3. In this question, assume all dollar units are real dollars in billions, so $150 means $150 bil-
lion. It is year 0. Argentina thinks it can find $150 of domestic investment projects
with an MPK of 10% (each $1 invested pays off $0.10 in every later year). Argentina
invests $84 in year 0 by borrowing $84 from the rest of the world at a world real in-
terest rate r*of 5%. There is no further borrowing or investment after this.
Use the standard assumptions: Assume initial external wealth W(Win year 1) is 0.
Assume G0 always; and assume I0 except in year 0. Also, assume
NUT KA 0 and that there is no net labor income so that NFIA r*W.
The projects start to pay off in year 1 and continue to pay off all years thereafter. In-
terest is paid in perpetuity, in year 1 and every year thereafter. In addition, assume that
if the projects are not done, then GDP QC$200 in all years, so that
PV(Q) PV(C) 200 200/0.05 4,200.
a. Should Argentina fund the $84 worth of projects? Explain your answer.
Answer: Yes. The criterion for undertaking an investment project is:
Q
K
r*
Because MPK 10% r*(5%), the country will benefit from the investment
project.
b. Why might Argentina be able to borrow only $84 and not $150?
Answer: Argentina may face borrowing limits. Because 150 units of output ac-
counts for three-fourths of the country’s total production, lenders might be un-
willing to lend this much, even for a productive investment project.
c. From this point forward, assume the projects totaling $84 are funded and com-
pleted in year 0. If the MPK is 10%, what is the total payoff from the projects in
future years?
Answer: The project will result in an 8.4 increase in Qeach period
(MPK K0.10 84).
d. Assume this is added to the $200 of GDP in all years starting in year 1. In dol-
lars, what is Argentina’s QGDP in year 0, year 1, and later years?
Answer: Q
0
200, Q208.4 in subsequent years.
Economics 141
UCSC Professor K. Kletzer
Spring 2017
Suggested Study Problems 2 Answers
Numbered as in Chapter 6 Problems
e. At year 0, what is the new PV(Q) in dollars? Hint: To ease computation, calcu-
late the value of the increment in PV(Q) due to the extra output in later years.
Answer: The present value of the increment in PV(Q) due to the extra output
equals 0 8.4/0.05 168, whereas the present value of entire stream of new
future output is:
PV(Q) Q
0
Q
r*
200
2
0
0
.
8
0
.
5
4
4,368
f. At year 0, what is the new PV(I) in dollars? Therefore, what does the LRBC say
is the new PV(C) in dollars?
Answer: The present value of investment is:
PV(I) K84
Using the LRBC, we can calculate the present value of consumption:
PV(C) PV(Q) PV(I) 4,368 84 4,284
g. Assume that Argentina is consumption smoothing. What is the percent change in
PV(C)? What is the new level of Cin all years? Is Argentina better off?
Answer: The percent change in the present value of consumption (compared
with the case with no investment project) is 2% (84(4,284 4,200)/4,200).
