Relative Supply and Relative Wage

1. Learning Unit 4
Relative Supply and Relative Wage
ECON452
International Economics

2. Objectives
1. Derive a relative supply in Ricardian model and determine an
equilibrium relative price
2. Describe a relative wage and its relationship with productivity
3. Explain multi-product and multi-country extensions of Ricardian
model

3. Determine Relative Price under Trade
• Prices of goods are determined by supply and demand.
• Partial equilibrium analysis: A standard supply-demand analysis
looks at a single market at time (e.g. equilibrium at cheese market)
– No guarantee that other markets at equilibrium, or country has a
balanced trade.
• General equilibrium analysis: All markets in all countries are at
equilibrium at the same time and all countries have a balanced
trade

4. Partial Equilibrium Analysis
• Home market and Foreign market must be combined to form a single world
market for each good.
– This ensures both countries have the same price and what one country exports is equal to
what the other country imports.
– Similar to deriving market demand & supply from individual demand & supply
• Prices are quoted by relative prices, which are free from monetary units.
– Once a relative price of one good is determined, a relative price of the other good will be
determine automatically. (e.g. Once we know Pc/Pw, then we will know Pw/Pc).
• It analyzes one market at time, but it still involves two markets.
– Must be at equilibrium in each market
– Equilibrium relative price in one market must be equal to equilibrium relative price in the
other market.

5. Partial Equilibrium Analysis - Example
• In Cheese market
– If a relative price of cheese is less than 1/2,
no nation wants to produce and sell cheese,
because it will cost ½ in Home and 2 in
Foreign to produce.
– If a relative price of cheese is more than 1/2,
Home will specialize to produce and sell
cheese up to 1,000 units because it will cost
½ in Home and make profits.
– If a relative price of cheese exceeds 2,
Foreign will also specialize to produce cheese
up to 500 units, totaling 1,500 units of supply
in world.
Home Foreign
Maximum Production
Cheese 1,000 500
Wine 500 1,000
Opportunity Cost
Cheese ½ wine 2 wine
Wine 2 cheese ½ cheese

6. Partial Equilibrium Analysis - Example
• In Wine market
– If a relative price of wine is less than ½, no
nation wants to produce and sell wine,
because it will cost 2 in Home and 1/2 in
Foreign to produce.
– If a relative price of wine is more than ½,
Foreign will specialize to produce and sell
wine up to 1,000 units because it will cost ½
in Foreign and make profits.
– If a relative price of wine exceeds 2, Home
will also specialize to produce wine up to 500
units, totaling 1,500 units of supply in world.
Home Foreign
Maximum Production
Cheese 1,000 500
Wine 500 1,000
Opportunity Cost
Cheese ½ wine 2 wine
Wine 2 cheese ½ cheese

7. Partial Equilibrium Analysis - Diagram
Sc & Sw: total supply of Cheese and Wine in the world
Dc & Dw: total demand for Cheese and Wine in the world
Pc/Pw & Pw/Pc: relative price of Cheese and Wine
• Given demand in each
market, an equilibrium
relative price is determined
where a supply curve
intersects a demand curve.
• In Cheese market , an
equilibrium relative price of
cheese is 1, while in Wine
market an equilibrium
relative price of wine is 1.
• At equilibrium, Home
produces 1000 units of
cheese and Foreign produces
1000 units of wine.

8. Partial Equilibrium Analysis - Diagram
Although the demand-supply diagrams look different from regular
demand-supply diagrams in microeconomics,
• The supply curve is usual upward-sloping: As a relative price of a good
increases, a quantity supplied of the good increases.
• It is a step-function (like stairs rather than smooth curve) because there are
only two countries. If more countries participate in trade, there will be many
more steps and it will look smoother stairs (like perfect competition).
• Because of constant opportunity cost, each country will either produce nothing
(if a relative price is less than its opportunity cost) or produce maximum (if a
relative price is greater than its opportunity cost). When a relative price is
equal to its opportunity cost, it is indifferent to produce – production can be
between zero and maximum.

