow or
lend (even if it can), but s

uestiom 1 (Am Ecomomy with a Govermmemt)
Gonsider a two-period endowment economy. Assume that households references are
described by the utility function:
fi
U(Cfi, CX) = lu Cfi
lu CX
fi.X
where Cfi and CX denote consumption in periods fi and . In each p

(a) [fi point] Suppose that ffi = 0. What is fX? What are private, public, and national
saving in periods fi and ?
Amswer: ffi = 0, then fX must be set to make the governmens intertemporal budget
constraint hold:
GX
fX
Gfi
= ffi
fi rfi
fi rfi
=c fX = (f