Chapter 8_Answers
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Chapter 8 problems
8-1
. 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 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:
and
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
8-3.
Patrick and Rachel live in Seattle. Patrick’s net present value of lifetime earnings in Seattle is $125,000, while Rachel’s is $500,000. The cost of moving to Atlanta is $25,000 per person
. In Atlanta, Patrick’s net present value of lifetime earnings would be $155,000, while Rachel’s would be $510,000. If Patrick and Rachel choose where to live based on their joint well-being, will they move to Atlanta? Is Patrick a tied-mover or a tied-stayer or neither? Is Rachel a tied-mover or a tied-stayer or neither?
As a couple, the net present value of lifetime earnings of staying in Seattle 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 Seattle.
For Patrick, staying in Seattle 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 Patrick would choose to move to Atlanta. Therefore, Patrick is a tied stayer
.
For Rachel, staying in Seattle 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, Rachel would choose to remain in Seattle. Thus, Rachel is not a tied stayer.
8-4
. Consider a household consisting of four college friends
. The friends have made a commitment to live together for the next five years. Presently they live in Milwaukee where Abby will earn $200,000, Bonnie will earn $120,000, Cathy will earn $315,000, and Donna will earn $150,000 over the next five years. They have the option of moving to Miami. Moving to Miami would impose a one-time moving cost of $5,000 on each person
. If they move to Miami, however, Abby will earn $180,000, Bonnie will earn $150,000, Cathy will earn $300,000, and Donna will earn $100,000 over the next five years. Moreover, each friend prefers to live in Miami over Milwaukee
. In particular, Abby and Bonnie both value the quality of life in Miami versus Milwaukee over the next five years at $40,000 while Cathy and
Donna place the value at $25,000 each. Should the household move to Miami or stay in Milwaukee? Is
anyone a tied-mover or a tied stayer?
The present value of staying in Milwaukee is calculated in thousands of dollars as:
PV
MIL
= $200 + $120 + $315 + $150 = $785.
The present value of moving to Miami is calculated as
PV
MIAMI
= $180 + $150 + $300 + $100 - $20 + $80 + $50 = $840.
Therefore, the household will move to Miami as PV
MIAMI
> PV
MIL
. As a result, no one can be a tied-stayer as the household doesn’t stay in Milwaukee. To determine if anyone is a tied-mover, one must calculate the present value calculations for each friend.
Abby: PV
MIL
= $200 vs PV
MIAMI
= $180 - $5 + $40 = $215 → Abby wants to move.
Bonnie: PV
MIL
= $120 vs PV
MIAMI
= $150 - $5 + $40 = $185 → Bonnie wants to
move.
Cathy: PV
MIL
= $315 vs PV
MIAMI
= $300 - $5 + $25 = $329 → Cathy wants to move.
Donna: PV
MIL
= $150 vs PV
MIAMI
= $100 - $5 + $25 = $220 → Bonnie wants to stay.
Thus, Donna is the only tied-mover
while the other three friends all strictly prefer to move to Miami.
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