Lectures 4-5: The specific factors model

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Lectures 4-5 The specific factors model

• Giovanni Facchini

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Outline

• Introduction
• The specific factors model
• International trade in the specific factors model
• Income distribution and the gains from trade
• The political economy of international trade
  policy
• Summary

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Introduction

• International trade has important income
  distribution consequences within a country.
• There are two fundamental reasons for why trade
  has important effects on income distribution
• Production factors cannot instantaneously
  relocate from one sector to another at zero cost.
  
• Factors demand vary by sector.
• The specific factors model highlights how trade
  affects the income distribution.

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The specific factors model

• Assumptions
• The economy produces two goods, manufactured
  goods (M) and food (F)
• There are three production factors labor (L),
  capital (K) and land (T).
• Manufactured goods are produced using capital and
  labor (but not land).
• Food is produced using land and labor (but not
  capital).
• Thus labor is mobile because it is used by both
  sectors
• Land and capital are specific factors that can be
  used in the production of one good only.
• All markets are perfectly competitive.

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The specific factors model

• How much of each good is produced?
• The production of manufactured goods depends on
  the quantity of labor and capital used in the
  sector.
• This relationship is captured by the production
  function.
• The production function for good X characterizes
  the maximum quantity of good X that can be
  produced using all possible combinations of
  factors.
• For example, the production function for
  manufactured goods (food) tells us the quantity
  of manufactured goods (food) that we can produce
  for any given quantity of capital (land) and
  labor.

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The specific factors model

• The production function for manufactured goods is
  given by QM QM (K, LM) (3-1)
• where
• QM is the output of manufactured goods
• K is the endowment of capital
• LM is the number of workers employed in the M
  sector
• The production function for manufactured goods is
  given by
• QF QF (T, LF) (3-2)
• where
• QF is the output of food
• T is the endowment of land
• LF is the number of workers employed in the F
  sector

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The specific factors model

• The labor market equilibrium under full
  employment implies that
• LM LF L (3-3)
• We can use these relationships to construct the
  production possibility frontier of the country.

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The specific factors model

• The production possibility frontier
• To analyze the production possibility frontier of
  the country we need to ask how the output mix of
  the country varies as labor relocates from one
  sector to the other.
• Figure 1 shows the production function for
  manufactured goods.

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The specific factors model
Figure 1 The manufactured goods production
function
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The specific factors model

• The shape of the production function highlights
  the presence of decreasing marginal product of
  labor
• Adding an extra worker to the production process,
  keeping capital constant, implies a reduction in
  the quantity of capital per worker.
• Therefore, every additional unit of labor will
  imply an increase in output at a decreasing rate.
• Figure 2 depicts the marginal productivity of
  labor, i.e. the increase of output brought about
  by an additional unit of labor.

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The specific factors model
Figure 2 The marginal product of labor
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The specific factors model
Figure 3 The PPF in the specific factors model
Food production function
Production possibility frontier(PP)
Manufactured goods production function
Labor allocation(AA)
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Slope of the PP curve

• Ricardian model
• The PP curve is a straight line because the
  opportunity cost of food in terms of
  manufacturing is constant
• Specific factors model
• The PP curve illustrates the presence of
  decreasing marginal productivity of labor in each
  sector. The slope is given by - MPLF /MPLM
• To increase the ooutput of manufactured goods by
  one unit, the economy needs to reduce the output
  of food by MPLF /MPLM

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The specific factors model

• Prices, wages and labor allocation
• How much labor will be used by each sector?
• To answer this question, we need to consider the
  demand and the supply of labor.
• Labor demand
• In each sector, employers will try to maximize
  profits, hiring workers up to the point in which
  the marginal product of labor is equal to the
  cost of hiring that additional unit.

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The firms problem

• In each sector, the firm maximizes profits, i.e.
  it solves the following problem

and the corresponding first order condition is
given by
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The specific factors model

• The labor demand curve in the manufacturing
  sector is given by
• MPLM x PM w
• The wage is equal to the value of the marginal
  product in the manufacturing sector.
• The labor demand in the food sector is instead
  given by
• MPLF x PF w
• Once again, the wage is equal to the value of the
  marginal product in the manufacturing sector.

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The specific factors model

• In equilibrium, the salary has to be the same in
  the two sectors, as a result of the perfect
  mobility of labor.
• The wage is determined as a result of market
  clearing
• LM LF L

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The specific factors model
The allocation of labor between sectors
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Labor demand in the food sector

• In equilibrium, the PPF is tangent to the line
  whose slope is given by the relative price of
  manufacturing in terms of food (with a minus
  sign).
• The relationship between relative prices and
  output levels is given by
• -MPLF/MPLM -PM/PF

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The specific factors model
Figure 5 Output in the specific factors model
Slope -(PM /PF)1
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The specific factors model

• What happens to the allocation of labor and the
  income distribution if the price of food and the
  price of the manufactured goods change?
• Two possible scenarios
• Proportional variation in prices
• Change in relative prices

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The specific factors model
Proportional increase in the two prices
PM increases by 10
PF increases by 10
Increase by 10 in the salary
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The specific factors model

• When prices change by the same proportion, there
  is no effect in real terms.
• The wage (w) increases proportionally with the
  prices, and as a result real wages are
  unaffected.
• The capital- and land- owners real incomes are
  also unaffected.

