Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model
-
Upload
daria-morrow -
Category
Documents
-
view
17 -
download
1
description
Transcript of Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model
![Page 1: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/1.jpg)
Factor Proportions and the Structure of Trade: HOS-
Krugman-DFS Model
The Explanation of International Trade: Differences across countries inrelative abundance of factors of production.
Assumptions: Identical TechnologiesIdentical Demand Patterns
The HOS Model:
![Page 2: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/2.jpg)
RelativeFactorIntensity
:
Full employment:
Y
X
AB*YLa
L
XKa
KXLa
LYK
XK
a
a
YL
XL
a
aL constant
K constant
Structural Bias: The Transformation Curve( = ABC) shifts asymmetrically with unbalanced changes in K and L. A Rise in K, with no change in L, leads to an increase(fall) in X (Y)).
C
YL
XL
YK
XK
a
a
a
a
YL
YK
XL
XK
a
a
a
aor
D
B
YKa
K KYaXa
LYaXa
YKXK
YLXL
E
F
![Page 3: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/3.jpg)
AT POINT F
1) Labor is unemployed: W=0.(2) The X-industry is active The Y-industry is inactive. Therefore:
AT POINT A
1) Capital is unemployed: R=0.(2) Y-industry is active X-industry is inactive. Therefore:
Y
X
a
a
P
P
a
PRW
YPRaWa
XPRaWa
YK
XK
Y
X
XK
X
YYKYL
XXKXL
,0
0
0
![Page 4: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/4.jpg)
AT Point A (continue):
0
,0
0
0
Y
X
a
a
P
P
a
PWR
YPRaWa
XPRaWa
YL
XL
Y
X
YL
Y
YYKYL
XXKXL
![Page 5: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/5.jpg)
At Point B
Y
x
P
P
YK
XK
a
a
YL
XL
a
a
Y
X
Relative Supply
0,0
YX
a
a
P
P
a
a
PRaWa
PRaWa
YL
XL
Y
X
YK
XK
YYKYL
XXKXL
![Page 6: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/6.jpg)
Two Countries: H and F: H is more capital abundant.
H’s Relative Supply is biased towards X:
Y
x
P
P
YK
XK
a
a
YL
XL
a
a
FRS
HRS
FH
FH
YY
XX
![Page 7: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/7.jpg)
Free Trade and Autarkic Equilibria
Y
x
P
P
YK
XK
a
a
YL
XL
a
a
FRS
HRS
FH
FH
YY
XX
3 2
1
2=Free trade1=autarky in H3=autarky in F
FH
HH
F
FH
H
HH
FH
FH
YY
Y
Y
X
Y
X
YY
XX
)1(
![Page 8: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/8.jpg)
Full Employment Supply of X and Y:
XKYLYKXL
XLXK
XKYLYKXL
YLYK
YKXK
YLXL
aaaa
LaKaY
aaaa
KaLaX
KYaXa
LYaXa
![Page 9: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/9.jpg)
The Heckscher-Ohlin Proposition #1:Any country will export the good
which makes intensive use in its production of relative abundant factor supply.
![Page 10: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/10.jpg)
YYKYL
XXKXL
PRaWa
PRaWa
Full Employment Factor Prices:
![Page 11: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/11.jpg)
Income Distribution and International Trade
R
W
XK
X
a
P
YK
Y
a
P
XL
X
a
P
XL
XK
a
a
YL
YK
a
a
A
BB’
D C
ABC=factor price frontier
A rise in XP (X is capital intensive) will raise R and decrease W.
risesPX
YL
Y
a
P Industry X-Line
Industry Y-Line
![Page 12: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/12.jpg)
The Heckscher-Ohlin Proposition #2(dual to Proposition #1):
Free trade causes an increase in the factor price of the factor of production which is used intensively in the export industry and a fall in the factor price used intensively in the import competing industry.
![Page 13: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/13.jpg)
Factor Price Equalization: Failures
Two ways to generate a failure of FPE:
• Assume that factor proportions are sufficiently different that they are outside the FPE set.
• Introduce costs to international trade, which could have strong effect on trade volume.
![Page 14: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/14.jpg)
Romalis (AER, March 2004, 94, No.1, 67-97)
• Generalizes a Heckscher-Ohlin model of Dornbusch-Fischer-Samuelson framework, and explains trade structure;
• Assumes a many-country version of the Heckscher-Ohlin model;
• Integrates this with Krugman intra-industry trade;
• Allows for transportation costs.
![Page 15: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/15.jpg)
The Model
There are 2M countries, M each in the North and South.
Southern variables are marked with an asterisk.
There are two factors of production: skilled and unskilled labor.
The proportion of skilled labor is
Northern countries are abundant in skilled labor
*
![Page 16: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/16.jpg)
Preferences
1)(
)(ln)(
1
0
1
0
dzzb
dzzQzbU
![Page 17: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/17.jpg)
Monopolistic Competition
1
1)(
0
*
)),(()),((
),()(
)]()([)(
)(
),(
wsizqizqTC
diizqzQ
znznMzN
zN
izq
SS
zND
S= Production of variety i
Number of of varieties in industry z
Sub-utility function
Fixedcost
DualUnit cost
Number ofcountries
![Page 18: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/18.jpg)
Transportation costs
1 Units of a good must be shipped for 1 unit to arrive in any other country
![Page 19: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/19.jpg)
Equilibrium in an industry
Solve for the share of world production that each country commands, conditional on relative production costs. Countries with lower costs capture larger market shares.
1
1
)('
1
)('
1
)'),(()(
'),(
),(),(
1
1
zIi
zIi
D
diizpzG
diizp
izpizq
Consumer price
IdealPrice index
![Page 20: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/20.jpg)
National income and Spending
wsY )1(
A constant fraction of income b(z) is spent on industry z
![Page 21: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/21.jpg)
![Page 22: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/22.jpg)
World Demand
111
11
)*
(*)()()1()(
])*(*
)()1([1
11
G
pbYM
G
pbYM
G
pbYpq
pMn
pnMnpG
S
![Page 23: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/23.jpg)
North-South relative price
1
1
)1(1,*
*)(
)1(*
1)(
MFp
pp
YYMW
wszp
SS
p
![Page 24: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/24.jpg)
If is low, (1) is the solution;if is high, (2) is the solution
0*,)1(*
*)(*,0
0*,)1(
*)(
np
YYbnn
np
YYbn
p
(1)
(2)
p
![Page 25: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/25.jpg)
General Equilibrium
***(
*1))(1
()()1(
*))(1
()(*
1
1)()()1(1
)()(1
1
0
1
0
1
0
1
0
SS
S
qpnnpqM
npq
dzzM
Wzzb
dzzM
Wzzbs
dzzWzbzw
dzzWzzbs
![Page 26: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/26.jpg)
Special Case
The Dornbusch-Fischer-Samuelson Model is a special case with no transportation costs
Perfect competition1
0
![Page 27: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/27.jpg)
Transport costs
The addition of the transport costs leads a stark structure of production and trade:
Share ofindustry
Skill intensity of industry (z)
Unskilled goods produced in southNon-traded goods Produced In North
Non-traded goods Produced In South
Skill-intensive goods Produced In North
![Page 28: Factor Proportions and the Structure of Trade: HOS-Krugman-DFS Model](https://reader035.fdocuments.in/reader035/viewer/2022081603/56813507550346895d9c56d9/html5/thumbnails/28.jpg)
Producer prices
p=factory-gate price domestically;
p Sold in M-1 markets abroad