--c->
.-----. ___________ <-.
v .~`¯`¬. .~'¯¯ ¯¯`-. .~'¯`¬. |
a | A B | b
| '-._.~' `-.__ __.~' `-._.~' ^
`-> ¯¯¯¯¯¯¯¯¯¯¯ `------'
<-d--
Model used to analyze the flow of goods and services among sectors in an economy. Developed by professor Wassily Leontief at Harvard.
Shown above in its most simple state, we'll say entity A makes 100 katydidics. entity A, while creating these katydidics, uses an average of 2 katydidics in repairing damaged manufacturing equipment. a = 0.02.
Entity B creates univators. Entity B uses up 4% of its univators in paying off loan sharks, and raising worker moral. b = 0.04.
A and B are in cahoots, where A gives B all the katydidics they need (c), and B gives A all the univators they can use (d). Creating katydidics is an exhausting process, so A has a high assembly worker turnover rate. They need approximatly 7 univators for every 100 katydidics that come out the end of the line. d = 0.07.
Creating univators on the other hand is fairly simple, but the katydidics are essential to the process. B only needs 1 katydidic for every 100 univators created. c = 0.01.
Using these values, we can express this system in the weighted digraph at the top, or we can use a technology matrix.
To
_A B_
A |.02 .07|
From | |
B |.01 .04|
¯ ¯
Now, lets suppose an order is put out, or demand is needed for production of 600 univators, and 200 katydidics. We need to know the number of univators and katydidics that must be manufactured.
Easy.
Pk = 200a + 600c + 200
Pu = 600b + 200d + 600
However, once again, this can grow in complexity exponentially, when new entities are introduced. Assuming we have our technology matrix, T, we can express our order, or demand matrix, as
_ _
| 200 |
D = | |
| 600 |
¯ ¯
and our production matrix as
_ _
| b |
P = | |
| a |
¯ ¯
we can find the number of katydidics and univators that need to be produced.
P = TP+D
total production = internal consumption + external demand
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