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INTERNATIONAL TRADE. THE HECKSCHER-OHLIN MODEL (FACTOR PROPORTIONS) – part B. Topic to be discussed. The Rybczynski theorem The Stolper-Samuelson Theorem The Factor Specific Model. The Rybczynski Theorem. The Relationship between Endowments and Outputs

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international trade

INTERNATIONAL TRADE

THE HECKSCHER-OHLIN MODEL

(FACTOR PROPORTIONS) – part B

topic to be discussed
Topic to be discussed
  • The Rybczynski theorem
  • The Stolper-Samuelson Theorem
  • The Factor Specific Model
the rybczynski theorem
The Rybczynski Theorem
  • The Relationship between Endowments and Outputs
  • The Rybczynski theorem demonstrates how changes in an endowment affects the outputs of the goods when full employment is maintained.
  • The theorem is useful in analyzing the effects of capital investment, immigration and emigration within the context of a H-O model
slide4

↑L →P constant →↑ production that labor intensive (SS factor)

  • Assume CRTS:
  • Relative factor (K/L) depends only on relative factor price (w/r) not on the scale of production
if p constant factor p also constant input k l also constant
If P constant: factor P also constant input (K,L) also constant
  • Suppose the amount of labor ↑by 10%, the amount of K constant

Production of one good must ↑, the other should ↓

Production of both good cannot ↑

Because there would not be enough K

Production of good X (labor intensive good) ↑ by more than 10%

Production of both good cannot ↓

Because there would not be enough L (unemployment)

Production of good Y (capital intensive) ↓

slide6

Qs

labor constraint

PPF at point A

capital constraint

A

s1

Qc

c1

when labor increase by 10
When labor increase by 10%

Qs

  • cause an outward parallel shift in the labor constraint.
  • production shift to point B.
  • Production of clothing, the labor intensive good, will rise from C1 to C2.
  • Production of steel, the capital-intensive good, will fall from S1 to S2.

suppose there is an increase in the labor endowment.

A

s1

B

s2

↑ in production of L-intensive gd (clothing)

↓ in production of K-intensive good (steel)

Qc

c1

c2

if capital increase
If capital increase…
  • If the endowment of capital rose

→ the capital constraint would shift out

→ causing an increase in steel production

→a decrease in clothing production.

Recall that since the

  • labor constraint is steeper than the capital constraint,

→ steel is capital-intensive and

→ clothing is labor-intensive.

slide11
The Rybczynski theorem says that if the capital endowment rises it will cause an increase in output of the capital intensive good (in this case steel) and a decrease in output of the labor intensive good (clothing).
  • In this numerical example QS rises from 24 to 36, Q C falls from 24 to 6.
magnification effect for quantities
magnification effect for quantities
  • The magnification effect for quantities ranks the percentage changes in endowments and the percentage changes in outputs.
  • K : (150-120/120) *100 = 25%

(capital stock rises by 25%)

  • Qs: (36-24/24)*100= 50%

(the quantity of steel rises by 50%)

  • Qc: (6-24/24)*100 = -75%

(the quantity of clothing falls by 75%)

  • L: 0%

(the labor stock unchanged)

summary rybczynski theorem
summary: Rybczynski Theorem
  • an increase in a country's endowment of a factor will cause an increase in output of the good which uses that factor intensively, and a decrease in the output of the other good.
the stolper samuelson theorem
The Stolper-Samuelson Theorem
  • demonstrates how changes in output relative prices affects the prices of the factors when positive production and zero economic profit is maintained in each industry .
  • It is useful in analyzing the effects on factor income, either when countries move from autarky to free trade or when tariffs or other government regulations are imposed within the context of a H-O model.
slide16
assumption of perfect competition in all markets,

→ if production occurs in an industry, → economic profit is driven to zero.

