This document provides an overview of resources and trade in the long run. It describes factor abundance and factor intensity, and how they relate to a country's production possibilities frontier. Factor abundance refers to a country having relatively more of a factor, while factor intensity refers to how intensively a good uses a factor in production. The document uses diagrams to illustrate concepts like isoquants, isocost lines, and relative factor demand curves. It explains theories like the Stolper-Samuelson theorem and the Rybczynski theorem, which relate changes in factor prices or amounts to changes in production and income distribution.

1. Learning Unit 8
Resources and Trade in Long Run
ECON452
International Economics

2. Objectives
1. Describe the concepts of factor abundance and factor intensity
2. Derive the relative factor demand
3. Explain a relationship between factor price and good price –
Stolper-Samuelson theorem
4. Explain how resources affect a shape of production possibilities
frontier – Rybczynski theorem

3. Introduction
• Trade occurs due to differences in resources across countries.
– differences in labor, labor skills, physical capital, capital, land, and
entrepreneurship across countries.
• Two aspects of resources
– Countries may have different quantities of resources: Factor abundance.
 U.S. has many capital and skilled labor, while Bangladesh has many unskilled labor.
– Each product may require different combinations of resources: Factor intensity.
 Production of car requires capital (assembly line), while production of apparels require
labor (operating sawing machine).

4. Factor Abundance
• Factor abundance: A nation is abundant in one factor if the ratio of the price of
the factor to the other factor in lower in the nation than that in the other nation.
– Based on both supply and demand condition of factor market
• Factor prices: costs of each unit of factor of production – wage (w) for labor and
rental cost (r) for capital.
– If supply of one factor is high or demand for the factor is low, then the factor is
abundant and its market price is low. Alternatively, if supply of one factor is low or
demand for the factor is high, then the factor is scarce and its market price is high.
• Because one country may have lower factor prices on all resources, a relative
factor price (ratio of the price of one factor to the other factor) is compared
across countries.

5. Factor Abundance - Example
• Wage-rental ratio (w/r): a ratio of wage rate of labor to rental cost of capital.
• Wag-rental ratios are 1 ($10/$10) in Home and 1.5 ($30/$20) in Foreign.
– Because the wage-rental ratio (w/r) is lower in Home than Foreign, Home is labor-abundant.
– Because the wage-rental ratio (w/r) is higher in Foreign than Home, the rental-wage ratio
(r/w) is lower in Foreign than Home, so Foreign is capital-abundant.
Home Foreign
Wage Rate of Labor (w) $10 $30
Rental Rate of Capital (r) $10 $20

6. Factor Abundance - Caveats
• A country cannot be abundant in all factors.
– Factor abundance is relative concept like relative price and comparative advantage. When two
countries are compared, each country is abundant in at least one factor.
• A country can be abundant in one factor relative to one country, but abundant in
other factor relative to other country.
– China is labor-abundant relative to the U.S., but capital-abundant relative to Bangladesh.
• Having more factors than other countries does not necessarily make factor
abundance.
– U.S. (330 million in 2019) has more population than Bangladesh (160 million in 2019), but
Bangladesh is considered as labor-abundant.
• Lower factor price does not necessarily make the country abundant in the factor.
– Both wage rate and rental rate are lower in Home than Foreign, but Home is NOT capital-
abundant.

7. Factor Intensity
• Factor intensity: A good can be produced cheaply by using more of one factor
than the other.
• Labor-Capital ratio (L/K): a ratio of quantity of labor to quantity of capital in
production.
• Labor-Capital ratios are 1 (100/100) for cloth production and 0.5 (20/40) for food
production.
– Cloth is labor-intensive because its labor-capital ratio is greater (using relatively more labor
and less capital) than food
– Food is capita-intensive because its labor-capital ratio is less (using relatively less labor and
more capital) than cloth
Cloth Food
Quantity of Labor (L) 100 20
Quantity of Capital (K) 100 40

8. Factor Intensity - Caveats
• The minim cost combination of inputs is compared for all products, when producers
are facing the same input prices.
– Input combinations vary as input prices change (input substitution)
• A product cannot be intensive in all factors.
– Factor intensity is relative concept. When two products are compared, each product is intensive
in at least one factor.
• A product can be intensive in one factor relative to one product, but intensive in
other factor relative to other product.
– Food production is capital-intensive as compared with apparel production, but labor-intensive
as compared with airplane production.
• Factor intensity reversal: A product can be intensive in one factor at one relative
input price, but intensive in other factor at other relative input price.

