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Trade and Resources: The Heckscher-Ohlin Model
Readings: Chap. 4, sections 1,3, plus Figure 4-6, 4-7, & related discussions.

Heckscher-Ohlin Model

Effects of Trade on Factor Prices

Extending the Heckscher-Ohlin Model

Conclusions

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Why Resources?

http://www.whitehouse.gov/raise-the-wage

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Skill Premium in the U.S.

Figure 7.6

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Why a new Model?

The specific factor model in the last chapter was a short run model since capital could not move between industries
Our new model is a long run model because all inputs (factors) of production can move between the industries
So our new model offers new perspectives about income inequality, and how U.S. trade policies are set.

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Road Map

Part 1
Assumptions and key elements of the model
No-Trade Equilibrium
Free Trade Equilibrium
Part 2
How does trade affect wage and capital earning?
Part 3
Who gain and who lose from trade?
Part 4
How to measure factor abundance

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Heckscher-Ohlin Model

There are two countries, Home and Foreign
Each country produces two goods, computers and shoes
Production uses two inputs (factors) of production, capital and labor

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Assumption 1. Mobile Factors

Both factors (inputs) can move freely between industries

Capital must earn the same rental rate, R, in both industries
All labor earns the same wage in both industries
Supply of capital = total capital employment
= KC + KS
Supply of labor = total labor employment
= LC + LS

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Diminishing Returns & Labor Demand

Diminishing returns still apply

Holding KC constant

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Diminishing Returns & Capital Demand

Diminishing returns still apply

Holding LC constant

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Substitution in Production

Suppose W is high and R is low. Do we want a lot of labor in production, or a lot of capital in production?

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Substitution and Relative Demand for Labor

The relative demand for labor by the computers industry

As labor becomes more expensive relative to capital, decrease LC and increase KC

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Substitution and Marginal Products

We have seen that as W/R increases, KC increases and LC decreases.

So MPL and MPK must adjust
So as KC/LC is high MPLC is also high.
However, KC/LC is high, MPKC is low.

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Assumption 2. Labor Intensity

Shoe production is labor-intensive; it requires more labor per unit of capital to produce shoes than computers, so that LS/KS > LC/KC for the same W and R

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Relative Demand Curves

Figure 4.1

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Notes: Assumption 2

Computer production is capital-intensive – more capital per worker is used to produce computers than to produce shoes
Shoes production uses more labor per unit of capital
Figure 4.1 shows relative demand curves for labor in each industry
Because shoe production is more labor intensive, the relative demand curve for shoes lies to the right of the labor demand for computers

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Assumption 3. Labor Abundance

Foreign is labor abundant; the labor-capital ratio in Foreign exceeds that in Home. Equivalently, Home is capital abundant.

This means

Intuitively, what is Home good at producing? What is Foreign good at producing?

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Assumption 3. Labor Abundance

Home’s PPF

Output of Computers, QC

Output of Shoes, QS

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Assumption 3. Labor Abundance

Output of Computers, QC

Output of Shoes, QS

Foreign’s PPF

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Notes: Assumption 3

Production Possibility Frontier
Home is capital abundant and computer production is capital intensive
Home is better at producing computers than shoes
Foreign is labor-abundant and shoe production is labor-intensive
Foreign is better at producing shoes

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Assumption 4. Free Trade

Shoes and computers can be traded freely, without restrictions, between nations, but labor and capital do not move between countries.

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Assumption 5. Same Technology

The technologies used to produce the two goods are identical across the countries. By “technology” we mean the input-output relationship.

