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:
PV PA = 20,000 + + 2 =$54,710.74
PV IL22,000 + + =$60,181.82
The worker will move, therefore, if
PVIL 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. Nicks present value of
lifetime earnings in his current employment is $300,000, and Janes present value is $200,000. They
are contemplating moving to Texas, where each of them would earn a lifetime income of $260,000.
The couples 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 Minnesotas frigid winters, so she figures she would be $2,000
worse off because of Texass 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 Nicks and Janes 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.
60 9-3. Mickey and Minnie live in Orlando. Mickeys net present value of lifetime earnings in Orlando
is $125,000. Minnies net present value of lifetime earnings in Orlando is $500,000. The cost of
moving to Atlanta is $25,000 per person. In Atlanta, Mickeys net present value of lifetime earnings
would be $155,000, and Minnies net present value of lifetime earnings would be $510,000. If
Mickey and Minnie choose where to live based on their joint well-being, will they move to Atlanta?
Is Mickey a tied-mover or a tied-stayer or neither? Is Minnie a tied-mover or a tied-stayer or
As a couple, the net present value of lifetime earnings of staying in Orlando is $500,000 + $125,000 =
$625,000 and of moving to Atlanta is $510,000 + $155,000 $50,000 = $615,000. Thus, as a couple,
they would choose to stay in Orlando. Thus, there can only be a tied-stayer. (There cannot be a tied-
mover, because the couple is not moving.)
For Mickey, staying in Orlando is associated with a net present value of $125,000, while moving to
Atlanta would yield a net present value of $155,000 $25,000 = $130,000. So Mickey would choose to
move to Atlanta. Therefore, Mickey is a tied-stayer.
For Minnie, staying in Orlando is associated with a net present value of $500,000, while moving to
Atlanta would yield a net present value of $510,000 $25,000 = $485,000. So Minnie would choose to
remain in Orlando. Thus, Minnie is not a tied-stayer.
9-4. Suppose a workers skill is captured by his efficiency units of labor. The distribution of
efficiency units in the population is such that worker 1 has 1 efficiency unit, worker 2 has 2
efficiency units, and so on. There are 100 workers in the population. In deciding whether to migrate
to the United States, these workers compare their weekly earnings at home (w 0) with their potential
earnings in the United States (w ). The wage-skills relationship in each of the two countries is given
w0 = 700 + 0.5s,
w = 670 + s,
where s is the number of efficiency units the worker possesses.
(a) Assume there are no migration costs. What is the average number of efficiency units among
immigrants? Is the immigrant flow positively or negatively selected?
The earnings-skills relationship in each country is illustrated in the figure below. The US line is steeper
because the payoff to a unit of skills is higher in the United States. All workers who have at least 60
efficiency units will migrate to the United States. Therefore, there is positive selection and the average
number of efficiency units in the immigrant flow is approximately 80 (the exact answer depends on
whether the person with 60 efficiency units, who is indifferent between moving or not, moves to the
60 Efficiency Units
(b) Suppose it costs $10 to migrate to the United States. What is the average number of efficiency
units among immigrants? Is the immigrant flow positively or negatively selected?
If everyone incurs a cost of $10 to migrate to the United States, the U.S. wage-skill line drops by $10, and
only those persons with more than 80 efficiency units will find it worthwhile to migrate. The immigrant
flow is still positively selected and has, on average, 90 efficiency units.