Download ECON 371 Spring 2010 Answer Key for Problem Set 3 (Chapters 16

ECON 371 Spring 2010
Answer Key for Problem Set 3
(Chapters 16-17)
Instructor: Kanda Naknoi
March 8, 2010
ANSWER 1 (2 points)
By definition, a debtor country has negative external wealth: W = A – L < 0, where W denotes
external wealth, A denotes external assets and L denotes external liabilities. Net capital income
(NCIF) flows accrued on external liabilities and assets are recorded in the net factor income
account (NFIA) which is a part of current account. Specifically, NCIF is the difference between
capital income accrued on external assets and capital income accrued on external liabilities:
NCIF = rA A – rL L,
(1)
where rA and rL are the rate of return on external assets and external liabilities, respectively. It is
possible for the U.S. to receive positive NCIF if rA > rL. In fact, this is the case in the actual
balance of payments statistics. The return on U.S. external assets is found to be 2%-3% higher
than the return on U.S. external liabilities. To give a numerical example, suppose A = $4 trillion,
L = $5 trillion, rA=7% and rL= 5%. Substituting these numbers into Equation (1) yields NCIF:
NCIF = 0.07(4) – 0.05(5) = 0.28-0.25 = $0.05 trillion > 0.
We can also verify that these numbers make the U.S. a debtor country by showing that they
produce negative external wealth:
W = 4-5 = - $1 trillion < 0.
ANSWER 2.a (1 point)
There is a one-time increase in output by 20%. The increase amounts to 0.20($1700)=$340. The
present value of output is:
PV(Q) = (1700+340) + 1700/1.07 + 1700/1.072+ 1700/1.073+ …
= 340 + (1700 + 1700/1.07 + 1700/1.072+ 1700/1.073+ …)
= 340 + 1700(1.07)/0.07
= 26,325.71
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In the closed economy, the country must absorb the entire change in output into consumption in
the initial period because international borrowing or lending is not possible. Therefore, C0=2040
and Ct=1700 for t>0.
ANSWER 2.b (1 point)
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 representative consumer plans a constant level of consumption:
Ct= C0 for all t:
PV(Q)
= C0 + C0/1.07 + C0/1.072 + C0/1.073 + …
340 + 1700(1.07)/0.07
= C0 (1.07)/0.07
C0
= 340(0.07)/1.07 + 1700
= 1722.24
ANSWER 3.a (1 point)
Yes, this U.S. should fund this project. The criterion for investing in a project is that:
PV(Cost of investment) < PV (Return on investment)
(2)
Since there is no new investment from Year 1,PV(Cost of Investment) = $30 billion. The present
value of return on investment now depends on the interest rate. Here, the domestic interest rate if
the economy is closed is the same as the MPK. The world interest rate is 0.04. However, when
this country opens to the world capital market, the domestic interest rate becomes the same as the
world interest rate. Thus, we use the world interest rate to evaluate the present value of the return
on investment. Every period this project pays 6% of $30 billion. Hence,
PV(Return on Investment) = 0+0.06(30)/1.04+ 0.06(30)/1.042 +… = 0.06(30)/0.04= $45 billion.
In this case, PV(cost of investment) < PV(Return on Investment). As a result, this investment
project should be undertaken.
ANSWER 3.b (1 point)
Present value of payoff is $45 billion. (See ANSWER 3.a)
ANSWER 3.c (1 point)
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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 two cases
we studied in class: (1) Closed economy without international borrowing; and (2) Open economy
with international borrowing without borrowing constraint.
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.
Case 1: Closed economy, no international borrowing : r = MPK = 0.06; investment return
= 0.06(30) = 1.80 (Unit = $billion)
Time
0
1
2
3
… Present Value
Q
300
301.80
301.80
301.80
…
5631.80
I
30
0
0
0
…
30.00
C
270
301.80
301.80
301.80
…
5601.80
In Case 2, the home country can borrow as much as it desires. Thus, the home residents
can smooth consumption and finance its investment from borrowing. They choose constant
consumption path C0 such that: PV(Q)= PV(C) + PV(I). Substitute the paths of Q and I into this
lifetime budget constraint:
300+301.80/1.04 + 301.80/1.042 +… = (C0+ C0/1.04 + C0/1.042 + …) + 30
300 + 301.80/0.04
= C0(1.04)/0.04 + 30
C0
= (7845-30)0.04/1.04 = 312.18
Case 2: Open economy without borrowing constraint: r = r* = 0.04; investment
return = 0.06(30) = 1.80 (Unit =$billion)
Present
Time
0
1
2
3
… Value
Q
300
301.80
301.80 301.80
…
7845
I
30
0
0
0
…
30
C
300.58
300.58
300.58 300.58
…
7815
TB = Q-I-C
-30.58
1.22
1.22
1.22
…
0
NFIA = -0.04(30), t>0
0
-1.20
-1.20
-1.20
…
30
CA = TB + NFIA
-30.58
0.02
0.02
0.02
…
-30
W(t) = W(t-1) + CA(t)
-30.58
-30.56
-30.54
-30.52
…
Note that the present value of income is different from that in Case 2, because the interest rate is
now 4%. We can calculate trade balance by substituting C0 = 312.18 into the trade balance
equation: TB = Q – I – C. In Year 0, the consumer borrows 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. Note that the external debt keeps shrinking, because the investment return is
higher than the cost of borrowing. As this continues indefinitely, the external wealth position can
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becomes positive and the home country can switch from being a debtor to a creditor! This is
possible simply because the home country possess more advanced technology than the rest of the
world.
Finally, let us consider the situation in Question 3, and call it Case 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;
investment return = 0.06(30) = 1.80
(Unit = $billion)
Time
0
1
2
3
Q
300
301.80 301.80
301.80
I with foreign fund
20
0
0
0
I with home fund
10
0
0
0
C = Q – I – TB
290
301.00 301.00
301.00
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
7845
20
10
7815
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. Thus, the
home residents are still better off with borrowing despite the borrowing constraint.
ANSWER 3.d (1 point)
See Case 3 in ANSWER 3.c.
ANSWER 4 (2 points)
If the interest rates rise to 8%, the interest payments needed to service its debt will be doubled
from $0.80 billion to 0.08($20) = $1.6 billion. 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.
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