9. General Equilibrium Analysis
• Problems of Partial Equilibrium Analysis
– No guarantee that an equilibrium relative price in one market is consistent with
an equilibrium relative price in the other market. (e.g. if Pc/Pw = 0.8 in cheese
market, in wine market Pw/Pc must be 1.25).
– Quantities of two markets must be coordinated to satisfy budget constraint of
aLCQc + aLWQw ≤ L in each country.
• Problem is on each diagram, both prices are determined (Pc and Pw in form of Pw/Pc),
but only one quantity is determined (Qc or Qw). If we can determine both quantities
(Qc and Qw) in one time, then it can guarantee to have the same equilibrium price and
satisfy budget constraint.
Like relative price combines two prices in one, we introduce relative quantity of goods
to combine quantities in two markets into one – what proportion of output is cheese –
and measure it along the quantity axis. Now one supply-demand diagram reflects
prices and quantities of two markets.

10. Relative Quantity
• Relative quantity of cheese: Total quantity of cheese divided by total quantity of
wine [(Qc+Qc*)/(Qw+Qw*)].
• Relative supply of cheese is the quantity of cheese supplied (produced) in all
countries relative to the quantity of wine supplied (produced) in all countries.
• Relative demand of cheese is the quantity of cheese demanded in all countries
relative to the quantity of wine demanded in all countries.

11. Relative Supply
• Total quantity of cheese supplied varies from zero to L/aLC + L*/aLC* units, while
total quantity of wine varies from L/aLW + L*/aLW* to zero.
• More quantity of cheese supplied, less quantity of wine supplied (given fixed
amount of labor resources available in each country to produce two goods), and
greater the relative quantity of cheese supplied.
• The relative quantity of cheese supplied [(Qc+Qc*)/(Qw+Qw*)] varies from zero
(when Qc + Qc* = 0 and Qw + Qw* = L/aLW + L*/aLW*) to infinity (when Qc + Qc*
= L/aLC+ L*/aLC* and Qw + Qw* = 0).

12. Deriving Relative Supply
• The relative quantity of cheese supplied [(Qc+Qc*)/(Qw+Qw*)] depends on a relative
price (Pc/Pw) as each of Qc, Qc*, Qw, & Qw* depends on (Pc/Pw).
• From Partial Equilibrium Model, five ranges of relative price (where vertical and flat
portions of step function) are possible:
– the relative price of cheese falls below the opportunity cost of cheese in both countries:
PC /PW < aLC /aLW < a*
LC /a*
LW, Neither country will produce cheese, and both produce only wine
– the relative price of cheese equals the opportunity cost in the home country:
PC /PW = aLC /aLW < a*
LC /a*
LW , Home may or may not produce cheese, and Foreign produces only wine
– the relative price of cheese settles strictly in between the opportunity costs of cheese:
aLC /aLW < Pc /PW < a*
LC /a*
LW , Home will produce cheese only, and Foreign produces wine only.
– the relative price of cheese equals the opportunity cost in the foreign country:
aLC /aLW < PC /PW = a*
LC /a*
LW , Home will produce cheese only, and Foreign may or may not produce cheese
– the relative price of cheese rises above the opportunity cost of cheese in both countries:
aLC /aLW < a*
LC /a*
LW < PC /PW, Both countries will produce cheese, and neither produce wine

13. Relative Supply Schedule
Relative Price
(Pc/Pw)
Home Foreign
Relative Quantity
[(Qc+Qc*)/(Qw+Qw*)]
Cheese
(Qc)
Wine
(Qw)
Cheese
(Qc*)
Wine
(Qw*)
PC /PW < aLC /aLW < a*
LC /a*
LW 0 L/aw 0 L*/aw* 0
PC /PW = aLC /aLW < a*
LC /a*
LW Qc Qw 0 L*/aw* 0 ~ (L/ac)/(L*/aw*)
aLC /aLW < Pc /PW < a*
LC /a*
LW L/ac 0 0 L*/aw* (L/ac)/(L*/aw*)
aLC /aLW < PC /PW = a*
LC /a*
LW L/ac 0 Qc* Qw* (L/ac)/(L*/aw*) ~ 
aLC /aLW < a*
LC /a*
LW < PC /PW L/ac 0 L*/ac* 0 
World relative supply
is a step function: The
relative quantity
supplied varies in five
different rages of
relative price.

