International Trade

1
International Trade

• Week 5 - Hecksher-Ohlin Model Relative Factor
  Endowments

2
Hecksher-Ohlin Model

• Two countries, two goods, X and Y, and two
  factors of prodn, labor, L and capital, K. (2 x
  2 x 2 model)
• Technology identical between countries.
• Production functions for both goods exhibit
  constant returns to scale.
• Each commodity has a different factor intensity,
  which are not affected by relative factor prices.
• Tastes and preferences identical between
  countries.
• Perfect competition in both industries and both
  countries.
• Factors are perfectly mobile within countries but
  perfectly immobile between countries.
• No transportation costs or tariffs or other
  barriers to trade.

3
Production Functions, Isoquants, and Relative
Factor Prices
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Production Theory

• Production Function Q F(K, L)
• Shows amount of output produced for given inputs
  of capital labor.
• Assume exhibits constant returns to scale (CRS),
  diminishing marg. returns.
• Production Isoquant Q0 F(K, L)
• Shows the various combination of capital labor
  that can be used to produce a chosen level of
  output, Q0.
• Bowed shape result of diminishing marginal
  returns as substitute capital for labor to keep
  production level constant.
• Isocost Line Production Equilibrium
• Combination of K L choose to produce any given
  level output Q depends on relative prices of
  capital and labor, i.e. w/r, the relative wage.
• Isocost line shows all comb. of K L with same
  total cost given w and r.
• Firm will choose production point (K L) which
  minimizes total cost for any desired level of
  output Q0.
• With CRS prodn function, these points fall on a
  straight line from origin.
• Slope of this line depends on relative wage vs.
  return on capital.

5
Isoquants, Isocosts Production
1. Good X is labor-intensive.
2. Good Y is capital-intensive.
Given (w/r)
Capital, K
Note that Labor- or Capital-intensity of a good
is Determined by shape of Isoquants, i.e. prodn.
Labor, L
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Factor Endowments and Factor Intensities
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Factor Intensities Factor Abundance

• Factor Intensities (A property of production
  technologies)
• A Good Y is said to be capital-intensive if the
  ratio of capital-labor in its production is
  higher than the ratio of that used to produce
  Good X, at any relative factor price ratio. i.e.
  (K/L)Y gt (K/L)X .
• In a two good world, if Good Y is
  capital-intensive then Good X will be
  labor-intensive, at any relative factor price
  ratio.
• Factor Abundance (A property of factor
  endowments)
• Physical Units definition A nation is
  capital-abundant if its capital/labor ratio (K/L)
  is larger than that of the other nation.
• Relative Factor Price definition A nation is
  capital-abundant if its ratio of wage rate for
  labor to rental price of capital (w/r) is larger
  than that of the other nation.
• We assume these two defns are equivalent
  (although they arent exactly).
• H-O model combines both factor intensities of
  goods and relative factor abundance of nations to
  determine trade patterns.

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Relative Factor Costs Intensities
1. Good X is labor-intensive.
2. Good Y is capital-intensive.
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Factor Prices and Input Choices

• Note from previous slide
• As (w/r) increases from low to high, K/L
  ratio used to produce Good X increases. The same
  is true for Good Y.
• Implies there is an upward-sloping relation
  between relative factor price w/r and K/L used in
  production of each good.
• Also, at any level of (w/r) Good Y always uses
  higher K/L in prodn. Thus its relation is below
  that for Good X.

Wage-rental ratio,
w/r
Capital-Labor Ratio
K/L
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Deriving a Nations PPF in the H-O Model
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Edgeworth Box Joint Prodn
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Allocation of Factors to Goods Prodn
Capital, K
OX
Labor, L
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Allocation of Factors Nations PPF
1. Box below shows allocation of capital and
labor to each good, for a given w/r ratio.
Capital, K
OY
K/LHX
K/LHY
OX
Labor, L
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Factor Endowments and Factor Intensities in the
H-O Model of Trade
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Relative Factor EndowmentsEstimates for 1966
Source Bowen, Leamer, Sveikauskaus, AER 1987
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Factor Endowments Intensities
1. Good X is labor-intensive in both nations.
Capital, K
2. Good Y is capital-intensive in both nations.
Foreign, Capital-Abundant K/L high (w/r) high
Home, Labor-Abundant K/L low (w/r) low
Capital, K
Labor, L
Labor, L
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Factor Prices and Input Choices

• Note from previous slide
• As (w/r) increases from Home to Foreign, K/L
  ratio used to produce Good X increases. The same
  is true for Good Y.
• Implies there is an upward-sloping relation
  between relative factor price w/r and K/L used in
  production of each good.
• Also, at any level of (w/r) Good Y always uses
  higher K/L in prodn. Thus its relation is below
  that for Good X.