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The specific factors model

• If only PM increases, labor relocates from the
  food to the manufacturing sector and the output
  level increases in the manufacturing sector,
  while it decreases in the food sector.
• The wage (w) does not increase as much as PM ,
  since employment in the manufacturing sector
  increases and thus the marginal productivity of
  labor in that sector decreases.

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The specific factors model
An increase in the price of manufacturing by 10
Increase in the relative demand by 10
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The specific factors model
Figure 8 The effect of a change in the relative
price of manufacturing
Solpe - (PM /PF)1
Slope - (PM /PF) 2
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The specific factors model

• Relative prices and income distribution
• Assume that PM increases by 10. Then, we expect
  an increase in wages by less than 10, for
  example 5.
• What is the effect of this increase on the income
  of the following three groups?
• Workers
• Capital owners
• Landowners

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The specific factors model

• Workers
• The effect is indeterminate. It depends on the
  relative importance of the consumption of the two
  goods.
• Capital owners
• They are better off. The inflow of additional
  workers in the manufacturing sector increases the
  marginal productivity of capital.
• Land owners
• They are worse off. The outflow of workers from
  the food sector decreases the marginal
  productivity of land.

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The specific factors model
Figure 9 Determining relative prices
PM /PF
QM/QF
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International trade in the specific factors model

• Assumptions
• Assume that both countries (say Japan and the US)
  share the same preferences and thus the same
  relative demand.
• Thus the only source of trade is represented by
  differences in the relative supply across
  countries. The relative supply might differ
  because of
• technology
• different endowments of production factors
  (capital, labor, land)
• We will assume that there are differences in
  factor endowments.

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International trade in the specific factors model

• Endowments and relative supply
• What are the effects of an increase in the
  capital endowment on the output of manufactured
  goods and food?
• A country with a large endowment of capital will
  produce a higher ratio of manufacturing to food
  for every given combination of relative prices.

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International trade in the specific factors model
Figure 10 An increase in the endowment of capital
Increase in the capital stock K
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International trade in the specific factors model

• An increase in the endowment of capital leads to
  a shift to the right of the relative supply
• An increase in the endowment of land leads to a
  shift to the left of the relative supply
• What happens if the labor supply increases?
• The effect on the relative output level is
  ambiguous, even though we know that both outputs
  will increase.

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International trade in the specific factors model

• International trade and relative prices
• Assume that Japan (J) has more capital per worker
  than the USA (A). Analogously, the USA have more
  land per worker than Japan.
• As a result, the relative price of manufactured
  goods in autarky is lower in Japan than in the
  USA.
• International trade brings about a convergence in
  relative prices.

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International trade in the specific factors model.
Figure 11 International trade and relative prices
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International trade in the specific factors model.

• The structure of trade flows
• In autarky, production must be equal to
  consumption
• If trade is possible, the combinations of
  manufactured goods and food that are consumed
  might differ from those that are produced.
• Still, a country cannot spend more than the value
  of its output (no borrowing in this model).

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International trade in the specific factors model.
Figure 12 The budget constraint of a trading
economy
Budget constraint (slope -PM/PF)
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International trade in the specific factors model
Figure 13 Equilibrium under free trade
US budget constraint
Japans budget constraint
QAF
DAF
DJF
QJF
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Income distribution and the gains from
international trade

• To assess the effect of trade on income
  distribution, we need to remember that
  international trade changes the relative good
  prices .
• International trade improves the welfare of the
  specific factor used in the sector producing
  export goods, but it reduces the welfare of the
  specific factor used in the production of import
  competing goods.
• International trade has an ambiguous effect on
  the mobile factor.

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Income distribution and the gains from
international trade

• It is possible for those who gains from
  international trade to compensate those who lose
  from it?
• If this is the case, international trade is
  potentially Pareto improving, i.e. it can make
  everybody better off.
• International trade increases overall welfare
  because it expands the consumption possibility
  set.
• The expansion of the consumption possibility set
  implies that everybody can potentially at least
  be made better off as a result of international
  trade.

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Income distribution and the gains from
international trade
Figure 14 International trade expands the
consumption possibilities of each country
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The political economy of trade policy a
preliminary look

• International trade creates winners and losers.
• The optimal trade policy
• The government needs to trade off the gains of
  some groups against the losses of some other
  groups
• Some groups ask for protection because they are
  already poor (for examples, US workers in the
  shoe, apparel industries).
• Most economists are still in favor of open trade
  policies.
• To understand how trade policies come about, we
  need to understand the true reasons behind trade
  policy choices.

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The political economy of trade policy a
preliminary look

• Income distribution and trade policies
• Usually, those who gain from trade are much less
  informed than thos who lose from trade.
• Example sugar producers and consumers in the
  United States.

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Summary

• International trade has important effects on the
  income distribution within a country, thus
  creating winners and losers
• Income distribution effects are due to
• Production factors cannot relocate costlessly
  between one sector and the other.
• Changes in the output mix have different effects
  on the demand for production factors.

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Summary

• The specific factors model is a useful tool in
  the analysis of the income distribution effects
  of trade
• In this model, differences in factor endowments
  might lead to differences in the relative supply
  curves and thus lead to international trade.
• In each country, specific factors used in the
  exporting sectors benefit from opening up trade,
  while the specific factors used in the import
  competing sectors lose.
• The mobile factor, which is used in both sectors,
  might gain or lose..

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Summary

• International trade brings about aggregate gains,
  which can be used at least as a matter of
  principle to compensate the losers, and thus
  bring about Pareto gains from trade.