# econ481

Order Details;

Econ

481

Spring

2015

Professor

Jessamyn

Schaller

Problem

Set

5:

Labor

Mobility

Due

in

class

April

23,

2015

1. A

worker

with

an

annual

discount

rate

of

5%

currently

resides

in

Tucson

and

is

considering

whether

to

remain

there

or

move

to

Phoenix.

There

are

three

work

periods

remaining

in

the

life

cycle.

If

the

worker

stays

in

Tucson,

she

will

earn

$40,000

per

year

in

each

of

the

three

periods.

If

she

moves

to

Phoenix

she

will

earn

$42,000

per

year

in

each

of

the

three

periods.

What

is

the

highest

(present-‐value)

migration

cost

she

will

be

willing

to

incur

and

still

make

the

move?

2. Looking

at

the

data,

suppose

that

we

see

that

immigrants

who

have

just

arrived

in

the

US

one

year

ago

earn

15%

less

than

their

native

equivalents

(same

age,

education,

etc),

while

immigrants

that

arrived

20

years

ago

earn

5%

more

than

their

US

equivalents.

How

might

assimilation

explain

this

phenomenon?

How

might

selection/composition

bias

instead

explain

this

phenomenon?

3. In

the

US,

the

wage-‐skills

relationship

in

the

labor

market

before

government

intervention

is

wUS=100+0.4s,

where

s

is

the

number

of

“efficiency

units

of

skill”

and

w

is

the

weekly

wage.

In

Canada,

the

wage-‐skills

relationship

is

wC

=

250

+

0.2s.

a. Draw

the

wage-‐skills

relationships

for

the

2

countries

on

a

graph.

Will

immigration

from

Canada

to

the

US

be

positively

or

negatively

selected?

Where

will

the

skill

cutoff

be

between

immigrants

and

non-‐immigrants

in

Canada

(i.e.

what

value

of

s)?

b. Now

suppose

the

US

creates

a

welfare

program

that

imposes

a

weekly

wage

floor

of

$280

(i.e.

it

provides

a

subsidy

for

any

worker

that

earns

less

than

$280

per

week

that

brings

them

up

to

that

level).

Draw

the

wage-‐skills

relationship

for

the

US

and

Canada

on

a

graph.

What

happens

to

migration

from

Canada

to

the

US?

Who

will

migrate?

What

are

the

new

cutoffs?

4. Consider

the

case

of

“extremity’

selection,

where

both

the

most

skilled

and

the

least

skilled

from

a

source

country

choose

to

migrate.

a. In

the

Roy

Model,

what

must

the

graph

of

the

return

to

skill

on

the

two

countries

look

like

to

generate

this

scenario?

Draw

an

example.

b. How

can

we

explain

this

type

of

selection?

Give

two

different

explanations.

c. Looking

at

immigrants

from

Mexico

to

the

US,

Chiquiar

and

Hanson

find

evidence

for

the

opposite

kind

of

selection–

“intermediate”

selection,

where

only

workers

from

the

middle

of

the

skill

distribution

migrate.

How

do

they

explain

this

finding

in

the

context

of

the

Roy

Model?

5. Phil

has

two

periods

of

work

remaining

prior

to

retirement.

Assume

that

Phil

maximizes

the

present

value

of

his

expected

lifetime

earnings

and

his

discount

rate

is

10

percent.

He

is

currently

employed

in

a

firm

that

pays

him

the

value

of

his

marginal

product,

$62,000

per

period.

There

is

one

other

firm

that

Phil

could

potentially

work

for.

There

is

an

80

percent

chance

of

Phil

being

a

good

match

for

the

other

firm

and

a

20

percent

chance

of

him

being

a

bad

match.

If

he

is

a

good

match,

his

VMP

at

the

new

firm

will

be

$65,000

per

period.

If

he

is

a

bad

match,

his

VMP

at

the

new

firm

will

be

$40,000

per

period.

a. Suppose

it

takes

a

full

period

to

discover

whether

Phil

is

a

good

or

bad

match

with

the

new

firm.

Thus,

when

the

firm

is

making

Phil’s

initial

offer,

the

managers

do

not

know

what

his

productivity

will

be,

though

they

do

know

the

distribution

of

possible

outcomes

described

above.

What

wage

will

the

firm

offer

in

this

initial

period?

b. After

the

value

of

the

match

is

determined,

Phil

will

then

be

offered

a

wage

equal

to

the

realized

value

of

his

marginal

product

in

the

firm.

When

offered

that

wage,

Phil

is

free

to

(a)

accept

or

(b)

return

to

his

original

firm

and

his

original

wage.

He

can

do

this

immediately,

so

that

if

he

gets

a

low

wage

offer

from

the

new

firm,

he

can

go

back

to

his

original

firm

and

earn

his

original

wage

in

the

second

period

(*Note

–

this

is

different

than

the

example

I

gave

in

class*).

What

should

Phil

do?

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