Transcript Ricardian Model - University of Hong Kong

Chapter 3
Ricardian Model
1
Ricardian Model
•
•
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•
•
•
•
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Opportunity costs and comparative advantage
An Example
Relative demand-relative supply analysis
A one factor Ricardian model
Production possibilities
Gains from trade
Wages and trade
Misconceptions about comparative advantage
Transportation costs and non-traded goods
Empirical evidence
2
Introduction
• Theories of why trade occurs can be grouped into three
categories:
• Market size and distance between markets determine
how much countries buy and sell. These transactions
benefit both buyers and sellers.
• Differences in labor, physical capital, natural resources
and technology create productive advantages for
countries.
• Economies of scale (larger is more efficient) create
productive advantages for countries.
3
Introduction (cont.)
• The Ricardian model (chapter 3) says differences in
productivity of labor between countries cause productive
differences, leading to gains from trade.
– Differences in productivity are usually explained by differences in
technology.
• The Heckscher-Ohlin model (chapter 4) says differences
in labor, labor skills, physical capital and land between
countries cause productive differences, leading to gains
from trade.
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Comparative Advantage
and Opportunity Cost
• The Ricardian model uses the concepts of
opportunity cost and comparative advantage.
• The opportunity cost of producing something
measures the cost of not being able to produce
something else.
5
Comparative Advantage
and Opportunity Cost (cont.)
• A country faces opportunity costs when it employs
resources to produce goods and services.
• For example, a limited number of workers could be
employed to produce either wine or cheese.
– The opportunity cost of producing wine is the amount
of cheese not produced.
– The opportunity cost of producing cheese is the amount of wine
not produced.
– A country faces a trade off: how much wine or cheese should it
produce with the limited resources that it has?
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Comparative Advantage
and Opportunity Cost (cont.)
• A country has a comparative advantage in
producing a good if the opportunity cost of
producing that good is lower in the country than
it is in other countries.
• A country with a comparative advantage in
producing a good uses its resources most
efficiently when it produces that good compared
to producing other goods.
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Production Possibilities Frontier
a
15
b
Unattainable
c
10
d
Attainable
5
e
z
f
0
1
2
3
4
5
wine (millions of bottles per month)
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An Example
• China
– can produce 4,000 wine/hour or
– Can produce 1,333 cheese/hour
– o.c. of 1 cheese is 3 wine
– o.c. 1 unit of wine is 0.333 cheese
• Montenegro
–
–
–
–
can produce 1,333 wine/hour or
can produce 4,000 cheese/hour
o.c. of 1 cheese is 0.333 wine
oc. of 1 unit of wine is 3 cheese
Opportunity cost
of
One
wine
one
cheese
China
1/3
cheese
3 wine
Montenegro
3
cheese
1/3 wine
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cheese (thousands per hour)
An Example (cont)
5
4
3
2
1
Montenegro’s
PPF
China’s
PPF
1
2
3
4
wine (thousands per hour)
10
cheese (thousands per hour)
An Example (cont)
5
4 b'
China’s opportunity cost:
1 wine costs 1/3 cheese,
and 1 cheese costs 3 wine
Montenegro’s opportunity cost:
1 wine costs 3 cheese,
and 1 cheese costs 1/3 wine
3
c
2
1
a
Montenegro’s
PPF
China’s
PPF
b
1
2
3
4
wine (thousands per hour)
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An Example (cont.)
• China has comparative advantage in
producing wine, and Montenegro has c.a.
in producing cheese.
• China specializes in wine production and
Montenegro in cheese production.
• Both countries are better off by engaging
in international trade!
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An Example (cont)
• China—the country with absolute cost
disadvantage—can benefit from trade
• Montenegro—the country with absolute
cost advantage—can benefit from trade
too
• But how much exactly do they produce?
At what prices?
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Relative Demand Relative Supply
Analysis
Pc
Pw
Dw
Sw
Dc
Sc
Dc, Sc
Dw, Sw
The two markets in the home country; there are two markets in the
foreign country
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Relative Demand Relative Supply
Analysis
Pc / Pw : relative price of cheese
Dc / Dw : relative demand for cheese
Sc / Sw : relative supply of cheese
Suppose income=expenditure
Dc  Sc and Dw  Sw
if and only if
Dc Sc