9. Factor Abundance and Factor Intensity
• Factor abundance is determined when two countries are compared in terms of
resource supply and demand.
– Example: Comparing U.S. and China, which country has relatively abundant in labor resource?
• Factor intensity is determined when two products are compared in terms of
cheapest input combinations.
– Example: Comparing production of apparels and production of airplane, which product uses
capital more intensively?
• Difference in factor abundance among countries and difference in factor intensity
among products will determine which country should produce which product.
– If China is labor-abundant, should China produce labor-intensive apparels or capital-intensive
airplanes?

10. Minimum Cost Combination of Input
• There are many combinations of two inputs to produce a fixed
number of output.
• Given input prices, there is one combination of two inputs which is
lowest in total cost.
• To find the minimum cost combination of inputs, we use isoquant-
isocost diagram.

11. Isoquant
• Isoquant: A curve showing all the
combinations of two inputs that will
produce the same level of output.
– Example: All three combinations of labor
and capital (A, B, C) can produce 100
units of output.
• One isoquant for each level of output.
– Example: Isoquant corresponding to 200
units of output lies above the isoquant
corresponding 100 units of output.
Quantity of Labor (L)
Quantity of Capital (K)
Isoquant (at Q = 100)
A
B
C
Isoquant (at Q = 200)
10
10 207
5
15

12. Marginal rate of Technical Substitution
• Marginal rate of technical substitution
(MRTS): a rate at which a firm can
substitute one input for another, while
keeping the level of output constant.
• MRTS is the slope of an isoquant.
MRTS = ΔK/ΔL
– Example: At B, MRTS = 1
• MRTS is a ratio of marginal product.
MRTS = MPL/MPK = (ΔQ/ΔL)/(ΔQ/ΔK) = ΔK/ΔL
Quantity of Capital (K)
B
10
Isoquant (at Q = 100)
Quantity of Labor (L)
10
5
15

13. Slope of Isoquant
• Isoquant becomes steeper as it uses
more capital (moving toward upper
left) and flatter as it uses more labor
(moving toward lower right).
– As K increases, MPK decreases and MPL
increases due to diminishing marginal
return, so MRTS increases.
– With more capital is used, it requires
more and more capital to replace labor
to maintain the output.
Quantity of Labor (L)
Quantity of Capital (K)
Isoquant (at Q = 100)
A
B
C
10
10

14. Isocost Line
• Isocost line: All the combinations
of two inputs that have the same
total cost.
– Example: All three combinations of
labor and capital (a, b, c) cost $2000 in
total.
• One isocost line for each total cost.
– Example: Isocost line corresponding to
$2000 total cost lies above the isocost
line corresponding $1000 of total cost.
Quantity of Labor (L)
Quantity of Capital (K)
Isocost (at TC = $1000)
a
b
c
Isocost (at TC = $2000)10
10 205
5
15
15
20

15. Slope of Isocost Line
• Slope of isocost line is equal to wage-
rental ratio (w/r).
TC = w*L + r*K
K = (TC/r) – (w/r)L
• Example: At w = $100 and r = $100, if L
= 100 and K = 100, TC = $2000.
w/r = $100/$100 = 1
Quantity of Labor (L)
Quantity of Capital (K)
b Isocost (at TC = $2000)10
10 20
20

16. Minimum Cost Combination
• There are many combinations of two
inputs to produce a fixed number of
output.
• Given input prices, there is one
combination of two inputs which is
lowest in total cost.
– Example: All three combinations (A. B, C)
can produce 100 units of output.
– At A and C, it costs $3000, while at B it costs
$2000.
– At D, it costs $1000, but it cannot produce
100 units of output.
Quantity of Labor (L)
Quantity of Capital (K)
Isoquant (at Q = 100)
B
10
10
A
C
D
Isocost (at TC = $2000)
Isocost (at TC = $3000)
Isocost (at TC = $1000)

17. Condition of Optimal Combination of Inputs
• At the optimal (minimum) combination of
inputs, the isocost line is tangent to the
isoquant.
• A slope of isocost line is equal to a slope
of isoquant.
w/r = MRTS = MPL/MPK
Quantity of Labor (L)
Quantity of Capital (K)
Isoquant (at Q = 100)
B
10
10
Isocost (at TC = $2000)

