Heckscher-Ohlin-Samuelson model

Econ

3

2

0

1

2-1

3

Professor Matilde Bombardini

Problem Set 3

Due Wed Feb 27 by 1pm either online or before class starts

1 Heckscher-Ohlin-Samuelson model

Two goods, Computers and Textiles, are produced using skilled labor (S) and unskilled labor (U)

according to the following production functions:

C = S
2
3
CU

1
3
C

T = S
1
3
T U

2
3
T

Skilled workers and unskilled workers are fully mobile between the two sectors.

The marginal product of skilled and unskilled workers in the two sectors are:

MPSC

=

2

3

(
UC
SC

)1
3

MPUC

=
1

3

(

SC
UC

)2
3

MPST =
1

3

(
UT
ST

)2
3

MPUT =
2

3

(
ST
UT

)1
3

1. Explain why the marginal product of skilled workers is increasing with U
S
and the marginal

product of unskilled workers is decreasing with U
S
.

2. Indicate with wS and wU the wages of skilled and unskilled workers. Take the price of

computers to be pC and the price of textiles to be pT . SHow that the relationship between

the relative wage wU

wS

and the factor intensity U
S
is

SC
UC

= 2∗
wU
wS

in the computers industry and
ST
UT

=
1

2

wU
wS

1

in the textile industry.

3. In what sense textiles are more “unskilled-labor intensive”than computers? What does it

mean? Draw the two relationships between relative factor prices and relative factor usage in

a graph where ST
UT

and SC
UC

are on the horizontal axis and wU
wS

is on the vertical axis.

4. I have calculated for you the relationship between goods prices and factor prices to be:

pT
pC

= 3

wU
wS

=

(
wU
wS

)1
3

Graph this relationship next to the other you drew before (like we did in class). So that now

you have a relationship between pT
pC
,wU
wS

and ST
UT

and SC
UC
.

5. Now consider a country, like the US, which is skilled-labor abundant. In autarky you are told

that the relative price of textiles to computers
(
pT
pC

)
A
= 1. What are the relative wage wU

wS

and relative factor usage in autarky?

6. Imagine the US opens up to trade with China (an unskilled-labor-abundant country) and as

a result the price of computers rises so that pT
pC
= 1

8
. Why did the price of computers relative

to textiles increase in the US (compared to autarky)? What good does the US export to

China?

7. What are wU
wS

and relative factor usage (in both sectors) under trade? Who wins and who

loses from opening up to trade in the US (how do the real wages of skilled and unskilled

workers change)? In case you did not recognize it, this is the Stolper-Samuelson theorem!

8. Now start from a situation in which the world price is pT
pC
= 1

8
and keep this price constant.

What happens to real wages of skilled and unskilled workers if the US suddenly receives a

large number of unskilled immigrants? What happens to the production of computers and

textiles? (Again, you should recognize this. It is the Rybczynski theorem).

2 True/False/Uncertain

Say whether the following statements are true, false or uncertain and BRIEFLY (one or two sen-

tences) explain why (if you want you can use graphs):

1. When a capital abundant country (country 1) starts trading with a labor abundant country

(country 2) the relative price of capital-intensive goods declines (relative to autarky in country

1)

2

2. The HOS theory predicts that, if countries start trading goods, the factor prices (returns to

factors, for example wages) will become more similar across countries

3. In a small open economy immigration of unskilled workers does not cause wages of unskilled

workers to decline.

4. An individual worker may be better offas a result of trade in the short run, but may be worse

off in the long run.

5. The Heckscher-Ohlin-Samuelson theory is likely to explain the rise of the skill premium in the

US and other industrialized countries in recent decades, because in the data we have observed

a rise in the price of skill-intensive goods relative to unskill labor-intensive goods over the

same period.

6. The HOS theory starts from the premise that countries have different technologies and this