economics assignment

ECO 364: International Trade

Problem Set 3

Due date: 5:00 PM, 18 October 2018

Consider the Heckscher-Ohlin model of international trade that we studied in class. There

are two countries, Home and Foreign, and two sectors, 1 and 2. Home is endowed with K̄H

units of capital and L̄H units of labor. Foreign is endowed with K̄F units of capital and L̄F

units of labor. Households have identical Cobb-Douglas preferences in Home and Foreign,

given by :

U (C1, C2) = (C1C2) 1 2

The production technology available is the same in each country:

Xi = min

{ Ki bKi

, Li bLi

} where Xi, Ki, and Li denote the output, capital input, and labor input of sector i respectively.

That is, production in each sector is Leontief, whereby one unit of output of good i requires

bKi units of capital and bLi units of labor.

In what follows, assume that factor endowments are K̄H = 6, L̄H = 5, K̄F = 5, and

L̄F = 6. Assume also that the unit factor requirements are bK1 = 2, bL1 = 1, bK2 = 1, and

bL2 = 2.

Solution given goods prices

First, we will solve for demand and supply in each country assuming that goods prices

in each country are known, i.e. assuming that we know pH1 , p H 2 , p

F 1 , and p

F 2 .

(a) What is equilibrium relative consumption in each country (i.e. CH1 /C H 2 and C

F 1 /C

F 2 )?

How does this vary with goods prices?

(b) Write down the factor market clearing conditions for each country.

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(c) What is equilibrium output of each sector in each country (i.e. XH1 , X H 2 , X

F 1 , X

F 2 )?

How does this vary with goods prices?

(d) What is the equilibrium allocation of factors in each sector in each country (i.e. Kci and Lci for c ∈{H, F} and i ∈{1, 2})? How does this vary with goods prices?

(e) Write down the zero-pro�t conditions for �rms in each sector in each country.

(f) What are equilibrium real factor incomes in each country (i.e. rc/pci and w c/pci for

c ∈{H, F} and i ∈{1, 2})? How do these vary with goods prices?

Autarky Now suppose that both Home and Foreign are in autarky.

(g) What is the equilibrium relative goods price in each country (i.e. pH1 /p H 2 and p

F 1 /p

F 2 )?

(h) What are equilibrium real factor incomes in each country?

Trade Now suppose that both Home and Foreign can trade at a world relative price of

pWr ≡ pW1 /pW2 = 1.

(i) At the world relative price, what are real factor incomes in each country? Which

factors in which countries gain or lose from trade?

(j) How do relative factor prices (i.e. r/w) compare in Home and Foreign?

(k) (Bonus) Show that the world relative price pWr = 1 is the price at which world relative

demand (i.e. CH1 +C

F 1

CH2 +C F 2 ) is equal to world relative supply (i.e.

XH1 +X F 1

XH2 +X F 2

). In other words,

show that in this two-country model, pWr = 1 is the equilibrium world relative price

that clears world markets for each good.

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