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•
Chapter 4
Specific Factors
and Income Distribution
Introduction
• So far we learned that countries are better off under free
trade.
• If trade is good for the economy, why is there such
opposition?
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Introduction
• Opening a country to trade has strong effects on the distribution
of income within a country:
– Some industries contract resulting in unemployment
– Some industries expand resulting in higher factor payments
• This happens because:
– Resources cannot move immediately or without cost from one
industry to another
– Industries differ in the factors of production they demand
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Introduction
What is the impact of trade on the
distribution of income within a country?
• In the Ricardian model, there is only one factor of production
(labor), so we cannot study the effect of trade on income
distribution.
• We need to develop new models that include multiple factors of
production.
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Multi-factor models
1. Specific-factors model (Chapter 4)
– The specific-factors model is a short-run model
– Some factors are specific to each sectors and cannot relocate
across sectors
2. Heckscher-Ohlin model (Chapter 5)
– The Heckscher-Ohlin model is a long-run model
– Factors can relocate across sectors at no costs
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Multi-factor models
• Recall that there are potential gains from trade whenever there is
cross-country variation in autarky prices.
• In the Ricardian model, differences in autarky prices come from
differences in technologies across countries.
• In the Multi-factor models:
– Technologies are the same in all countries
– Trade patterns are explained by cross-country differences in
relative factor endowments
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The Specific-Factors Model
• Assumptions
• Earnings of labor
• Earnings of specific factors
• Summary and conclusions
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Specific-Factors Model
• Assumptions of the model
1. Two sectors: Agriculture and Manufacture
2. Three factors of production: labor (L), capital
(K) and land (T for terrain)
3. Perfect competition prevails in all markets
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Specific-Factors Model
1. Supply
• The economy produces Manufacturing and Agricultural goods
– Manufacturing uses labor and capital:
– Agriculture uses labor and land:
Q M = FM (L M , K M )
Q A = FA (L A , TA )
• Labor is perfectly mobile across sectors but capital and land are
specific to their industry.
– For simplicity, factors cannot relocate across countries.
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Specific-Factors Model
• Full employment in factor markets implies that supply
is equal to demand:
LM + LA = L
KM = K
TA = T
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Specific-Factors Model
§ In each industry, the marginal product of labor declines as the
amount of labor used in the industry increases.
§ This happens because there is a fixed amount of the specific
factor.
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Specific-Factors Model
¶Q A
MPL A
MRT =
=¶Q M
MPL M
MPL M
MPLA
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Specific-Factors Model
Production Possibilities Frontier
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Specific-Factors Model
• The profit maximization problem can be written as:
max Π = 𝑃' 𝑄' + 𝑃* 𝑄* − 𝑊' 𝐿' − 𝑊* 𝐿* − 𝑅/ 𝐾' − 𝑅1 𝑇*
s.t.
𝑄' = 𝐹' (𝐿' , 𝐾' )
𝑄* = 𝐹* (𝐿* , 𝑇' )
𝐿7 = 𝐿' + 𝐿*
8 = 𝐾'
𝐾
𝑇7 = 𝑇*
𝑊* = 𝑊' = 𝑊
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Specific-Factors Model
• After replacing with the constraint in the objective function we get
8 + 𝑃* 𝐹* 𝐿7 − 𝐿' , 𝑇7 − 𝑊𝐿
8 − 𝑅/ 𝐾
8 − 𝑅1 𝑇7
max Π = 𝑃' 𝐹' 𝐿' , 𝐾
• The only choice variable is 𝐿' . The first order condition is given
by:
;
;
8 − 𝑃* 𝐹*,:
𝑃' 𝐹',:
𝐿' , 𝐾
𝐿7 − 𝐿' , 𝑇7 = 0
ó
;
𝐹*,:
𝐿7 − 𝐿' , 𝑇7
𝑃'
=−
≡ 𝑀𝑅𝑇
;
8
𝑃*
𝐹',: 𝐿' , 𝐾
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Specific-Factors Model
2. Demand
• Assume that consumer preferences can be represented by wellbehaved indifference curves
• The representative consumer maximizes utility subject to the
budget constraint.