14. Relative Supply - Example
• Home can produce up to
1,000 units of cheese or up
to 500 units of wine.
• Foreign can produce up to
500 units of cheese or up
to 1,000 units of wine.
• Total quantity of cheese
supplies varies from 0 to
1,500, while total quantity
of wine supplied varies
from 1,500 to 0.
• At the range of 1/2 < Pc /PW
< 2 , when Home produces
only cheese and Foreign
produces only wine, Qc =
1,000 and Qw* = 1,000, so
a relative quantity of
cheese supplied is 1.
Relative Price
(Pc/Pw)
Home Foreign
Relative Quantity
[(Qc+Qc*)/(Qw+Qw*)]
Cheese
(Qc)
Wine
(Qw)
Cheese
(Qc*)
Wine
(Qw*)
0 ≤ PC /PW < 1/2 0 500 0 1000 0
PC /PW = 1/2 0 ~ 1000 500 ~ 0 0 1000 0 ~ 1
1/2 < Pc /PW < 2 1000 0 0 1000 1
PC /PW = 2 1000 0 0 ~ 500 1000 ~ 0 1 ~ 
2 < PC /PW 1000 0 500 0 

15. World Relative Supply and Demand
• Given a world relative demand curve, an
equilibrium relative price and relative quantity
is determined where the relative supply curve
intersects the relative demand curve.
• For RD, the equilibrium point is at 1, and the
equilibrium relative price is between ½ and 2
and the equilibrium relative quantity is 1,where
Home produces 1000 units of cheese and
Foreign produces 1000 units of wine.
• For RD’, the equilibrium point is at 2, and the
equilibrium price is ½ and the equilibrium
quantity is between 0 and 1, where Home
produces some cheese and wine, and Foreign
produces 1000 units of wine.
(1 in our example)

16. Relative Price and Gains from Trade
• For Relative demand at RD
– Home produces only cheese since it costs less to produce cheese than the world relative
price.
– Foreign produces only wine since it costs more to produce cheese than the world relative
price.
– Two countries trade at the rate of exchange of Pc/Pw.
– Since the world relative price is higher than the relative price of cheese under autarky in
Home, Home gains from exporting cheese to Foreign. Since the world relative price is lower
than the relative price of cheese under autarky in Foreign, Foreign gains from importing
cheese to Home.
• For Relative demand at RD’
– Home produces both cheese and wine.
– Foreign produces only wine.
– Home exports some of cheese and import wine from Foreign.
– Since the world relative price is equal to the relative price of cheese under autarky in Home,
Home will not gain from trade. All gains from trade will be captured by Foreign, since it can
purchase cheese at the lowest possible price.

17. Relative Demand and Gains from Trade
• If consumers prefer cheese and wine equally (relative to supply), its relative
demand for cheese is middle (RD) and it may reach Equilibrium point 1.
– Since Home sells cheese at higher price to Foreign and Foreign sells wine at higher price to
Home (as compared with their domestic prices under autarky), both countries gain from
trade.
• If consumers prefer wine much more than cheese, its relative demand for
cheese is low (RD’) and it may reach Equilibrium point 2.
– If Home produce goods whose demand are relatively low to all other goods produced in the
world, then Home may not gain from trade – selling its goods to the rest of world at the same
price as domestic market.

18. Relative Supply and Gains from Trade –
Implications
• Implication #1: If a country exports goods which are over-supplied relative to world
demand, the country will not gain much from international trade (like RD’).
If a country exports goods which are under-supplied relative to world demand, the
country will gain greatly from international trade.
– When the world demand is low relative to world supply, the country must sell at a price close to
domestic production cost and will make less profits. When the world demand is high relative to
world supply, the country can sell at higher price than its production cost and will make more
profits.
• Implication #2: If a country is very small relative to the world market in terms of
production of goods, the country will gain more from international trade.
If a country is very large relative to the world market in terms of production of goods, the
country will not gain much from international trade (like RD’).
– Large country supplies goods greatly to world market and depress its price close to tis
production cost and makes less profits. Small country cannot produce enough to influence
world relative price and is able to sell at higher price than its production cost.

