Download ECON 371 Spring 2009 Answer Key for Problem Set 3 (Chapters 16

ECON 371 Spring 2009
Answer Key for Problem Set 3
(Chapters 16-17)
Instructor: Kanda Naknoi
March 5, 2009
Question 1 (2 points)
(1. a) From the GDP identity: GDP = GNE + TB = $8,000 + $700 million = $8,700 million.
From the GNI identity: GNI = GDP + NFIA = $8,700 + $350 million = $ 9,050 million
From the GNDI identity: GNDI = GNI + NUT = $9,050 + (-$50) million = $ 9,000 million
From the definition of GNE: GNE = C + I + G. Thus,
I = GNE – C – G
= $8,000 - $5,000 - $1,100 million = $1,900million
From the current account identity: S = I + CA = $1,900 +$1,000 million = $ 2,900 million.
From the definition of private, national savings and government savings:
S = SP + SG; SP = S- SG = $2,900 – (-$250) million = $3,150 million
(1.b) From the BOP identity:
BOP = CA + FA+ KA = 0
FA = - (CA+KA)
Using the data given in the question:
FA = - ($1,000 + $75) million = - $1,075 million.
Because FA<0, foreign purchases of assets of Freedonia < Freedonia’s purchases of foreign
assets implying Freedonia is a net importer of assets.
(1.c) From the definition of the current account:
CA = TB + NFIA + NUT
NFIA = CA – TB – NUT
1
Using the data given in the question:
NFIA = $1,000 + $700 – (- $50) million
= $ 350 million
Since net factor income from abroad is income earned from the home country’s factor services
abroad (EXFS) less income paid to foreign factors by the home country (IMFS):
NFIA = (EXFS – IMFS)
EXFS = NFIA + IMFS
From the data, we know IMFS = $150 million. Therefore,
EXFS = $350 + $150 = $ 500 million.
Thus, Freedonia factors abroad earned $ 500 million.
(1.d) Freedonia is a net lender because it has current account surplus. The current account
surplus corresponds to the deficit in its financial account.
Question 2 (2 points)
(2.a) There is a one-time increase in output of $240(=1,200*0.2). Therefore, the present value of
output is: PV = 1440 + (1200/0.06) = $ 21,440
(2.b) In the closed economy, the country must absorb the entire change in output into
consumption in the initial period because borrowing or lending is not possible. Therefore,
C0=1440 and Ct=1200 where t>0.
(2.c) In the open economy, the present value of consumption is the same as in the closed
economy. The difference is that the country is able to save the gain in output to increase
consumption by a small amount today and increase consumption in subsequent years too. To
determine the level of consumption each period, the country wants to maintain a given level of
consumption:
PV(C) = C + (C/r*);
21,440 = C + (C/0.06); C =1,213.6.
Therefore, consumption increases from 1,200 to 1,213.6 in Year 0 and remains at 1,213.6
thereafter.
Question 3 (4 points)
(3.a) Yes. The criterion for undertaking an investment project is that:
PV(Cost of Investment) < PV (Return on Investment)
2
From the question, PV(Cost of Investment) = 24, since there is no new investment from Year 1.
The present value of return on investment now depends on the interest rate. Here, the domestic
interest rate in if the economy is closed is the same as the MPK, or 0.08. The world interest rate
is 0.04. However, when this country opens to the world capital market and borrows the fund for
investment, the domestic interest rate will become the same as the world interest rate. Thus, we
use the world interest rate to evaluate the present value of the return on investment.
PV(Return on Investment) = 0 + 0.08(24)/1.04 + 0.08(24)/1.04^2 + … = $48 billion.
In this case, PV(cost of investment) < PV(Return on Investment). As a result, this investment
project should be undertaken.
(3.b) See the answer for (3.a)
(3.c) and (3.d)
Note that the home country can borrow less than the cost of investment project. In other words,
the home country faces “borrowing constraint” in the world capital market. Before solving for
paths of consumption and other variables in this case, it is instructive to consider the cases we
studied in class. One is the closed-economy case without international borrowing. The other is
the open-economy case with international borrowing without borrowing constraint.
Case 1: Closed economy, no international borrowing : r = MPK = 0.08
(Unit = $billion)
Time
0
1
2
3
… Present Value
Q
300
301.92
301.92
301.92
…
4074
I
24
0
0
0
…
24
C
276
301.92
301.92
301.92
…
4050
C w/o I
300
300
300
300
…
4050
In Case 1, the closed economy must finance investment with domestic saving or Q – C.
