,C w r p

r

w

,L Ka a

rK wL p

Factor-price determination in the 1 good, two-factor case

11,C w r p

22,C w r p

r

w

2 2,L Ka a

2 2,L Ka a

1 11K La r a w p

Factor-price determination in the 2x2 case (i)

11,C w r p

22,C w r p

r

w

2 2,L Ka a

2 2,L Ka a

2

2L

K

a

a

2

2L

K

a

a

111 1

L

K K

p ar w

a a

Factor-price determination in the 2x2 case (ii)

11,C w r p

22,C w r p

r

w

2 2,L Ka a

2 2,L Ka a

2

2L

K

a

a

2

2L

K

a

a

Factor-price determination in the 2x2 case (iii)

11,C w r p

22,C w r p

r

w

2 2,L Ka a

2 2,L Ka a

2

2L

K

a

a

2

2L

K

a

a

w(p)

r(p)

111 1

L

K K

p ar w

a a

Factor-price determination in the 2x2 case (iv)

11 1, 'C w r p p r

w

2 2,L Ka a 2 2,L Ka a

2

2L

K

a

a

2

2L

K

a

a

w(p’)

r(p’)

The Stolper-Samuelson theorem

1

1 11 , 1f L Kp

2

2 22 , 1f L Kp

K

L

The Lerner diagram (i)

unit-revenue isoquant

Step 1: set technologies and good prices

1

1 11 , 1f L Kp

2

2 22 , 1f L Kp

K

L

wL/y1 + rK/y1 = 1 (unit isocost, common to both

sectors)

1/w

1/r

-w/r

unit-revenue isoquant

Profit-max. point for sector 1

Profit-max. point for sector 2

Step 2: determine profit-maximization points and factor prices

The Lerner diagram (ii)

1

1 11 , 1f L Kp

2

2 22 , 1f L Kp

2

2 2/

KK y a

K

L

(w,r)

(w,r)

1

1K

L

a

a

wL/y1 + rK/y1 = 1 (unit isocost)

1/w

1/r

1

1 1/

KK y a

1

1 1/

Ly aL 2

2 2/

Ly aL

-w/r

unit-revenue isoquant

2

2K

L

a

a

Step 3: determine equilibrium factor intensities given factor prices

The Lerner diagram (iii)

1

1 1

1

1,f L K

p

2

2 2

2

1,f L K

p

2

2 2/

KK y a

K

L

(w,r)

(w,r)

wL/y1 + rK/y1 = 1

1/w

1/r

1

1 1/

KK y a

1

1 1/

Ly aL 2

2 2/

Ly aL

-w/r

This one can’t: out of the DC

Step 4: identify diversification cone

This endowment can be fully employed by a linear combination of industries 1 and 2’s factor intensities: in the DC

The Lerner diagram (iv)

1

1K

L

a

a

2

2K

L

a

a

1

1 11 , 1f L Kp

2

2 22 , 1f L Kp

2

2 2/

KK y a

K

L

(w,r)

(w,r)

1

1K

L

a

a

wL/y1 + rK/y1 = 1 (unit isocost)

1/w

1/r

1

1 1/

KK y a

1

1 1/

Ly aL 2

2 2/

Ly aL

-w/r

The Lerner diagram with everything in it

unit-revenue isoquant

Profit-max. point for sector 1

Profit-max. point for sector 2

2

2K

L

a

a

K

LO

V1’

V2

11La y2

2La y

11Ka y

22 'Ka y

1 1 1, , ,L KA a w r a w r

2 2 2, , ,L KA a w r a w r

Home diversification cone

Home labor endowment

Home capital endowment

= V2’

22Ka y

V2’

11 'La y

The Rybczynski Theorem

K

L

K*

O

O’L*

V1

V2

11La y2

2La y

11Ka y

22Ka y

1 1 1, , ,L KA a w r a w r

2 2 2, , ,L KA a w r a w r

Home diversification cone

Home labor endowment

Home capital endowment

= V2

The factor-price equalization set

22,C w r p

r

w

2 2,L Ka a

1 1,L Ka a

Factor-price determination in the 2x2 case: Factor-intensity reversal

2 2,L Ka a

1 1,L Ka a

More flexible technologyIn this cone, both industries are more labor intensive than in the other one

K

L

K*

O

O’L*

Fi (factor content of trade)

ADi = Vi - Fi (consumption)

Home labor endowment

Home capital endowment

(home is cap-abundant) Vi (production)

The factor content of production and consumption

1KF

1LF

K

L

K*

O

O’L*

ADi = Vi - Fi (consumption)

Home labor endowment

Home capital endowment

Vi (production)

The factor content of production and consumption: Trade surplus

1LF

1KF

y1

y2

Rybczynski effect in goods space

“Rybczynski expansion path”

Chemicals

Machinery

Textiles

Apparel

K

L

y

time

y

time

Chemicals

Machinery

Apparel

y

time

y

time

Textile

Time path of capital accumulation

Leontieff isoquants

A

B

y

time

Portable radios

Satellites

k1 k2 k3k3

Intra-industry specialization

wS/wU

H/L

Skill premium under autarchy

FPE set

Skill premium after liberalization

H/L

wS/wU

Stolper-Samuelson effects

No FPE set

Autarky

wS/wU

H/L

Skill premium under autarchy

FPE set before the big 5’s entry

Skill premium after liberalization

H/L

wS/wU

FPE set after the big 5’s entry

Asia in the 70s

LA in the 90s

LA’s liberalization vs. Asia’s: Wood’s argument

Defensive skill-biased technical change (Thoenig-Verdier)

α (proportion of low-tech firms)

(unit hazard rate of innovations)

/RH c

α0

E0

“No-bias condition”

R&D sector’s resource constraint

1 0S

dV V

dt

0d

dt

1 0S

dV V

dt

Defensive technical change

0 V1 down

VS up

meaning “per sector” (look at R&D resource constraint)

Defensive skill-biased technical change (Thoenig-Verdier)

α (proportion of low-tech firms)

(unit hazard rate of innovations)

/RH c

/RnH c

0d

dt

α0

α1

E0

E2 “No-bias condition”: unaffected by trade opening

R&D sector’s resource constraint: shifts up with trade opening

before trade

after trade

0 21

E1

i

unit costs

C(.)

C*(.)

C’(.)

Production migrating to the South

i

E0

E1

'i

Production staying in the North

C*’(.)

Offshoring with a continuum of goods

MC

Inverse demand

MR

MC + TC (for the foreign firm)

pm

1/

n

zero-profit condition

Consumers’ budget constraint

c (consumption per head)

markup

Monopolistic competition: fixed markup

1/

n

zero-profit condition

Consumers’ budget constraint

c (consumption per head)

markup

Monopolistic competition: variable markup

ij ij ijS f

ijd

ijM

0ij 0ij

0ij

firm 1

firm 2

firm 1firm 2

no exports

OLS estimate

Elasticity to estimate (constant and common to all firms)

Figure 5.1