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Assumption 6. Same Taste

Consumer tastes are the same across countries; i.e. Home and Foreign have the same set of indifference curves

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closed-economy equilibrium

Figure 4.2

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Notes: closed-economy equilibrium

Consumer tastes are the same across countries, so the shape of the indifference curves is the same
The tangency with the country’s PPF is different because of the different shapes of the PPF’s
When the indifference curves are tangent to the PPF, the slopes are equal
The relative price that consumers are willing to pay for computers equals the opportunity cost of producing them – the no trade equilibrium
The slope at tangency equals the relative price of computers – steeper the slope, the higher the relative price of computers

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Notes: closed-economy equilibrium

Equilibrium Price Before Trade
Different relative prices exist in each country because of the different shapes of the PPF’s
At Home, the slope of the Home price line (PC/PS) is quite flat
Low relative price of computers
In Foreign, the slope of the price line (PC*/PS*) is quite steep
High relative price of computers
The no-trade relative price of computers at Home is lower than in Foreign
The No trade relative price of shoes at Home is higher than in Foreign

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Summary: closed-economy equilibrium

Home has comparative advantage in computers
Why? (1) Computers require a lot of capital in production. (2) Home has a lot of capital.

How does the price of computers change as Home opens up to trade with Foreign?

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Free-trade Equilibrium

Going into Free Trade
For the Home country, the price of computers goes up (relative to the price of shoes)

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Free-trade Equilibrium

QS1

Output of Computers, QC

QC1

Output of Shoes, QS

We start with Free Trade Equilibrium for Home

When trade opens, Home now faces the World Price.

New production moves to point B increasing Q of Computers and decreasing Q of Shoes

Home can now increase their utility by increasing consumption because of trade

New consumption is now at point C consuming more shoes and the same amount of computers

World price line, slope = (PC/PS)W

QS2

QC2

QS3

=QC3

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Heckscher-Ohlin Theorem

Pattern of Trade
Home exports computers – the good that uses their abundant factor of production intensively – capital
Foreign exports shoes – the good that uses their abundant factor of production intensively – labor
This is the Heckscher-Ohlin Theorem:

With two goods and two factors, each country will export the good that uses intensively the factor of production it has in abundance, and will import the other good

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Summary Part 1

Diminishing Returns: how does marginal product of capital (labor) change with capital and labor employments?
Substitution between capital and labor in production
Why PPF of Home differs from PPF of Foreign? Labor intensity and labor abundance.

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How does trade affect W and R?

When trade opens:
The relative price of computers in Home rises
This gives home an incentive to produce more computers
Assume that PC rises and PS does not change

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How does trade affect W and R?

Framework
We can use the relative demand for labor in each industry to derive an economy-wide relative demand for labor
We can then compare it to the economy-wide relative supply of labor, L/K
This will determine Home’s relative wage and what happens after the relative price of computers changes

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Relative Demand for Labor

Labor/Capital

Wage

Rental

LC /KC

LS /KS

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Relative Demand for Labor

Economy-Wide Relative Demand for Labor
The quantities of labor and capital used in each industry add up to the total available labor and capital
K = KC + KS and L = LC + LS
We can divide total labor by total capital to get the relative supply equal to the relative demand

Relative Supply

Relative Demand

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Relative Demand for Labor

Labor/Capital

Wage

Rental

LC /KC

LS /KS

Economy-wide relative demand for labor

W/R

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Notes: Relative Demand for Labor

Home country’s relative demand is a weighted average of the labor-capital ratio to each industry
This weighted average is obtained by multiplying the labor-capital ratio for each industry by KC/K and KS/K. The weights reflect the industries’ importance in Home’s economy.
The Home country’s relative demand curve, therefore, lies between the relative demand curves of the two industries, computers and shoes.

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Notes: Relative Demand for Labor

The equilibrium wage is determined by the intersection of the relative supply (L/K) and the relative demand curves in Home
Where the curves intersect gives the wage relative to the rental: W/R
Point A describes an equilibrium in the labor an capital markets – it combines these 2 markets into a single diagram.

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How does trade affect W and R?

Work Backwards
W and R determined by RD
RD has 3 components, relative labor demand by computers, relative labor demand by shoes, and their weights
The weights depend on capital employments, or total outputs

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How does trade affect outputs?

Figure 4-11

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How does RD shift?

Wage

Rental

(W/R)1

Labor/Capital

LC /KC

LS /KS

L/K

The increase in the output of computers causes the relative demand curve to shift left – toward computers

RD1

RD2

(W/R)2

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How does L/K change?

