# ECO101H1 Chapter Notes - Chapter 9: Route Nationale 17, Marginal Product, Longrun

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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

PVIL – C > PVPA,

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.

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9-3. Mickey and Minnie live in Orlando. Mickey’s net present value of lifetime earnings in Orlando

is $125,000. Minnie’s net present value of lifetime earnings in Orlando is $500,000. The cost of

moving to Atlanta is $25,000 per person. In Atlanta, Mickey’s net present value of lifetime earnings

would be $155,000, and Minnie’s 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

neither?

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 worker’s 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 (w0) with their potential

earnings in the United States (w1). The wage-skills relationship in each of the two countries is given

by:

w0 = 700 + 0.5s,

and

w1 = 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

United States).

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(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.

(c) What would happen to the selection that takes place if migration costs are not constant in the

population, but are much higher for more skilled workers?

If migration costs are much higher for skilled workers, it is possible that no skilled workers will find it

worthwhile to migrate. We already know that even in the absence of migration costs no worker with

fewer than 60 efficiency units finds it worthwhile to migrate. If highly skilled workers find it very costly

to migrate it might be the case that there is no migration to the United States.

Income

700

670

60 Efficiency Units

Source

Country

US

Income

Efficiency Units

700

660

80

Source

Country

US

## Document Summary

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 ,000 per year in each of the three periods. If the worker moves to illinois, he will earn ,000 in each of the three periods. The worker must compare the present value of staying in pennsylvania to the present value of moving to. 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: The worker will move, therefore, if where c denotes migration costs. Nick"s present value of lifetime earnings in his current employment is ,000, and jane"s present value is ,000.