Dw S w
• Hence, we don’t
need two
separate
diagrams for the
home country
• We just need to
look at one
relative demandrelative supply
diagram
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Relative Demand-Relative Supply
Analysis
Suppose income=expenditure
Dc  Dc *  Sc +Sc * and Dw  Dw *  S w  S w *
if and only if
Dc  Dc * Sc  Sc *

Dw  Dw * S w  S w *
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Relative Demand Relative Supply
Analysis
• To study the Ricardian Model, we need
to clarify what the RD and RS are.
• The RS is determined by the
technology
• The RD is determined by consumers’
preferences
– The preferences to be introduced are
general, applicable to other models
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Demand
• Assume identical,
homothetic preferences
• Each consumer’s relative
demand depends only on
relative price, and not on
her income level
• Given the relative price,
each consumer’s relative
demand is determined, so
is that of the whole
population
• One example is CobbDouglas utility function
Qw
I’=PcQc+PwQw
I’>I
I=PcQc+PwQw
Qc
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Cobb-Douglas Utility Function
max Qc ,Qw U (Qc , Qw )  Qc Qw1
subject to I  PcQc  PwQw
marginal utility of Cheese =  Qc 1Qw1
marginal utility of Wine = 1-  Qc Qw 
At Optimum
MU c MU w MU c Pc

or

Pc
Pw
MU w Pw
 Qc 1Qw1
Pc
Qc
 Pw





Pw
Qw 1   Pc
1-  Qc Qw
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Relative Demand
Pc/Pw
Qc