Wage

Rental

(W/R)1

(LC/KC)1 (LS/KS)1 Labor/Capital

LC /KC

LS /KS

L/K

The decrease in w/R increases the amount of workers per unit of capital in both industries

(LC/KC)2

(LS/KS)2

(W/R)2

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Shifting of RD and Change of L/K (Animation)

Wage

Rental

(W/R)1

(LC/KC)1 (LS/KS)1 Labor/Capital

LC /KC

LS /KS

L/K

Initial equilibrium before change in relative price of computers

The increase in the relative price of computers causes the relative demand curve to shift left – toward computers

The real wage falls which increases the amount of workers per unit of capital in both industries

RD1

RD2

(LC/KC)2

(LS/KS)2

(W/R)2

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Notes: How does RD shift after trade?

PC/PS increases at Home (Assume that PC increases and PS does not change)
Production shifts away from shoes to computers
Shoe production decreases and computer production increases
Labor and capital both move from shoe production to computer production
Relative labor supply does not change
Since capital has shifted to the computer industry, the relative demand for labor changes
The terms used in the weighted average, KC/K and KS/K, change

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Notes: How does RD shift after trade?

The relative demand for labor is now more weighted toward computers
The relative demand for labor is now less weighted toward shoes
The relative demand curve shifts left from RD1 to RD2
Shifts in the direction of computers
Equilibrium moves from point A to B

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How does trade affect W and R?

Result 1: W/R decreases
Intuition:
Computers industry expands, shoes industry contracts
Computers industry accounts for larger fraction of economy, and it is capital intensive
This reduces relative demand for labor.

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How does trade affect W and R?

Result 2: the labor-capital ratio rises in both shoes and computers
The relative labor demand curves of shoes and computers do not shift. We move along them.
Intuition: substitution
As W/R decreases, labor is cheaper relative to capital
Both industries substitute labor for capital in production

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Summary part 2

Relative demand for labor
What does it mean?
How is RD constructed?
How does RD shift when trade opens up?
Key Results for effects of trade on Home
Assumption: PS unchanged, PC rises
W/R falls
L/K ratios rise for both industries

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Winners and Losers from trade: Home

Determination of the Real Wage and Real Rental
Assumption: PC rises but PS does not change
We need to determine how the real wage and real rental rate change

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Real Wage

Change in the Real Wage
As before the wage is determined by the marginal product of labor and the price of goods
W = PC*MPLC and W = PS*MPLS
Rearranging
MPLC = W/PC, MPLS = W/PS
So real wage equals marginal product of labor

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Notes: Real Wage

Change in the Real Wage
W/PC is the quantity of computers that can be purchased the with wage
W/PS is the quantity of shoes that can be purchase with the wage
Again we make use of the fact that the labor/capital ratio increases in both industries
Therefore, the marginal product of labor must decrease in both industries
MPLC and MPLS decrease, so W/PC and W/PS decrease
Labor is clearly worse off due to the increase in the price of computers; i.e. W/PS decreases
This means ΔW/W < ΔPS/PS = 0.

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Real Rental Rate

Change in the Real Rental
The rental rate of capital is determined as
R = PC*MPKC
R = PS*MPKS
Rearranging
MPKC = R/PC, MPKS = R/PS
So real rental rate equals marginal product of capital

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Notes: Real Rental Rate

Change in the Real Rental
we make use of the fact that the labor/capital ratio increases in both industries
Therefore, the marginal product of capital must increase in both industries
R/PC measures the quantity of computers that can be purchased with the rental.
R/PS measures the quantity of shoes that can be bought with the rental
Since the MPKC and MPKS both increase, R/PS and R/PC must increase as well
Therefore, capital owners are clearly better off when rental rate increases relative to wage.
This means ΔR/R > ΔPC/PC > 0.

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Summary: Winners and Losers from Trade: Home

When trade opens up with Foreign, PC rises. We can assume that PS does not change (i.e. ΔPS/PS = 0),
ΔW/W < 0 < ΔPC/PC < ΔR/R
Real wage falls, real rental increases

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Summary: Winners and Losers from Trade

The Stolper-Samuelson Theorem

In the long run when all factors are mobile, an increase in the relative price of a good will increase the real earnings of the factor used intensively in the production of that good and decrease the real earnings of the other factor.

