Download Factor Price Equalization and Stolper

INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;
 Charles van Marrewijk, 2006; 1
FPE and Stolper-Samuelson; tool: Lerner diagram
Let’s look at point A on the blue X = 1 isoquant for good X
Suppose we look at another isoquant through point A, dashed green
Isoquants of a good cannot intersect (the same
combination of capital and labor would then give rise
K
X = 1 to 2 different levels of output, which is nonsense), so
this must be the isoquant of a different good.
Let’s say it’s the isoquant Y = 0.5
Suppose px = 1, then the value of production
along the X = 1 isoquant equals 11 = 1
Similarly, along the Y = 0.5 isoquant,
A
provided py = 2 (20.5 = 1)
Y = 0.5
These are the unit
value isoquants
L
INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;
 Charles van Marrewijk, 2006; 2
FPE and Stolper-Samuelson; tool: Lerner diagram
One unit of cost for the producer is given by wL+rK = 1
In the figure this is given by a straight line with slope w/r and
intercept 1/r for K and 1/w for L. Note that at point B the value of
K
production of good X is 1 and the cost is also 1
X=1
At any other point on the X = 1 isoquant
the cost of production is higher
1/r
Similarly, for point C on the Y = 0.5
isoquant
B
Production of both goods simultaneously
is only possible if this figure is consistent
C
Y = 0.5
1/w
L
INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;
capital
 Charles van Marrewijk, 2006; 3
FPE and Stolper-Samuelson; tool: Lerner diagram
X  1 / px
Unit value isoquant good X
1/ r
A
B
 w
1 r  w
1  r
Unit value isoquant good Y
Y  1/ py
Unit value cost line
1/ w
0
labor
INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;
 Charles van Marrewijk, 2006; 4
FPE and Stolper-Samuelson; FPE
Given the prices of final goods px and py the unit value isoquants are
determined exactly. They are drawn here in the figure
There is only one isocost line which touches these two isoquants
This determines exactly the values 1/r and 1/w
K
X=1
This implies that if trade between two
countries equalizes the prices of final
goods and these two countries have
1/r
identical CRS production functions,
then the reward to factors of production
B
w and r are also equalized (FPE)
C
Y = 0.5
1/w
L
INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;
 Charles van Marrewijk, 2006; 5
FPE and Stolper-Samuelson; FPE
Similarly, the prices of inputs w and r give the unit cost line
There is only one isoquant for good X which touches it
This determines exactly the price px
K
Similarly, there is only one isoquant for
X=1
good Y which touches the isocost line;
this determines exactly the price py
1/r
There is a one-to-one correspondence
between the prices of final goods and the
reward to factors of production
B
C
Y = 0.5
1/w
L
INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;
 Charles van Marrewijk, 2006; 6
FPE and Stolper-Samuelson; Stolper - Samuelson
Take a situation as depicted in the figure and note that good X uses
relatively more capital than good Y (slope of line through origin)
Suppose the price of good X increases to px = 5/4; this shifts the unit
value isoquant for good X inward to 0.8
K
X=1
As a result the isocost line touching the unit
value isoquants rotates counter-clockwise
To touch at B’ and C’
1/r
1/r’
1/r falls to 1/r’, so r rises
1/w rises to 1/w’, so w falls
B
B’
C
C’
Y = 0.5
1/w 1/w’
L
INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;
 Charles van Marrewijk, 2006; 7
FPE and Stolper-Samuelson; Stolper - Samuelson
To summarize: the price of good X rises, this results in a rise in the
rental rate of capital (the input used intensively in the production of
good X) and a fall in the wage rate (the other input)
This is the Stolper-Samuelson theorem
K
It generalizes to arbitrary settings in terms
X=1
of ‘friends’ and ‘enemies’: if the price of a
final good rises the reward to some input
1/r
rises and to some other input falls
Also note that the rise in
B
r and the fall in w causes
1/r’
a substitution away from
capital in the production
C
B’
of both goods X and Y
C’
Y = 0.5
1/w 1/w’
L