1

Qw 1   ( Pc / Pw )
High α
Relative demand by a
single consumer
=Relative demand by
the whole country
=Relative demand by
the whole world
Low α
Relative Demand,
Qc/Qw, or
(Qc+Qc*)/(Qw+Qw*)
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Relative Supply
• Assume that we are dealing with an economy
(which we call Home). In this economy:
–
–
–
–
Labor is the only factor of production.
Only two goods (say wine and cheese) are produced.
The supply of labor is fixed in each country.
The productivity of labor in each good is fixed (c.r.t.s.
technology).
– Perfect competition prevails in all markets.
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A One-Factor Economy
• The unit labor requirement is the number of
hours of labor required to produce one unit of
output.
• Denote with aLW the unit labor requirement for wine (e.g. if aLW =
2, then one needs 2 hours of labor to produce one gallon of
wine).
• Denote with aLC the unit labor requirement for cheese (e.g. if aLC
= 1, then one needs 1 hour of labor to produce a pound of
cheese).
• The economy’s total resources are defined as L,
the total labor supply (e.g. if L = 120, then this
economy is endowed with 120 hours of labor or
120 workers).
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Relative Price and Supply
• “I have a unit of labor, should I produce
cheese or wine?”
• To produce cheese, I can make 1/ aLC units
and get a revenue of Pc/ aLC.
• To produce wine, I make 1/aLw units and
hence get a revenue of Pw/ aLW.
• Hence,
• If Pc/Pw> aLC / aLW, I should produce cheese
• If Pc/Pw< aLC / aLW, I should produce wine
• If Pc/Pw= aLC / aLW, I don’t mind produce any
combination
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Relative Price and Supply
• The above relations imply that if the relative
price of cheese (PC / PW ) exceeds its
opportunity cost (aLC / aLW), then the
economy will specialize in the production of
cheese.
• In the absence of international trade, both
goods are produced, and therefore PC / PW =
aLC /aLW.
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Equilibrium under Autarky
Relative price of
cheese, PC/PW
aLC/aLW
RS
RD (low α)
Q
RD (high α)
Relative quantity
of cheese, QC /QW
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Trade in a One-Factor World
• Assumptions of the model:
– There are two countries in the world (Home and
Foreign).
– Each of the two countries produces two goods (say
wine and cheese).
– Labor is the only factor of production.
– The supply of labor is fixed in each country.
– The productivity of labor in each good is fixed.
– Labor is not mobile across the two countries.
– Perfect competition prevails in all markets.
– All variables with an asterisk refer to the Foreign
country.
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Trade in a One-Factor World
• Absolute Advantage
– A country has an absolute advantage in a production
of a good if it has a lower unit labor requirement than
the foreign country in this good.
– Assume that aLC > a*LC and aLW > a*LW
• This assumption implies that Home has an absolute
disadvantage in the production of both goods. Another way to
see this is to notice that Home is less productive in the
production of both goods than Foreign.
• Even if Home has an absolute disadvantage in both goods,
beneficial trade is possible.
• The pattern of trade will be determined by the
concept of comparative advantage.
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Trade in a One-Factor World
• Comparative Advantage
– Assume that aLC /aLW < a*LC /a*LW
(2-2)
• In other words, in the absence of trade, the relative
price of cheese at Home is lower than the relative
price of cheese at Foreign.
• Home has a comparative advantage in cheese
and will export it to Foreign in exchange for wine.
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Trade in a One-Factor World
• Determining the Relative Price After Trade
– What determines the relative price (e.g., PC /
PW) after trade?
• To answer this question we have to define the
relative supply and relative demand for cheese in
the world as a whole.
• The relative supply of cheese equals the total
quantity of cheese supplied by both countries at
each given relative price divided by the total
quantity of wine supplied, (QC + Q*C )/(QW + Q*W).
• The relative demand of cheese in the world is a
similar concept.
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Relative Word Supply
• Recall aLC /aLW < a*LC /a*LW
• If Pc/Pw< aLC /aLW, no workers will produce
cheese: RS=0
• If Pc/Pw= aLC /aLW, workers in Foreign will
produce wine only, workers in Home are
indifferent. RS=Sc/(Sw+L*/a*Lw)
• If a*LC /a*LW>Pc/Pw> aLC /aLW, all Home workers
produces cheese, all Foreign workers produce
wine. RS=(L/ aLC)/(L*/a*LW)
• ….
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Trade in a One-Factor World
World Relative Supply
Relative price
of cheese, PC/PW
a*LC/a*LW
RS
aLC/aLW
L/aLC
L*/a*LW
Relative quantity
of cheese, QC + Q*C
QW + Q*W
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Trade Equilibrium
Relative price
of cheese, PC/PW
Autarky equil for Foreign
a*LC/a*LW
RS
Trade equil
aLC/aLW
Autarky equil for Home
2
RD
L/aLC
L*/a*LW
Relative quantity
of cheese, QC + Q*C
QW + Q*W
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Gains from Trade
• If countries specialize according to their
comparative advantage, they all gain
from this specialization and trade.
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Gains from Trade
•
•
•
•
L=L*=120
aLC=4, aLW=8, hence aLC/aLW=1/2
a*LC=2, a*LW=1, hence a*LC/a*LW=2
If free trade relative price is in between ½
and 2
• Home specializes in Cheese production.
• Foreign specializes in Wine production.
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Gains from Trade
Quantity
of wine, Q*W
Quantity
of wine, QW
T
P
Slope
=-aLC/aLW
=-1/2
Slope=Pc/Pw
F
Quantity
of cheese, QC
(a) Home
F*
Slope=-a*LC/a*LW
=-2
Slope=Pc/Pw
T*
P*
Quantity
of cheese, Q*C
(b) Foreign
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Gains from Trade
Quantity
of wine, QW
Trade moves
Home country’s
consumption
bundle from A to
B, surely an
improvement!
B
A
Quantity
of cheese, QC
(a) Home
A similar
conclusion for
Foreign country.
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When is complete specialization?
Relative price
of cheese, PC/PW
Autarky equil for Foreign
2
RS
Trade equil
Autarky equil for Home
1/2
RD
1/4
Relative quantity
of cheese, QC + Q*C
QW + Q*W
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When is complete specialization?
Complete specialization if and only if
RD=1/4 and 1/2  PC /PW  2
Using RD 

