FPE and Stolper-Samuelson; tool: Lerner diagram

1
FPE and Stolper-Samuelson tool Lerner diagram
Lets 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 to 2 different levels of output, which is
nonsense), so this must be the isoquant of a
good.
different
Lets say its 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, provided
py 2 (2?0.5 1)
These are the unit value isoquants
Y 0.5
2
FPE and Stolper-Samuelson tool Lerner diagram
One unit of cost for the producer is given by
wLrK 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.
At any other point on the X 1 isoquant the cost
of production is higher
Similarly, for point C on the Y 0.5 isoquant
Production of both goods simultaneously is only
possible if this figure is
consistent
3
FPE and Stolper-Samuelson tool Lerner diagram
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 isocost line which touches
these two isoquants
one
This determines the values 1/r and 1/w
exactly
This implies that if trade between two countries
equalizes the prices of final goods and these two
countries have identical CRS production
functions, then the reward to factors of
production w and r are also equalized (FPE)
5
FPE and Stolper-Samuelson FPE
Similarly, the prices of inputs w and r give the
unit cost line
There is only isoquant for good X which
touches it
one
This determines the price px
exactly
Similarly, there is only isoquant for good Y
which touches the isocost line this determines
the price py
There is a one-to-one correspondence between the
prices of final goods and the reward to factors
of production
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)
inward
As a result the isocost line touching the unit
value isoquants rotates counter-clockwise
To touch at B and C
7
FPE and Stolper-Samuelson Stolper - Samuelson
It generalizes to arbitrary settings in terms of
friends and enemies if the price of a final
good rises the reward to some input rises and to
some other input falls
Also note that the rise in r and the fall in w
causes a substitution away from capital in the
production of both goods X and Y