1. FPE and Stolper-Samuelson; tool: Lerner diagram, 1
 Charles van Marrewijk
FPE and Stolper-Samuelson; tool: Lerner diagram, 1
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 to 2 different levels of output, which is nonsense), so this must be the isoquant of a good. L K
X = 1 A
different
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, provided py = 2 (20.5 = 1)
These are the unit value isoquants
Y = 0.5

2. FPE and Stolper-Samuelson; tool: Lerner diagram, 2
 Charles van Marrewijk
FPE and Stolper-Samuelson; tool: Lerner diagram, 2
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
production of good X is 1 and the cost is also 1 L K
X = 1 B
At any other point on the X = 1 isoquant the cost of production is higher
1/r
1/w
Y = 0.5 C
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, 3
 Charles van Marrewijk
FPE and Stolper-Samuelson; tool: Lerner diagram, 3

4. FPE and Stolper-Samuelson; FPE, 4
 Charles van Marrewijk
FPE and Stolper-Samuelson; FPE, 4
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 L K
X = 1
Y = 0.5
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)
1/r
1/w B C

5. FPE and Stolper-Samuelson; FPE, 5
 Charles van Marrewijk
FPE and Stolper-Samuelson; FPE, 5
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 L K
1/r
1/w
Similarly, there is only isoquant for good Y which touches the isocost line; this determines the price py
one
exactly
X = 1 B
Y = 0.5 C
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, 6
 Charles van Marrewijk
FPE and Stolper-Samuelson; Stolper - Samuelson, 6
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 to 0.8
inward L K
1/r
1/w
X = 1 B
Y = 0.5 C
As a result the isocost line touching the unit value isoquants rotates counter-clockwise
To touch at B’ and C’
1/w’
1/r’
1/r to 1/r’, so r
1/w to 1/w’, so w
rises
falls
Study guide Picture 6 B’ C’

7. FPE and Stolper-Samuelson; Stolper - Samuelson, 7
 Charles van Marrewijk
FPE and Stolper-Samuelson; Stolper - Samuelson, 7
This is the Stolper-Samuelson theorem
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) L K
1/r
1/w
X = 1 B
Y = 0.5 C
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
1/w’
1/r’
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 B’ C’