60
CHAPTER 9
9-1. Suppose a worker with an annual discount rate of 10 percent currently resides in Pennsylvania
and is deciding whether to remain there or to move to Illinois. There are three work periods left in
the life cycle. If the worker remains in Pennsylvania, he will earn $20,000 per year in each of the
three periods. If the worker moves to Illinois, he will earn $22,000 in each of the three periods.
What is the highest cost of migration that a worker is willing to incur and still make the move?
The worker must compare the present value of staying in Pennsylvania to the present value of moving to
Illinois. A worker will move if the present value of earnings in Illinois minus the costs of moving there
exceed the present value of earnings in Pennsylvania:
74
.
710
,
54
$
)
1
.
1
(
000
,
20
1
.
1
000
,
20
000
,
20
2
=
+
+
=
PA
PV
and
82
.
181
,
60
$
)
1
.
1
(
000
,
22
1
.
1
000
,
22
000
,
22
2
=
+
+
=
IL
PV
The worker will move, therefore, if
PV
IL
–
C
>
PV
PA
,
where
C
denotes migration costs. Thus, the worker moves if
C
< 60,181.82 - 54,710.74 = $5,471.08
9-2. Nick and Jane are married. They currently reside in Minnesota. Nick’s present value of
lifetime earnings in his current employment is $300,000, and Jane’s present value is $200,000. They
are contemplating moving to Texas, where each of them would earn a lifetime income of $260,000.
The couple’s cost of moving is $10,000. In addition, Nick very much prefers the climate in Texas to
that in Minnesota, and he figures that the change in climate is worth an additional $2,000 to him.
Jane, on the other hand, prefers Minnesota’s frigid winters, so she figures she would be $2,000
worse off because of Texas’s blistering summers. Should they move to Texas?
Yes. The “climatic” aspects of the move exactly balance each other, so we should not take them into
account. On the monetary side, the sum of Nick’s and Jane’s lifetime present value of earnings in
Minnesota is $500,000. The corresponding amount in Texas will be $520,000. The difference between the
two ($20,000) exceeds the cost of moving ($10,000), so the move will make the couple jointly better off.