Wage-rental ratio,
w/r
Capital-Labor Ratio
K/L
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Differences in PPFs across Nations in the H-O
Model
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Labor-Abundant Nations PPF
1. Box below shows allocation of capital and
labor to each good, for a given w/r ratio.
Capital, K
OY
K/LHX
K/LHY
OX
Labor, L
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Capital -Abundant Nations PPF
1. Assume Foreign has more capital than labor .
Capital, K
OY
OX
Labor, L
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Equilibrium in the Hecksher-Ohlin Model
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Differing Technology/Endowments
Y
X
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Hecksher-Ohlin Theorem

• Countries will export goods that use their
  abundant factors intensively and import those
  goods that use their scarce resources
  intensively.
• Previous slides showed how factor endowments
  determine shape of each nations PPF.
• Assuming identical utilities, then Hecksher-Ohlin
  theorem result arises for the pattern of trade.
• Effects of trade
• Trade results in mutual gains.
• Countries reallocate factors to increase
  specialization in goods that use their abundant
  factors intensively.
• Relative commodity prices are equalized across
  nations after trade. (This will have implications
  for relative factor prices across nations also.)

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Net Export () of Factor Services - 1967
Source Bowen, Leamer, Sveikauskaus, AER 1987
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Trade, Distribution, and Welfare in the H-O Model
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Relative Product Prices Factor Prices

• Relative product price (PX/PY) is linked to
  relative factor returns (w/r) in the H-O model by
  the mobility of factors between industries within
  a country.
• Assume relative price of X rises in Home from
  opening trade.
• Higher (PX/PY) leads Home producers to raise
  supply of X relative to Y.
• Good X is labor-intensive so generates larger
  increase in demand for labor than labor released
  by fall in supply of capital-intensive Good Y.
• Result is increase in demand for labor, driving
  up real wage, w.
• Exact opposite result for capital in Home as
  prodn shifts to Good X.
• Higher (PX/PY) thus leads to higher (w/r) as a
  result of different factor intensities of the
  Goods combined with labor mobility between
  industries within Home.
• Diagram on next slide illustrates this
  relationship between relative product prices and
  relative factor prices in H-O model.

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Relative Factor Prices and Product Prices

• As (PX/PY ) increases suppliers switch production
  from Good Y to Good X.
• Good Y is capital-intensive, while Good X is
  labor-intensive.
• Reducing production of Y increases capital by
  more than that needed for X. Implies fall in
  return to capital, r.
• This also increases labor by less than that
  needed for X. Implies rise in return to labor, w.
• Rise in (PX/PY ) thus results in rise in (w/r).

Relative Price of X,
PX/ PY
SS
Wage-rental ratio
w/r
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From Relative Prices to Production

• In the Hecksher-Ohlin Model
• For a given set of factor prices, firms choose
  specific, but different, ratios of factor inputs
  (K/L) to produce each Good.
• A given set of relative product prices (PX/PY) is
  associated with a given relative factor price
  (w/r).
• Combining these two results allows us to examine
  what capital/labor ratios are used in prodn of
  each good in each nation before trade.
• Provide diagrams linking the two results on next
  slide.
• Will also be able to examine the consequences of
  the equalization of relative product prices as
  result of trade for the relative factor prices
  and capital/labor ratios across countries.

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Relative Factor Prices and Product Prices
Wage-rental ratio,
w/r
SS
K/L
PX/ PY
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Capital/Labor Ratios by Industry (For U.S. 1985)
Source U.S. Dept. of Commerce, Annual Survey of
Manufactures
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Trade, Distribution Welfare

• Factor Price Equalization Theorem
• International trade will bring about the
  equalization in the relative and absolute returns
  to homogenous factors of production across
  nations.
• Trade in final goods essentially substitutes for
  movement of factors between countries to equalize
  differences in relative factor returns.
• Stolper-Samuelson Theorem
• Free trade will result in an increase in the
  reward to the abundant factor and a decrease in
  the reward to the scarce factor, i.e. the
  relative return earned by the abundant factor
  will rise with the opening of trade.
• Assuming full employment before and after trade.
• Do not find complete factor price equalization of
  H-O theory.
• May be barriers to adjustment trade barriers,
  transportation costs, heterogeneous capital or
  labor, non-traded goods, imperfect competition,
  unemployed factors, etc.

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Relative Factor Prices and Product Prices
Wage-rental ratio,
w/r
SS
K/L
PX/ PY
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Convergence of Real Wages
Real Hourly Wage in Manufacturing (as Percentage
of U.S. Wage)
Source IMF, OECD, and US BLS
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Factor Growth in the H-O Model
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Rybczinski Theorem

• At constant product prices, an increase in the
  endowment of one factor will increase by a
  greater proportion (magnification effect) the
  output of the good intensive in that factor, and
  will reduce the output of the other good.
• Intuition
• Assume that the supply of capital increases.
• Constant product prices imply constant relative
  factor returns, (w/r).
• But relative factor returns can remain constant
  only if K/L and productivity of K and L remain
  constant in prodn of both goods.
• To fully employ new capital, while keeping K/L
  constant in both goods, requires fall in output
  of labor-intensive Good X to release enough labor
  to absorb increase in K in prodn of Good Y.
• Thus output of capital-intensive Good Y increases
  while output of labor-intensive Good X falls.

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Factor Growth the Rybczinski Theorem
Good Y
K0
K/LHX
OX
Labor, L
Good X
37
Changes in Relative Factor Endowments
Source Mutti Morici, Changing Patterns of U.S.
Economic Activity Comparative Advantage