18. Factor Price and Factor Substitution
• As one factor becomes more expensive
relative to another factor, a cost-minimizing
firm substitutes relatively-cheap factor for
relatively-expensive factor.
• A rise in wage-rental ratio (w/r) shifts the
lowest-cost input choice from point B to point
A; that is, it leads to the choice of a lower
labor-capital ratio (L/K).
– As capital becomes relatively cheaper to labor,
more capital and less labor are used to produce at
the lowest total cost.
– An inverse relationship between w/r and L/K.
Slope = w/r = 1
Slope = w/r = 2
Quantity of Labor (L)
Quantity of Capital (K)
Isoquant (at Q = 100)
A
B
10
10

19. Relative Factor Demand
• Relative Factor Demand: A relationship
between a relative input price (wage-
rental ratio) and a relative input
quantity demanded (Labor-capital ratio).
– Relative factor demand curve is downward-
sloping.
– As labor becomes relative more expensive
to capital (w/r rises), more capital and less
labor are used to produce the same
quantity of output (L/K falls).

20. Factor Intensity and Isoquant
• Given the same wage-rental ratio (w/r),
the isoquant of Cloth production (CC)
requires more labor and less capital,
while the isoquant of Food production
(FF) requires more capital and less
labor to produce at the lowest costs.
– Example: L/K of Food = 1/6 (5/30), and L/K
of Cloth = 2 (20/10).
• Food is capital-intensive, while Cloth is
labor-intensive. 5
10
30
20

21. Factor Intensity and Relative Factor Demand
• Relative factor demand curve of labor-
intensive good (CC) lies right to
relative factor demand curve of
capital-intensive good (FF).
– At any given wage-rental ratio, cloth
production uses a higher labor-capital
ratio than food production.
w/r
L/KCCL/KFF

22. Factor Prices and Good Prices
• In competitive markets, the price of a good should
equal its cost of production, which depends on the
factor prices.
• How changes in the wage and rent affect the cost of
producing a good depends on the mix of factors used.
– An increase in the wage rate of labor should affect
the price of cloth more than the price of food since
cloth is labor-intensive.
• The higher the relative cost of labor, the higher must be
the relative price of the labor-intensive good.

23. Stolper-Samuelson Theorem
• Stolper-Samuelson theorem: If the relative price of a good increases, then the
real wage or rental rate of the factor used intensively in the production of that
good increases, while the real wage or rental rate of the other factor decreases.
– When the relative price of labor-intensive Cloth (PC/PF) increases, profit-maximizing firms
increase the production of Cloth.
– To produce more cloth, they demand more labor relative to capital because Cloth is labor-
intensive.
– Given full employment of resources, labor must be released from Food industry. Because
Food industry is capital-intensive, as Food industry reduce its production, it makes labor and
even more capital available. However, capital is not demanded much from Cloth industry.
– Then, the wage rate increases relative to rental rate (w/r) as demand for labor high and
demand for capital low.

24. Relative Price of Good and Relative Factor
Demand
• When the relative price of labor-
intensive cloth rises
– from PC/PF
1 to PC/PF
2
• the wage-rental ratio must rise
– from w/r1 to w/r2
• the labor-capital ratio used in the
production of both goods must
decrease
– from LF/KF
1 to LF/KF
2 in food industry
– from LC/KC
1 to LC/KC
2 in cloth industry

25. Relative Price and Income Distribution
• An increase in the relative price of labor-intensive cloth (PC/PF) raise income of
workers relative to that of capital owners (w/r).
• It raises the real income (purchasing power) of workers and lowers the real
income of capital owners.