1
1   PC / PW

PC
or

RD
1   PW
1

1


8 1 2
Hence, complete specialization if and only if 1/9    1/ 3
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Incomplete specialization
• If α≤1/9, then Home has incomplete
specialization, it is neither better off nor
worse off under trade. But Foreign still has
complete specialization and is still strictly
better off
• If α≥1/3, then Foreign has incomplete
specialization, it is neither better off nor
worse off under trade. But Home is still
better off
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Incomplete Specialization
If α is low enough, there will
be incomplete specialization
by Home.
Relative price
of cheese, PC/PW
2
RS
-1/2
RD for lower α
-1/4
RD for higher α
Relative quantity
of cheese, QC + Q*C
QW + Q*W
40
Wages
• Relative Wages
– Because there are technological differences
between the two countries, trade in goods
does not make the wages equal across the
two countries.
– A country with absolute advantage in both
goods will enjoy a higher wage after trade.
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Wages
– This can be illustrated with the help of a
numerical example:
• Assume that PC = $12 and that PW = $12. Therefore, we
have PC / PW = 1.
• Since Home specializes in cheese after trade, its wage will
be (1/aLC)PC = ( 1/4)$12 = $3.
• Since Foreign specializes in wine after trade, its wage will be
(1/a*LW) PW = (1/1)$12 = $12.
• Therefore the relative wage of Home will be $3/$12 = 1/4.
• Thus, the country with the higher absolute advantage will
enjoy a higher wage after trade.
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Comparative Advantage
with Many Goods
• Setting Up the Model
– Both countries consume and are able to
produce a large number, N, of different goods.
• Relative Wages and Specialization
– The pattern of trade will depend on the ratio of
Home to Foreign wages.
– Goods will always be produced where it is
cheapest to make them.
• For example, it will be cheaper to produce good i in
Home if waLi < w*a*Li , or by rearranging if a*Li/aLi >43
w/w*.
Comparative Advantage
with Many Goods
Table 2-4: Home and Foreign Unit Labor Requirements
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Comparative Advantage
with Many Goods
• Which country produces which goods?
– A country has a cost advantage in any good
for which its relative productivity is higher than
its relative wage.
• If, for example, w/w* = 3, Home will produce apples,
bananas, and caviar, while Foreign will produce
only dates and enchiladas.
• Both countries will gain from this specialization.
45
Comparative Advantage
with Many Goods
• Determining the Relative Wage in the
Multigood Model
– To determine relative wages in a multigood
economy we must look behind the relative
demand for goods (i.e., the relative derived
demand).
– The relative demand for Home labor depends
negatively on the ratio of Home to Foreign
wages.
46
Comparative Advantage
with Many Goods
Figure 2-5: Determination of Relative Wages
Relative wage
Rate, w/w*
RS
Apples
10
8
4
3
2
0.75
Bananas
Caviar
Dates
Enchiladas
RD
Relative quantity
of labor, L/L*
47
Comparative Advantage
With Many Goods (cont.)
• Finally, suppose that relative supply of labor is
independent of w/w* and is fixed at an amount
determined by the populations in the domestic
and foreign countries.
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Comparative Advantage
With Many Goods (cont.)
49
Transportation Costs
and Non-traded Goods
•
The Ricardian model predicts that countries
should completely specialize in production.
•
But this rarely happens for primarily
3 reasons:
1. More than one factor of production reduces the
tendency of specialization (chapter 4)
2. Protectionism (chapters 8–11)
3. Transportation costs reduce or prevent trade,
which may cause each country to produce the
same good or service
50
Transportation Costs
and Non-traded Goods (cont.)
• Non-traded goods and services (e.g.,
haircuts and auto repairs) exist due to
high transportation costs.
– Countries tend to spend a large fraction of national
income on non-traded goods and services.
– This fact has implications for the gravity model and for
models that consider how income transfers across
countries affect trade.
51
Empirical Evidence
• Do countries export those goods in which their
productivity is relatively high?
• The ratio of US to British exports in 1951
compared to the ratio of US to British labor
productivity in 26 manufacturing industries
suggests yes.
• At this time the US had an absolute
advantage in all 26 industries, yet the ratio of
exports was low in the least productive
sectors of the US.
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Empirical Evidence (cont.)
53
Summary
1. A country has a comparative advantage in producing a
good if the opportunity cost of producing that good is
lower in the country than it is in other countries.
–
A country with a comparative advantage in producing a good
uses its resources most efficiently when it produces that good
compared to producing other goods.
2. The Ricardian model focuses only on differences in the
productivity of labor across countries, and it explains
gains from trade using the concept of comparative
advantage.
54
Summary (cont.)
3.
When countries specialize and trade according to the
Ricardian model; the relative price of the produced
good rises, income for workers rises and imported
goods are less expensive for consumers.
4.
Trade is predicted to benefit both high productivity and
low productivity countries, although trade may change
the distribution of income within countries.
5.
High productivity or low wages give countries a cost
advantage that allow them to produce efficiently.
55
Summary (cont.)
7. Although empirical evidence supports
trade based on comparative advantage,
transportation costs and other factors prevent
complete specialization
in production.
56