Classic Trade Theory

• Ricardian Model - Technological Comparative Advantage:– Basic 2 Good Ricardian model (Feenstra, Chapter 1)– Continuum of Goods [Dornbush, Fischer and Samuelson

(1977)]• Heckscher-Ohlin Factor Endowment Model:– 2 Good 2 Factor Model (Feenstra, Chapters 1)– Stolper Samuelson– Leontief Paradox

• Heckscher-Ohlin-Vanek Model and Tests of HO theory

Basic Ricardian 2 Good Model• We assume country specific technologies in the form of labor

requirements: Home [ no *] : ai

Foreign [*] : ai*• The basic model allows 2 goods/ industries, i = 1, 2• Labor is exogenous, and mobile across industries: L, L*• Markets clear so workers are paid value of marginal product:

• The mobility of workers implies that wages equalize across industries:

• Set p2 as the numeraire and denote relative price p:

y1*y1

y2*y2

L/a2

L*/a2*

L/a1 L*/a1*

papa*

A

A*

Home PPF Foreign PPF

Economic Output under Autarchy (no trade)

L is labor endowmentA is consumption point is the output of industry I is the autarchy price

Define Relative home productivity:

Suppose Home has a comparative advantage in good 1:

Comparative advantage is a function of relative wages and technology, but wages are endogenous.

Technology determines Comparative Advantage

(𝑦¿¿1+𝑦1∗)/(𝑦2+𝑦2

∗)¿

p

pa*

pe

pa

Relative Demand

Relative Supply

World Relative Supply and Demand

(𝑦¿¿1+𝑦1∗)/(𝑦2+𝑦2

∗)¿

p

pe = pa*

pa

Here the demand for good one is high enough that the equilibrium price of trade is equal to the autarchy foreign price

Foreign is no better off with trade. When might this occur?

Relative Demand

Relative Supply

(𝑦¿¿1+𝑦1∗)/(𝑦2+𝑦2

∗)¿

p

pa*

pe

pa

Relative Demand

Relative Supply

Gains from Trade

Here the trade price of good one is higher than in autarchy at home, and lower than in autarchy in foreign.

Both countries can gain from trade, and will fully specialize in their comparative advantage.

y1*y1

y2*y2

L/a2

L*/a2*

L/a1 L*/a1*

papa*

A

A*

B

B*

C*C

p

p

Points B and B* represent the level of production of goods 1 and 2 in each country under specialization.

C and C* are consumption in home and foreign.

Comparative advantage and Wages (Feenstra pg. 4 note 2)

• Suppose Home has a comparative advantage in good 1.a1/a2 < a1*/a2*

and an absolute disadvantage in both goods.• a1 > a1*

• a2 > a2*• In Free Trade suppose each country specializes (pa < p < pa*)

-workers at home produce good 1 and earn w = p / a1

-workers in foreign produce good 2 earn w* = 1 / a2*

• p = a1/a2 < a1*/a2*, rearranging: 1 / a2* > p / a1*

• We assumed a1 > a1*, resulting in p / a1* > p / a1

• Wages in Foreign, w* = 1 / a2* > p / a1*> p / a1 = w

Beyond 2 Goods, Dornbush, Fischer and Samuelson (1977)

Generalization of Ricardian model to a continuum of goods, to allow integration.

Again 2 countries, one factor of production, labor, in fixed supply (L and L*)

Country-specific constant unit labor requirements: a (z) and a*(z)With relative home productivity which can be written as before:

Assume that we can rank all goods so that A(z) is continuous and decreasing in z.

price = marginal cost: P(z) = a(z)w and P*(z) = a*(z)w*

Assume home production: P (z) < P*(z) or A(z) > w/w*

Strong Structure on Demand

• Homothetic Demand: after winning the lottery I take my grocery list and double the purchases of every item.

• Constant expenditure Share b, demand C, total income Y • Identical tastes across countries• Many products:

• Continuum of products:

– b(z)=b*(z)

• Production at home:

Trade Equilibrium (DFS 1977)

Domestic wages must equal world spending on domestic goodsRewriting in terms of relative wages:

Combine with the conditions for Home Production:

Gains from Trade (DFS 1977)

Rest of the World

Hypothetical DFS Population Growth

• Suppose that the foreign country increases their population (possibly by integrating with another country).

• B(L*/L) is increasing in L*.• Home will produce fewer goods, but wages rise. Home

is better off, Real income rises• Workers in F lose, wages decline in terms of goods

produced abroad.– This is a Terms of Trade effect. The terms of trade are said to

improve if the index of the price of a country's exports in terms of its imports rises.

DFS and a Gravity Equation

• Note from equilibrium conditions

• Trade Volume is

Notice similarity to Newton's law of universal gravitation

Image © The Whipple Museum.

Criticisms of DFS/ Ricardian Model

• Does not generalize easily to more than two countries

• Comparative Advantage is generated by an exogenous technology– Assuming that costs are different across countries

makes prediction difficult.– Why wouldn’t technology spill across borders?

