Transcript 4.1-5 Proof of HO Theorem

Appendix 4.1
Alternate Proofs
of Selected
HO Theorems
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Production Isoquant
• An isoquant shows the various combinations of
labor and capital required to produce a fixed
quantity of a product.
• The curvature of an isoquant indicates the ease of
subsitutability between the two inputs, holding
output constant.
• A straight line isoquant indicates that the inputs are
perfect substitutes; right angles indicate that inputs
are not substitutable.
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4.1-2
FIGURE A4.1 Isoquant Map for the
S Industry
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4.1-3
Heckscher-Ohlin Theorem (Price
Definition)
• If country A (B) is relatively abundant in K
(L) and if good S (T) is relatively K (L)–
intensive in its production, then country A
(B) should have a comparative advantage in
the production of good S (T).
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4.1-4
Proof of HO Theorem
• See Figure A4.2
• There are two isoquants, each representing the
production of one unit of good S (T).
• The S isoquant is closer to the K-axis indicating
that S is more K-intensive.
• The least costly input combination for producing a
desired output level occurs at the tangency of an
isocost line (such as GH) and an isoquant (such as
point R for good S).
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4.1-5
FIGURE A4.2 Proof of the HO
Theorem (Price Definition)
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4.1-6
HO Theorem Proof (cont.)
• If isocost line GH is tangent to both S and T
isoquants (at points R and Q), then the cost of
producing each product must be identical.
• The slope of isocost line GH is equal to country A’s
autarky wage/rent ratio; GH cannot apply to
country B.
• Since B is more labor abundant than A, its
wage/rent ratio is lower than A’s.
• The isocost line to produce good S in country B is
higher than the isocost line to produce T; thus, B
has a comparative advantage in good T.
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4.1-7
Proof of the Rybczynski Theorem
• Refer to Figure A4.3
• Given isoquants representing $1 each of
goods S and T and an isocost line tangent to
both, the tangency points F and D represent
optimal input combinations.
• The slopes of the rays from the origin
passing through F and D indicate the optimal
capital/labor use ratios.
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4.1-8
Rybczynski Theorem (cont.)
• Given factor endowments represented by
point E, draw a parallelogram connecting E
to the two rays from the origin. Adding the
factor combination OG (OH) to point H (G)
will result in total endowment level E.
• When the country’s labor rises (capital and
prices constant), the endowment level
moves from E to E’. As a result, the output
of S falls to G’ while T rises to H’.
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4.1-9
FIGURE A4.3 Proof of the
Rybczynski Theorem
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4.1-10
Proof of Stolper-Samuelson
Theorem
• Refer to Figure A4.4
• The initial optimal input combinations are indicated
by the tangency points F and D.
• If the price of T rises, then a $1 worth of this good
is now on a lower isoquant T’. A new isocost line is
tangent to the isoquants S and T’.
• A comparison of the isocost lines shows that wages
have risen while rents have fallen. As a result, labor
(capitalists) can purchase more (less) of both
goods.
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4.1-11
FIGURE A4.4 Proof of the Stolper–
Samuelson Theorem
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4.1-12
Appendix 4.2
The Specific
Factors Model
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FIGURE A4.5 Equilibrium in the
Specific Factors Model
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4.1-14
Specific Factors (Ricardo-Viner)
Model
• Same assumptions as HO Model except
capital is immobile between industries
• Refer to Figure A4.5
• The horizontal axis measures labor input in
A, with labor units in S (T) industry
measured from point 0S (0T). The vertical
axes measure wage rate in A.
• The VMPS curve shows the S industry’s
demand for labor; the industry will hire labor
until W =PS x MPLS. Likewise for VMPT curve.
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4.1-15
Equilibrium in Specific Factors
Model
• Labor market equilibrium occurs at the
intersection of the VMPS and VMPT curves.
• 0SD workers are employed in the S industry
and D0T workers in the T industry.
• Wage rate paid to workers in both sectors is
W0.
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4.1-16
Effects of a Rise in Price of Good
S
• Country A has a comparative advantage in
S. When trade opens up, the price of S rises.
• Demand for labor will increase in industry S;
employment in S rises while employment in
the T sector falls. Wages also increase.
• Capital owners in industry S are better off as
their rental payments rise.
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4.1-17
FIGURE A4.6 Effects of an
Increase in PS
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4.1-18