MATH 1711: SECTION 2.6
INPUTOUTPUT ANALYSIS
Basic Idea
: Consider an economy consisting of a set of industries, where each industry
depends on the other for goods.
Inputs
are what each industry needs to create a final product.
Outputs
are the final
products.
We build an
inputoutput
matrix to hold all the information in a given problem. The entry
a
ij
represents the amount of industry
i
’s product needed to produced $1 worth of industry
j
’s product (given as percentages).
In general, if
A
is the inputoutput matrix,
X
is the variable matrix (how much monetary
value each industry should produce), and
D
is the consumers’ demand for the products,
we have the formula
X

AX
=
D,
which we solve by factoring out an
X
: (
I

A
)
X
=
D
and multiplying by the inverse of
I

A
:
X
= (
I

A
)

1
D.
Here,
X
= amount produced,
AX
=amount used in production, or internal demand, and
D
=amount left for consumers, or external demand.
Example
: A particular town has a farmer, a butcher, and a baker. To produce $1 worth
of farming products, the farmer requires $0.20 of his goods, $0.10 of the butcher’s goods,
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
and $0.40 of the baker’s goods. To produce $1 of the butcher’s products, the butcher needs
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Evans
 Math, Multiplication, Regression Analysis, Baking, Invertible matrix, Linear least squares

Click to edit the document details