This is because the closed economy is subject to the static budget constraint: Q = I + C. When
we look at the present value of consumption, it turns out investment does not increase the present
value of consumption at all. This is because PV(Cost of Investment) = PV(Return on Investment)
= 24. PV(Return of Investment) in this case is below that in Question (3.a) because the interest
rate here is 0.08, not 0.04.
Case 2: Open economy without borrowing constraint: r = r* = 0.04
(Unit =$billion)
Time
Q
I
C
TB = Q-I-C
NFIA = - 0.04*24, t>0
CA = TB + NFIA
W(t) = W(t-1) + CA(t)
0
300
24
300.92
-24.92
0
-24.92
-24.92
1
301.92
0
300.92
1.00
-0.96
0.04
-24.89
2
301.92
0
300.92
1.00
-0.96
0.04
-24.85
3
3
301.92
0
300.92
1.00
-0.96
0.04
-24.81
…
…
…
…
…
…
…
…
Present
Value
7848
24
7824
0.08
-24
-23.92
In Case 2, the home country can borrow as much as it desires. Thus, the home residents
can smooth consumption and finance its investment from borrowing. They choose constant
consumption path, which is their first best. Thus, in Year 0 they borrow to finance both
investment and an increase in consumption. This is because they foresee “permanent increases”
in their output and lifetime income. Thus, they can afford to increase consumption even before
the investment begins to pay off. We assume that the debt is sustainable, i.e. the foreign lenders
do not require payment of the principal.
However, even though the foreign lender does not demand payment of the principal, the
external wealth (W) keeps rising. This is because the home residents can invest the current
account surplus in assets of the 3rd country. As you can see, the accumulation of wealth in the 3rd
country is $0.04 billion every year. As this continues indefinitely, the external wealth position
can becomes positive and the home country can switch from being a debtor to a creditor! Why is
this possible? It is possible because the home country has an advanced technology that pays
much higher return than other countries.
Finally, let us consider Case 3, which is the situation in Question 3. In this case, the home
country faces the borrowing constraint. This implies that the investment project must be partially
financed by the domestic fund. The only way to do this is to cut consumption in Year 0. Thus,
the static budget constraint binds in Year 0. From Year 1, the static budget constraint also binds
because the home residents do not need to borrow any more. The home residents use income to
consume and to service debt. Again, we assume that the foreign lenders do not require payment
of the principal. Thus, from Year 1 the home residents will run trade surplus only to service the
interest rate payment = 0.04(20), and consume the rest of output.
Case 3: Open economy with borrowing constraint: r = r* = 0.04
(Unit = $billion)
Time
0
1
2
3
Q
300
301.92 301.92
301.92
I with foreign fund
20
0
0
0
I with home fund
4
0
0
0
C = Q – I – TB
296
301.12 301.12
301.12
TB = - NFIA
-20
0.80
0.80
0.80
NFIA = - 0.04(20), t>0
0
-0.80
-0.80
-0.80
CA = TB + NFIA
-20
0
0
0
W(t) = W(t-1) + CA(t)
-20
-20
-20
-20
…
…
…
…
…
…
…
…
…
Present Value
7848
20
4
7824
0
-20
-20
Let us compare the paths of consumption in all cases. Even with the borrowing constraint,
consumption still displays smaller volatility than consumption in the closed economy. (See the
diagram below.) Thus, the home residents are still better off with borrowing despite the
borrowing constraint.
4
Comparison of paths of consumption
310
300
C (closed economy)
C
290
280
C (open economy, no
borrowing constraint)
270
C (open economy, with
borrowing constraint)
260
1
2
3
4
5
6
Time
Question 4 (2 points)
Let W(t) denotes the external wealth in Year t. Since current account is the change in the net
foreign assets, then
W(t) = W(t-1) + CA(t).
Given that the initial external wealth is 0, we can use the current account in Question (3.d) to
calculate the external wealth. The path of W is provided in Case 3 in Question (3.c) and (3.d).
If the interest rates rise to 12%, the interest payments needed to service its debt will rise from
$0.80 billion to $2.4 billion (=0.12*20). The interest payments will be tripled! To finance the
increase in debt service burden, the consumers must reduce its consumption to finance the
increase in debt service. The reduction of consumption can be alleviated if the firms can find a
way to increase productivity among workers without a need to finance a new technology.
5