19. Wage Rate
• Wage rate: Under assumption of no profit (e.g. perfect competition), all revenue
must go to labor as wage. Then, the price of good and unit labor requirement
determine a wage rate of labor in each industry.
– Unit labor requirement to produce one unit of cheese in Home = aLC hours
– Unit labor requirement to produce one unit of wine in Home = aLW hours
– Price of cheese: Pc
– Price of wine: Pw
– Wage rate in cheese industry = Pc/aLC
– Wage rate in wine industry = Pw/aLW

20. Wage Rate without Trade
• In order to produce both goods under autarky, wage rate in both industries must
be equal:
Pc/aLC = Pw/aLW
• This implies that the relative price of a good equals the opportunity cost of
producing that good.
Pc/Pw = aLC/aLW
– If Pc/aLC > Pw/aLW (Pc/Pw > aLC/aLW), then every labor wants to work in
cheese industry – specializing in production of cheese.
– If Pc/aLC < Pw/aLW (Pc/Pw < aLC/aLW), then every labor wants to work in
wine industry – specializing in production of wine.

21. Wage Rate - Example
Unit labor requirement to produce one pound of cheese in Home = 1 hour
Unit labor requirement to produce one gallon of wine in Home = 2 hours
Price of cheese: $12
Price of wine: $24
Wage rate in cheese industry = $12/1 = $12
Wage rate in wine industry = $24/2 = $12
Relative price of cheese = $12/$24 = ½
Opportunity cost of cheese = 1/2

22. Relative Wages
• Relative wages: the wages of the home country relative to the wages in the
foreign country.
– w/w* where w is wage rate in Home and w*is wage rate in Foreign
• Productivity (technological) differences determine relative wages across
countries.
Higher the productivity, higher the relative wage rate.
• The home wage relative to the foreign wage will settle in between the ratio of
how much better Home is at making cheese and how much better it is at making
wine compared to Foreign.
• Equilibrium relative wages under trade cause Home to have a cost advantage in
only cheese and Foreign to have a cost advantage in only wine.

23. Relative Wages - Example
• Suppose that PC = $12/pound and PW = $12/gallon under trade.
• Since domestic workers specialize in cheese production after trade, their hourly
wages will be
w = PC/aLC = $12 /1= $12
• Since foreign workers specialize in wine production after trade, their hourly
wages will be
w* = PW/a*
LW = $12/3 = $4
• The relative wage of domestic workers is therefore
w/w* = $12/$4 = 3

24. Relative Wages under Trade
• The relative wage lies between the ratio of the productivities in each industry.
a*
LW/aLW ≤ w/w* ≤ a*LC/aLC
• Example: aLC = 1 and aLW = 2 in Home and a*LC = 6 and a*
LW = 3 in Foreign.
– a*LC/aLC = 6/1: The home country is 6 times as productive in cheese production as
Foireign.
– a*
LW/aLW = 3/2: The home country is 1.5 times as productive in wine production as
Foreign.
– The home country can have a wage between 1.5 and 6 times higher than the foreign
country.
• Equilibrium relative wage rate depends on the equilibrium relative price since prices of
products and productivities determine wage rates.

25. Relative Wages and Cost Advantage
• These relationships imply that both countries have a cost advantage in production.
– High wages can be offset by high productivity.
– Low productivity can be offset by low wages.
• Because foreign workers have a wage that is only 1/3 the wage of domestic workers,
they are able to attain a cost advantage in wine production, despite low productivity.
– Low wages in developing countries are reflection of their low productivities.
• Because domestic workers have a productivity that is 6 times that of foreign workers in
cheese production, they are able to attain a cost advantage in cheese production,
despite high wages.
– Workers in developed countries can maintain higher wage only if they can maintain
higher productivities.

26. Do Wages Reflect Productivity?
• Do relative wages reflect relative
productivities of the two countries?
• Evidence shows that low wages are
associated with low productivity.
– Wage of most countries relative to
the U.S. is similar to their
productivity relative to the U.S.

27. Productivity and Wage Rate - Evidence
• Other evidence shows that wages
rise as productivity rises.
– As recently as 1975, wages in
South Korea were only 5% of those
of the United States.
– As South Korea’s labor
productivity rose (to about half of
the U.S. level by 2007), so did its
wages.