→The zero profit conditions in each industry imply

example
Example
  • Assume country A is labor abundant
  • Good X is labor intensive ( use more labor)
  • Under HOM: country A specialize in good X
slide18

Since production in good X

→ demand more labor

  • At the same time country A produce less capital intensive good (good Y) →demand less capital
  • When Y decrease in A

→ release some labor that use to work in Y

when trade occur
When trade occur
  • in country A
  • Increase production of good X

→ increase demand for labor in industry X

  • Decrease production y

→Decrease demand for labor in industry Y

  • ↑labor in X > ↓labor in Y
  • Wages increases
when trade occur1
When trade occur
  • Country A reduces production Y,

→ causing demand for K decrease

  • Production of X increases

→ It involve small increase in K

  • ↓ K in Y > ↑ K in X
  • Rental rate (r ) ↓
refer to country a
Refer to country A
  • An ↑ in relative P of L-intensive (Pc/Ps) good
  • Pc ↑; Ps ↓
  • Since W ↑↑
  • And ↑↑W > ↑Pc

→↑ real return to labor (w/Pc)

  • Since r ↓↓
  • And ↓↓ r > ↓Ps

→↓ real return to capital (r/Ps )

wage rental space
Wage- rental space
  • PS=aLSW + aksr and Pc=aLCW + aKCr

Rental rate

price

Dollar payment to capital owners per of steel produced

slide24
firms treat pricesexogenously since any one firm is too small to affect the price in its market.
  • Since the factor output ratios are also fixed --- wages and rentals remain as the two unknowns.
wage rental space1
wage-rental space

Slope of blue line

  • At wage and rental combinations above the line,
  • as at points A and D,

→ the per unit cost of

  • production would exceed the price,

→ thus profit would be negative.

  • At wage-rental combinations below the line as at points B and C,

→ the per unit cost of production would fall short of the price

→ profit would be positive.

r

Pc/aKC

The set of all wage and rental rates which will generate zero profit in the steel industry at the price PS

D

A

Ps/aKs

E

C

B

w

PC/aLC

Ps/aLs

wage rental space2
wage-rental space
  • At wage and rental combinations above the line,
  • as at points B and D,

→ the per unit cost of

  • production would exceed the price,

→ thus profit would be negative.

  • At wage-rental combinations below the line as at points A and C,

→ the per unit cost of production would fall short of the price

→ profit would be positive.

r

Pc/aKC

D

A

Ps/aKs

E

C

B

w

PC/aLC

Ps/aLs

wage rental space3
wage-rental space
  • wage-rental combination that can simultaneously support zero profit in both industries is found at the intersection of the two zero-profit lines - point E.

r

Pc/aKC

D

A

the equilibrium wage and rental rates that would arise in an HO model when the price of steel is PS and the price of clothing is PC

Ps/aKs

E

C

B

w

PC/aLC

Ps/aLs

wage rental space increase p
wage-rental space: increase P
  • In the case a country moves from autarky to free trade

→ cause an outward parallel shift in the blue zero-profit line for steel

→The equilibrium point will shift from E to F

→ causing an increase in the equilibrium rental rate from r1 to r2,

→ and a decrease in the equilibrium wage rate from w1 to w2.

r

an increase in the price of one of the goods (price of steel, PS↑)

r2

F

E

r1

w

w2

w1

effect of increase price of steel
Effect of increase Price of steel
  • Only with a higher rental rate and lower wage can zero profit be maintained in both industries at the new set of prices.
  • Using the slopes of the zero-profit lines we can show that

aLC/aKC > aLS/aKS

clothing is labor intensive

steel is capital intensive.

summary
summary
  • Thus, when PS↑
    • the payment to the factor used intensively in steel production (r) ↑
    • while the payment to the other factor (w) ↓
if price of clothing increase
If Price of clothing increase
  • If the PC↑

→ the zero-profit line for clothing would have shifted right

→ causing an increase in the equilibrium wage rate (↑w)

→ a decrease in the rental rate.(↓r)

Result:

→ an increase in the payment to the factor used intensively in clothing production (labor) ↑w