The Heckscher-Ohlin (HO) Model

• The law of comparative advantage says that countries trade when autarky prices are different from free trade prices

• Assuming persistent differences in technology seemed unprincipled.

• Variation in autarky prices can come from differences in factor endowments (capital, labor, skilled labor, land)

• Heckscher-Ohlin modelAt least two factorsFactors are stuck in countriesTechnology is identical in all countries

H-O Two good, Two Factors (Labor and Capital)One Production Function (identical technology):

f is increasing, concave, and homogenous of degree 1 in L and K (Constant Returns to Scale)Resource Constraints:

• Feenstra works with the dual of the production function:

• The solution of this function is written:

• Note that using the envelope theorem (Shephard’s Lemma):

Duality: Unit Cost Functions

Equilibrium Conditions

• Zero Profit Conditions: Free entry in perfectly competition determines prices

• Full employment Conditions: All resources are consumed: and

– Notice that fixing prices, ZP determine w and r.– The remaining equations determine and .

• In equilibrium sectoral output levels will depend on K and L but not factor intensities.

Factor-price Insensitivity (Feenstra Theorem 1)

• With two goods and two factors, factor prices are uniquely determined by goods prices, irrespective of factor endowments.

Factor-price equalization (Feenstra Theorem 2)

• Assume free trade, no transport cost, two goods, two countries, two factors, identical technologies, no factor-intensity reversals, and both countries produce both goods.

• Then factor prices are equalized in both countries irrespective of factor endowments.

Stolper Samuelson Theorem

• An increase in the price of a good will more than proportionally increase the returns to the factor intensively used in the production of that good.

• Trade raises the real reward of a country’s abundant factor and reduces the real reward of its scarce factor.– Trade leads to a conflict of interest between the scarce

and abundant inputs.– Trade leads to factor price convergence (Ohlin emphasized

the tendency towards factor price convergence, but not equalization).

Mathematical Statement of the Stolper Samuelson Theorem

Suppose that: then Proof:Take total derivative of for i=1,2 with respect to :

Eliminate term:

(1)

From homogeneity of cost function and Shephard’s lemma:

Divide by w and see that

(2)

Putting equations (1) and (2) together:

Many Goods Heckscher-Ohlin-Vanek Model (Feenstra chapter 2)

• M factors, world endowment vector , indexed by k• C countries with endowments , indexed by i• factors are immobile across countries, perfectly

mobile within countries• N industries produced with CRS as before.• is the factor requirement of production. The

transposition implies that columns are the industries, rows are the factors.

Factor Content of Trade

• is the vector of outputs in each industry for country i.• is the vector of demands for goods in each country i.• is the net exports of country i.• Factor content of trade is • is the demand for factors in i, set equal to endowment .• is homothetic and identical across countries, and trade

is balanced so must be the share of income times world demand.

World consumption equals world production:

Pattern Of Trade in Each Factor

• is the Heckscher-Ohlin-Vanek Theorem for each factor .

• Comparative advantage in each factor k can be determined by the share of world endowment of factor k over the share of world GDP.– If then country is abundant in factor .– This implies that , or that the abundant factor is

exported.

The Leontief Paradox

• Using U.S. input-output tables from 1947:– The capital labor ratio in U.S. exports was $13,700

of capital per man-year– The capital labor ratio in U.S. imports was $18,200

of capital per man-year• The U.S. is relatively capital abundant after

WWII and should export capital intensive products and import labor intensive products.

Leamer 1980 Observation

• Leontief studied the factor content of exports and imports, but what matters is the relative factor abundance of production and consumption.

• is the factor content of consumption of capital, while is the factor content of consumption of labor.

• For a capital abundant country

We would expect U.S. production to be more capital intensive than its consumption, which according to Feenstra Table 2.2, it is (slightly).

𝑳𝑾=𝑳𝟏+𝑳𝟐

𝑲𝑾=𝑲𝟏+𝑲 𝟐

𝑂1

𝑂2

𝐹 𝑘1

𝐹 𝑘2

Edgeworth Box of Factor content of Trade

Good 1

Good 2

is employment in industry 1.

𝑄1

𝑳𝑾=𝑳𝟏+𝑳𝟐

𝑲𝑾=𝑲𝟏+𝑲 𝟐

𝑂1

𝑂2

Edgeworth Box and Share of trade

w/r

Integrated Equilibrium: Imagine there are no countries

• Zero profit conditions

Factor markets clear

Where is the quantity of good i.• Goods market clear

Notice that the number of equations is equal to the number of unknown parameters.

Return to Factor Price Equalization

• Goal is to replicate the equilibrium in the integrated equilibrium using trade in goods.

• Assume: – every country uses the same input mix as in the integrated

equilibrium.– Full employment of factors in all countries.

• Because every country is using the same technologies, the factor prices will be the same. Because the factor prices are the same the goods prices p will be the same.

• Full employment and identical (p, w) imply the same income and production as the integrated equilibrium.