28. Comparative Advantage with Many Goods
• The basic two-goods Ricardian model can be extended to the case
of many goods.
• When a country produces many different goods and trade with its
partner, which goods should the country export to and which goods
should the country import from its partner?
• Applying the comparative advantage, the country should export
those goods which the country has cost advantages to its partner,
given relative productivities and relative wage rates.

29. Comparative Advantage with Many Goods –
Model
• Model
– N goods produced, indexed by i = 1,2,…N.
– Unit labor requirement for good i in Home = aLi,
Unit labor requirement for good I in Foreign = a*
Li .
– w = the wage rate in Home and w* = the wage rate in Foreign
• Goods will be produced wherever cheapest to produce them.
– If waLi < w*a*
Li then only Home will produce good i, because total wage
payments are less there.
– Or equivalently, a*
Li/aLi < w/w* if the relative productivity of a country in
producing a good is higher than the relative wage, then the good will be
produced in that country.

30. Comparative Advantage with Many Goods –
Example
• If w/w* = 3, then
• Home will produce apples,
bananas, and caviar,
because the relative
productivities of Home in
producing apples, bananas,
and caviar are higher than
the relative wage.
• Foreign will produce dates
and enchiladas.
Good
Home Unit Labor
Requirement aLi
Foreign Unit Labor
Requirement aLi*
Relative Home
Productivity
Advantage aLi*/aLi
Apples 1 10 10
Bananas 5 40 8
Caviar 3 12 4
Dates 6 12 2
Enchiladas 12 9 0.75
Suppose there are 5 goods produced in the world: apples, bananas, caviar, dates, and
enchiladas.

31. Determination of Relative Wages
• In a many-good Ricardian model, relative wages are
determined by the intersection of the derived relative
demand curve for labor, RD, with the relative supply, RS.
• The relative demand for labor depends on the relative
productivity (a*
Li/aLi) and the relative wage rate (w/w*). As
domestic labor services become more expensive relative to
foreign labor services (w/w*↑), goods produced in the
home country become more expensive, and demand for
these goods and the labor services to produce them falls
(L/L*↓).
• The relative supply of labor is fixed at an amount
determined by the populations in Home and Foreign (L/L*).

32. Specialization and Export Concentration
Leading export as a percentage of total
exports of a county indicates how much
the country specializes in production of
that commodity.
– Due to increasing costs, large
countries do not specialize in
production of a particular product.
– Small countries are more likely to
specialize in production of a
particular product.

33. Comparative Advantage with Many
Countries
• The basic two-countries Ricardian model can be extended to the
case of many countries.
• When many countries produce goods and trade with its partners,
which countries should produce and export one good to others
while import the other good from others?
• Applying the comparative advantage, a country should produce and
export a good whose opportunity cost is less than the equilibrium
relative price in the world.

34. Comparative Advantage with Many
Countries – Model
• Model
– N countries, indexed by i = 1,2,…N.
– Unit labor requirement for good 1 in Country i = aL1
i,
Unit labor requirement for good 2 in Country i = aL2
i .
– The world equilibrium relative price of Good 1: P1/P2.
• A country should produce a good whose opportunity cost (relative price under
autarky) is less than the equilibrium relative price in the world.
– If aL1
i / aL2
i < P1/P2, then Country i should produce and export Good 1, because
its opportunity cost to produce Good 1 is less than the equilibrium relative
price of Good 1.

35. Comparative Advantage with Many
Countries – Example
Country Opportunity Cost
(aL1
i / aL2
i )
A 1
B 2
C 3
D 4
E 5
• If the equilibrium relative price
(P1/P2) is 3, then
• Country A and B will export Good 1
and import Good 2.
• Country D and E will export Good 2
and import Good 1.
• Country C will not trade.

36. Disclaimer
Please do not copy, modify, or distribute
this presentation
without author’s consent.
This presentation was created and owned
by
Dr. Ryoichi Sakano
North Carolina A&T State University
Disclaimer
Please do not copy, modify, or distribute
this presentation
without author’s consent.
This presentation was created and owned
by
Dr. Ryoichi Sakano
North Carolina A&T State University