26. Factor Abundance and Factor Intensity
• Because of a difference in factor abundance
between two countries, the isocost lines in two
countries have different slopes (w/r).
– A labor-abundant Home has flatter isocost line (lower
wage-rental ratio) than a capital-abundant Foreign.
• Assuming the same technology, both countries face
the same isoquants.
– Home uses more labor and less capital at H, while Foreign
uses more capital and less labor at F.
– Labor-capital ratio is higher in Home than Foreign.
Slope = w/rH
Slope = w/rF
Quantity of Labor (L)
Quantity of Capital (K)
Isoquant
F
H
LHLF
KF
KH

27. Factor Abundance and Relative Factor Demand
• In each country Cloth is labor-intensive and Food is
capital-intensive.
– Assuming the same technology across countries, the
relative factor demands are identical among the countries.
• Labor-abundant country produces all goods at higher
labor-capital ratio.
– Home is labor-abundant and its wage-rental ratio is low.
– Home uses more labor to produce both goods as compared
with Foreign.
 LF/KF
H > LF/KF
F for production of food
 LC/KC
H > LC/KC
F for production of cloth HH
H
FF
F

28. Factor Abundance and Production Possibilities
• An economy with a high ratio of labor to capital
produces a high output of cloth relative to food.
• Comparing two countries, a labor-abundant country can
produce relatively more labor-intensive goods and its
PPF is skewed more toward labor-intensive goods
production.
• Example: Home is relatively abundant in labor and
Foreign in capital.
– Home will be relatively efficient at producing cloth because
cloth is labor-intensive and labor is relatively cheap in Home.
– Home can produce relatively more of Cloth than Foreign and
its production possibilities frontier is skewed toward the
horizontal axis (measuring quantity of labor-intensive cloth).

29. Factor Abundance and Output
• Comparing two countries, facing the same
relative price, a labor-abundant country
chooses to produce more labor-intensive
goods.
• Given a relative price at PC/PF,
– Labor-abundant Home will produce QC
H of Cloth
and QF
H of Food.
– Capital-abundant Foreign will produce QC
F of
Cloth and QF
F of Food.
QC
H
QF
F
QF
H
QC
F
Slope = PC/PF

30. Rybczynski Theorem
• When resources increase, a resulting expansion of production possibilities is
biased toward goods whose production requires intensive use of increased
resources.
– When the U.S. increases its skilled-labor, its production of skilled-labor-intensive goods will
increase more than proportional, while its production of unskilled-labor-intensive goods will
decrease.
• Rybczynski theorem: Holding output prices constant, as the amount of a factor of
production increases, then the supply of the good that uses this factor intensively
increases and the supply of the other good decreases.
– Constant relative price means constant wage-rental ratio, and constant labor-capital ratio in
each industry.

31. Rybczynski Theorem - Formula
• Changes in resources affect the allocation of factors across sectors, holding the
prices of outputs constant.
• L/K = (LC/KC)(KC/K) + (LF/KF)(KF/K)
– Where LC/KC >LF/KF (labor-capital ratio in Cloth and Food industries) are constant.
– KC/K and KF/K are proportions of capital allocated in Cloth and Food industry, respectively.
• When labor resource increases,
– Labor-capital ratio increases (L/K)
– Capital will be allocated more in labor-intensive cloth industry and less in capital-intensive
food industry (KC and KF↓)
– Labor will also be allocated more in labor-intensive cloth industry and less in capital-intensive
food industry (LC and LF↓)

32. Rybczynski Theorem - Diagram
• An increase in the quantity of labor resource
shifts the economy’s production possibility
frontier outward disproportionately in the
direction of labor-intensive cloth production.
• At an unchanged relative price of cloth, labor-
intensive cloth production increases and capital-
intensive food production declines.
– Before expansion at TT1, at PC/PF a country produces
QC
1 of Cloth and QF
1 of Food.
– After expansion to TT2 due to an increase in labor
resources, at PC/PF a country will produces QC
2 of
Cloth and QF
2 of Food.
Decrease
Increase

33. Rybczynski Theorem – Numerical Example
• Originally, with 6 units of capital and 6 units of
labor, a country produces 2 units of cloth and 2
units of food.
– Labor-capital ratios are ½ in Cloth industry
and 2 in Food industry.
• When labor resources increase by 50% from 6
units to 9 units, at constant relative price
(constant labor-capital ratios) under constant
returns to scale.
– the country increases its output of cloth by
100% from 2 units to 4 units
– its output of food decreases by 50% from 2
units to 1 unit
Labor Capital L/K Output
Cloth 2 4 2/4 = ½ 2
Food 4 2 4/2 = 2 2
Total 6 6
Labor Capital L/K Output
Cloth 4 8 4/8 = ½ 4
Food 2 1 2/1 = 2 1
Total 6 9

34. 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