MIDTERM - FALL, 2013

ECO-13101 Economia Internacional I (International Trade Theory)

October 16, 2013

Instructions: Write your name and clave on the first page of your answer booklet/sheets

and on the question booklet/sheets. Number all the sheets carefully, and staple them with the

question sheets. You have 1 hour and 30 minutes to finish the exam. All questions have to be

answered. All the best!

Question 1 (60 points)

Consider a world with two countries, home (h) and foreign (f). Both countries produce two goods,

X and Y , using three inputs, land (N), labor (L) and capital (K). Output of each good in country

j = {h, f} is given by the following production function:

Xj =(

Kjx

)α (Ljx

)δ (N j

x

)1−α−δ, Y j =

(

Kjy

)β (Ljy

)γ (N j

y

)1−β−γ,

where 0 < α, β, δ, γ < 1, α + δ < 1, β + γ < 1. Assume perfect mobility of factors across the two

sectors within each country and perfectly competitive markets. Denote the return to land, labor

and capital by qj , wj and rj in country j. Let the prices of the two goods in country j be denoted

by pjx and pjy.

1. (10 points) Set up the profit maximization problem of the firms in the two sectors. Obtain

the first order conditions.

2. (20 points) Use the first-order conditions to express the labor-to-land ratio and the capital-

to-land ratio of each sector as a function of the factor price ratios (qjwj

andqjrj, respectively)

and parameters.

3. (20 points) Use the result from the previous part to derive an expression for the price ratio

(pjx/pjy) as function of factor price ratios (

qjrj

andqjwj

) and parameters.

4. (10 points) When these countries trade (suppose the world prices are p∗x and p∗y), will factor

price equalization necessarily hold? Why or why not? Explain your answer by using the

expression for price ratio derived in part (3).

Question 2 (40 points)

Consider a world with two countries, home (h) and foreign (f). Both countries produce two goods

- cars (c) and televsions (tv). Labor (L) is the only factor of production. The production functions,

labor endowments and wages in the two countries are given below:

1

Home Foreign

Production of Cars Qc = 3Lc Qc = 2Lc

Production of Televisions Qtv = 2Ltv Qtv = 3Ltv

Labor force 400 400

Wage $6000 £900

1. (10 points) Which country has absolute advantage in which good?

2. (10 points) Compute the autarky prices of the two goods in the two countries and compare

the autarky price ratios (Pc/Ptv). What is the pattern of comparative advantage? Explain

the intuition.

3. (10 points) Suppose home consumes 900 cars and 200 televisions and foreign consumes 200

cars and 900 televisions. What fraction of income is spent on cars and televsions in home and

foreign?

4. (10 points) Write down Cobb-Douglas utility functions for the home and foreign consumers

which would be consistent with your answer to part (3).

2