→ a decrease in the payment to the other factor (capital).↓r

conclusion stolper samuelson theorem
Conclusion: Stolper-Samuelson theorem
  • An increase in the price of a good will cause an increase in the price of the factor used intensively in that industry and a decrease in the price of the other factor.
the magnification effect for prices
The Magnification Effect for Prices
  • more general version of the Stolper-Samuelson theorem.
  • It allows for simultaneous changes in both output prices and compares the magnitudes of the changes in output and factor prices.
  • Example:
  • Given aLS = 3 ; aKS = 4 ; PS = 120
  • aLC = 2 ; aKC = 1 ; PC=40
slide34
aKS/aLS (4/3) > aKC/aLC (1/2)
  • Steel K-intensive ; clothing L-intensive
  • Zero profit steel: 3w + 4r =120
  • Zero profit clothing: 2w + r =40
slide35
Equilibrium: w = 8 ; r =24
  • Suppose, PC rises from $40 to $60.
  • Zero profit steel: 3w + 4r =120
  • Zero-profit clothing: 2w + r = 60
  • New equilibrium: w = 24 ; r =12
slide36
The Stolper-Samuelson theorem says that if the price of clothing rises, it will cause an increase in the price paid to the factor used intensively in clothing production (in this case the wage rate to labor) and a decrease in the price of the other factor (the rental rate on capital).
  • In this numerical example:
  • w ↑ ($8 to $24); r ↓ ( $24 to $12)
percentage changes in the goods and factor prices
Percentage Changes in the Goods and Factor Prices
  • PC: (60-40/40)*100 = +50%
  • W: (24-8/8)*100= +200%
  • R: (12-24/24)*100= -50%
  • Ps: 0%
  • The rank order of these changes is the Magnification Effect for Prices
  • W> PC > PS > r

If output prices change by some percentages, then the wage

rate paid to labor will rise by a larger percentage than the price of steel changes

Output prices appear in the middle of inequality

conclusion factor price
Conclusion: factor price
  • The magnification effect for prices can be used to determine the changes in real wages and real rents whenever prices change in the economy.
  • These changes would occur as a country moves from autarky to free trade and when trade policies are implemented, removed or modified.
the factor specific model
The Factor Specific Model
  • Under assumption of factors are perfectly mobile among industry or sector
  • It true if it in the long run
  • However, in the short run, the assumption may not true
  • Especially when on of the factor no mobile among the industry
slide40

Suppose the nation is relatively labor abundant produces 2 goods

  • X in L intensive; Y is K-intensive
  • Both goods use L and K
  • L is mobile between two industries; K is specific to each industry.
  • Let say K is used in production X (textiles) but cannot be used in production Y (steel)
with trade
With trade
  • Nation specialize in the production X and export X ; import Y
  • Increase (Px/Py); demand and nominal wage of L in the nation.
  • Some labor move from production Y to X
  • Since L is mobile; Industry Y have to pay higher nominal wage rate for labor
  • And facing reduction (Px/Py)
  • And Labor is transfer to production X
the effect of real wage of labor ambiguous
The effect of real wage of labor: ambiguous
  • ↑ in (Px/Py) and demand for labor > ↑ in nominal wage rate (W)
  • So the real wage (W/Px) of labor fall
  • Since the nominal wage rate (W) ↑; the price of Y ↓
  • Thus the real wage (W/Py) ↑
  • Conclusion:

(W/Px) decrease; (W/Py) increase

the effect of real wage of capital specific factor
The effect of real wage of capital (specific factor)
  • Since capital is fixed to each industry
  • Open the trade does not lead to any transfer of K from production of Y to X
  • In production X: more Labor used in specific-K

→ The real return on K increase

  • Production Y: less labor used with the same amount of specific-K

→ The real return of specific-K falls

conclusion factor specific model
Conclusion: factor specific model
  • Trade will have an ambiguous effect on the nation’s mobile factor (L)
  • benefit the immobile factor specific (K) to nation’s export commodities or sectors
  • harm the immobile factor specific (K) to the nation’s import competing commodities or sector
what we have discessed
What we have discessed
  • The Rybczynski theorem
  • The Stolper-Samuelson Theorem
  • The Factor Specific Model