• The optimal relative demand for good M is such that
MRS = −
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PM
PA
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Specific-Factors Model
3. Equilibrium
• Consumers maximize their utility: MRS = −
• Firms maximize profits: MRT = −
PM
PA
PM
PA
• All markets clear
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Specific-Factors Model
• In a competitive economy, profit maximizing firms will hire labor
up to the point where the marginal cost of labor equals the
marginal revenue.
W = P ´ MPL
• Since labor is perfectly mobile across sectors, the wage rate must
be the same in both sectors whenever both goods are produced:
W = PA ´ MPLA = PM ´ MPLM
• This implies that the closed economy equilibrium relative price is
equal to the opportunity cost:
PA MPLM
=
PM MPLA
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Specific-Factors Model
4. Foreign country
• Same as Home expect for endowments of labor, capital, and land
• Assume Home has comparative advantage in manufacturing
– The autarky relative price of manufactures in Foreign is
higher than in Home ( PM*/PA* > PM/PA )
– When trade is allowed the relative price of manufacturing
goes up in Home
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Specific-Factors Model
5. Autarky and Trade Equilibrium
QA
Slope = –(PM/PA)W
§ Autarky (point A):
production and
consumption are equal.
§ With trade supply (B) and
demand (C) no longer need
to be equal.
§ Home exports M and
imports A
A
U1
B
PPF
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§ The rise in utility from U1
to U2 is a measure of the
gains from trade for the
QM economy.
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Specific-Factors Model
• As in the Ricardian model, the country’s aggregate consumption
is higher so welfare for the average consumer is higher.
• However, in the specific factors model that does not imply that
everyone is better off. When input ownership is not distributed
evenly across consumers, there will be both losers and winners
How are earnings of labor, capital, and land affected
in importing and exporting industries after trade?
• Specific factors model notes
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Summary
• Following an increase in the relative price of manufactures:
– Labor can buy more food but less manufactures. So the
welfare effect on workers (the mobile factor) is ambiguous.
– Capital (specific to manufactures, the export good) owners
can afford more of both goods, they are better off.
– Land (specific to agriculture, the import good) owners can
afford less of both goods, they are worst off.
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Trade Policy
• In the specific-factors, trade benefits a country by
expanding choices but not everyone gains from trade.
• However, those who gain from trade could compensate
those who lose and still be better off themselves.
• Redistribution usually hard to implement.
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Trade Policy
• Trade shifts jobs from import-competing to export-competing
sectors.
– Process not instantaneous – some workers will be unemployed
as they look for new jobs
– Governments usually provide a safety net of income support
to cushion the losses to groups hurt by trade (or other
changes)
• How much unemployment can be traced back to changes in trade
policy?
– No clear pattern
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Trade Policy
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Trade Policy
• Trade policy must weigh one group s gain against
another s loss
– Some groups may need special treatment because
they are already relatively poor
– Typically, those who gain from trade are a much
more concentrated, informed, and organized group
than those who lose
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Trade Policy
• Economists tend to favor free trade
– It is easier to use “macro” policies than to regulated
each industries separately
– Policies introduce distortions which makes it difficult
to evaluate their (full general equilibrium) impact
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Conclusion
In the specific-factors model an increase in the relative
price of an industry’s output will:
• Have an ambiguous impact on the welfare of the
mobile factor
• Increase the real rental earned by the factor specific
to that industry
• Decrease the real rental of factors specific to other
industry
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Conclusion
In the specific-factors model:
– Trade benefits a country by expanding choices
– Not everyone gains from trade
• However, the gains outweigh the losses:
– Those who gain from trade could compensate those who lose
and still be better off themselves
– That everyone could gain from trade does not mean that they
actually do – redistribution usually hard to implement
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