5.1. The Heckscher-Ohlin Model Flashcards
Model summary
The Heckscher-Ohlin theory shows that comparative advantage is influenced by the interaction between nations’ resources (the relative abundance of factors of production) and the technology of production.
Different countries have different relative abundances of factors of production. Each different production process uses these factors with differing relative intensity.
Setting up the economy
The world economy consists of Home and Foreign, who produce cloth and food.
Immobile factors are now mobile in the long-run (so capital can be used for food production and land can be used for cloth production). Capital and land are now referred to as capital.
The supply of labour and capital in each country is constant but varies across countries.
In the long-run, both labour and capital can move across sectors, equalising their returns across sectors.
Prices and production
Both capital and labour are used to produce cloth and food.
The amount of each good produced is determined by a production function for each good:
QC=QC(KC, LC).
QF=QF(KF, LF).
QC and QF refer to the output levels of cloth and food.
KC and LC refer to the capital and labour used in cloth production.
KF and LF refer to the capital and labour used in food production.
Overall, the economy has a fixed supply of capital and labour that is divided between employment in the two sectors:
aKC: capital used to produce one unit of cloth.
aLC: labour used to produce one unit of cloth.
aKF: capital used to produce one unit of food.
aLF: labour used to produce one unit of food.
This refers to the quantity of capital and labour used to produce a given amount of cloth or food, not the quantity required.
This is because, when there are two factors of production, there may be some room for choice in the use of inputs.
These choices will, in general, be dependent on factor prices for labour and capital.
Numerical H-O example
Production of one unit of cloth requires a combination of two work-hours (aLC=2) and two machine-hours (aKC=2).
Production of one unit of food requires a combination of one work-hour (aLF=1) and three machine-hours (aKF=3).
An economy has 3000 units of machine-hours and 2000 units of work-hours, there is no possibility to substitute labour for capital or vice versa.
The resource constraints show that the total machine- or work-hours used in production cannot exceed the total supply.
(aKCQC)+(aKFQF)K:
2QC+3QF<3000.
(aLCQC)+(aLFQF)L:
2QC+QF<2000.
Building the PPF
Food production:
Requires one work-hour and three machine-hours.
Therefore, the maximum food that can be produced is equal to 1000 units, as K=3,00030003=1000.
At this point, there is spare labour capacity of 1000 work-hours, as only 1000 work-hours have been utilised.
Cloth production:
Requires two work-hours and two machine-hours.
Therefore, the maximum cloth that can be produced is equal to 1000 units, as L=2,000 -> 2000 / 2=1000.
At this point, there is spare capital capacity of 1000 machine-hours, as only 2000 machine-hours have been utilised.
Producing together:
When the economy employs its entire supply of labour and capital it can produce both goods.
(2Qc+3QF)-(2QC+QF)=3000-2000,
2QF=1000,
F=500.
Therefore, 2QC+500=2000,
2QC=1500,
QC=750.
Opportunity costs:
The opportunity cost of one extra unit of cloth, in terms of food, is not constant.
As the economy produces mostly food, there is spare labour capacity:
Producing two fewer units of food releases six machine-hours that can be used to produce three units of cloth.
Therefore, the opportunity cost of cloth, in terms of food, is 2/3.
As the economy produces mostly cloth, there is spare capital capacity:
Producing two fewer units of food releases two work-hours that can be used to produce one unit of cloth.
Therefore, the opportunity cost of cloth, in terms of food, 2(/1).
Therefore, the opportunity cost is higher when more units of cloth are being produced.
Allowing substitution of labour and capital
This substitution removes the kink in the PPF, converting it to a bowed shape.
This shows us that the opportunity cost of cloth, in terms of food, rises as the economy produces more cloth and less food.
Where on this production function does an economy produce?:
The economy produces at the point that maximises the value of production, V.
V=(PCQC)+(PFQF).
An isovalue line, on which the value of output is constant, can be formed, with slope -PC/PF.
The economy produces at Q, the point on the PPF that touches the highest possible isovalue line.
At this point, the slope of the PPF is equal to the slope of the isovalue line.
The opportunity cost of cloth, in terms of food, is equal to the relative prices.
Choosing the inputs
Producers may have a choice in their use of inputs.
Therefore, producers face trade-offs between labour and capital.
For example, a farmer can choose between using a mix of labour and capital.
A curve can be generated that shows the mix of inputs that yields the same output.
The choice producers make is based on the relative cost of capital and labour:
- If capital rental rates are high and wages low, farmers will choose to produce using relatively little capital and a lot of labour.
- If labour wage rates are high and rental rates low, farmers will choose to produce using relative more capital and a little labour.
Where w is the wage and r is the rental rate:
- The farmers input choice will depend on the ratio of these two factor prices.
w/r.
This shows the relationship between factor prices and the ratio of labour to capital use in production of food.
The corresponding relationship between the ratio of factor prices and the labour-capital ratio used in cloth production is also shown, shifted out.
This shows that, given any factor prices, production of food is capital-intensive, while food production is labour-intensive.
‘Definitions of intensity’ depend on the ratio used in production.
These are the relative factor demand curves:
- The downwards slope represents the substitution effect in the producers’ factor demand.
- As the wage rises, producers substitute capital for labour in production decisions.
Factor and goods price
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 rental rate of capital should affect the price of food more than the price of cloth, since food is a capital intensive industry.
- An increase in the wage rate of labour should affect the price of cloth more than the price, since cloth is a labour intensive industry.
Changes in w/r are tied to changes in PC/PW.
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 price of one good increases, demand for the factors of production used to produce that good increases.
Whether this be labour or capital, the wage rate or rental rate increases too.
Since the other factor’s demand decreases, the wage rate or rental rate decreases.
Any change in the relative price of goods therefore alters the distribution of income.
Raising the relative price of cloth
Raise income of the workers relative to that of capital owners, as cloth is a labour intensive industry.
Raise the ratio of capital to labour, K/L, used in both industries.
Raise the real income of workers and lower the real income of capital owners.
Rybczynski theorem
If you hold 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.
Resources and output
Assume an economy’s labour force grows, which implies that its ratio of labour to capital, LK, increases.
The PPF will expand towards production of cloth, as this is a labour intensive industry.
At a given relative price of cloth, the ratio of labour to capital used in both sectors remains constant.
To employ the additional workers, the economy expands production of the relatively labour-intensive good, cloth, and contracts production of the relatively capital-intensive good, food.
An economy with a high ratio of labour to capital produces a high output of cloth, relative to food:
Suppose that Home is relatively abundant in labour and Foreign is relatively abundant in capital:
L/K>L/K.
Likewise, Home is relative scarce in capital and Foreign in labour:
K/L<K/L.
Home will be relatively efficient at producing cloth because cloth is relatively labour intensive.