The Heckscher-Ohlin model

The abundant factor gains from trade, and the scarce factor loses from trade

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Summary: Winners and Losers from Trade

Friends and enemies

Computers	Shoes
Capital	Friends	Enemies
Labor	Enemies	Friends

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Application: Support for and Opposition to Free Trade

ΔW/W < 0 < ΔPC/PC < ΔR/R

This shows how changes in the prices of goods have magnified effects on the earnings of factors (so it is called the “magnification effect”)

This shows why some are opposed to trade and some support it.

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Congressional Voting for Free Trade

Source: “Is Trade Policy for Sale? Congressional Voting on Recent Trade Bills”, Robert E. Baldwin and Christopher S. Magee, NBER working paper 6376.

Vote for NAFTA	Vote for GATT
Actual	229	283
Predicted by Model	229	290
Without Labor Contributions	291	346
Without Business Contributions	195	257

NAFTA is in 1993. GATT is in 1994. House of representatives. Positions of labor and business were very clear: labor against, business for.

Point: without labor contributions, more would have voted for free trade. Without business contributions, more would have opposed free trade.

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Summary Part 3

Home continues to make both computers and shoes after trade
Real wage depends on MPLC and MPLS
Real rental rate depends on marginal products of capital
Who win and who lose from trade? Friends and enemies

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How to measure factor abundance?

Measuring Factor Abundance
How should we measure factor abundance when there are many countries and many factors?
To determine whether a country is abundant in a certain factor, we count the quantities of that factor
We then compare the country’s share of that factor with its share of world GDP
If the share of a factor > share of world GDP
The country is abundant in that factor
If the share of factor < share of world GDP
The country is scare in that factor

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measure factor abundance. Fig. 4-6

Figure 4.9

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Notes: Figure 4-6

Capital Abundance
We can use the data in Figure 4.6
For example, 24% of the world’s physical capital is located in the US, 8.7% is located in china, 13.3% in Japan, etc.
The final bar in the graph shows the % of each country in world GDP
In the US had 21.6% of world GDP, China had 11.2%, Japan had 7.5%, etc.
We can conclude that the US was abundant in physical capital in 2000

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Notes: Figure 4-6

Capital Abundance
This is true for Japan and Germany
The opposite holds for China and India – their shares of world capital are less than their share of GDP and so they are scarce in capital
Other Inputs/factors
We can use a similar comparison to determine whether each country is abundant or not in R&D scientists, in types of labor distinguished by skill, in arable land, or any other factor of production

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Puzzle

China is abundant in R&D scientists!

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Puzzle Solved: Effective Labor Force

R&D scientists are not the same in China and the U.S. e.g. 1 U.S. scientist = 2 Chinese scientists
If labor is highly productive in the US and less productive in the rest of the world, the effective labor force in the US is much larger than if we just count people

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Effective Labor Force

Effective labor force is number of workers times worker productivity
The amount of effective labor in the world is found by adding up the effective factor endowments across all countries
we compare the country’s share of that effective factor with share of world GDP
If share of an effective factor is less than its share of world GDP then that country is abundant in that effective factor
If share of an effective factor is less than its share of world GDP, then that country is scarce in that effective factor

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measure factor abundance. Fig. 4-7

Figure 4.10

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Notes: Figure 4-7

Effective R&D Scientists
The effectiveness of an R&D Scientist depends on what they have to work with
One way to measure this is through a country’s R&D spending per scientist
If more spending, then scientist will be more productive
Take the total number of scientists and multiply that by the R&D spending per scientists
Figure 4-7 shows these shares
With these productivity corrections, the US is more abundant in effective R&D scientists and China is lower

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Part 4 Summary

How to measure factor abundance?
Compare share of labor (capital, land, etc.) with share of GDP
Supply of effective labor (land, etc.)

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