The Leontief Input-Output Method, Part 1
The Leontief Input-Output Method was
developed by Wassily Leontief (1906-1999).
The Leontief Input-Output Method, Part 1
The Leontief Input-Output Method was
developed by Wassily Leontief (1906-1999).
He used this method to study the interactions
between different sectors of the U.S. economy.
His examples studied the interactions of about
70 different sectors, but our examples will be
simpler than that.
The Leontief Input-Output Method, Part 1
The Leontief Input-Output Method can take
advantage of two strategies we have previously
studied:
Graph Theory and Matrices
The Leontief Input-Output Method, Part 1
Example 1: Sunny Summer Beverages
produces and bottles a variety of fruit juices.
For every dollar worth of juice it produces, it
keeps $.04 worth of juice in house to help keep
the workers hydrated and happy.
If the company produces $200 worth of juice,
how much will be available for sale?
The Leontief Input-Output Method, Part 1
Example 1: Sunny Summer Beverages
produces and bottles a variety of fruit juices.
For every dollar worth of juice it produces, it
keeps $.04 worth of juice in house to help keep
the workers hydrated and happy.
D: Demand
P: Total Production P - .04P = D
.96P = D
.96(200) = $192 = D
The Leontief Input-Output Method, Part 1
Example 1: Sunny Summer Beverages
produces and bottles a variety of fruit juices.
For every dollar worth of juice it produces, it
keeps $.04 worth of juice in house to help keep
the workers hydrated and happy.
How much juice must the company produce in
order to sell $300 worth?
The Leontief Input-Output Method, Part 1
Example 1: Sunny Summer Beverages
produces and bottles a variety of fruit juices.
For every dollar worth of juice it produces, it
keeps $.04 worth of juice in house to help keep
the workers hydrated and happy.
P - .04 P = D
.96P = 300
P = $312.50
The Leontief Input-Output Method, Part 1
Example 2: ABC Furniture manufactures a
variety of office furniture. It also manufactures
bolts, some of which are used in its furniture.
Every dollar worth of bolts produced requires
an input of $.03 worth of bolts and $.02 worth
of office furniture. Each dollar worth of office
furniture requires an input of $.04 worth of
bolts and $.05 worth of office furniture.
The Leontief Input-Output Method, Part 1
Example 2: $1 of bolts requires: $.03 bolts,
$.02 office furniture. $1 of office furniture
requires: $.04 of bolts, $.05 of office furniture.
Draw a weighted digraph that represents
this situation.
The Leontief Input-Output Method, Part 1
Example 2: $1 of bolts requires: $.03 bolts,
$.02 office furniture. $1 of office furniture
requires: $.04 of bolts, $.05 of office furniture.
Draw a weighted digraph that represents
this situation.
.03
B
F
The Leontief Input-Output Method, Part 1
Example 2: $1 of bolts requires: $.03 bolts,
$.02 office furniture. $1 of office furniture
requires: $.04 of bolts, $.05 of office furniture.
Draw a weighted digraph that represents
this situation.
.03
B
.02
F
The Leontief Input-Output Method, Part 1
Example 2: $1 of bolts requires: $.03 bolts,
$.02 office furniture. $1 of office furniture
requires: $.04 of bolts, $.05 of office furniture.
Draw a weighted digraph that represents
this situation.
.04
.05
.03
B
.02
F
The Leontief Input-Output Method, Part 1
Example 2: $1 of bolts requires: $.03 bolts,
$.02 office furniture. $1 of office furniture
requires: $.04 of bolts, $.05 of office furniture.
Construct a consumption matrix for this
company.
(Pay careful attention to the To and From
labels.)
The Leontief Input-Output Method, Part 1
Example 2: $1 of bolts requires: $.03 bolts,
$.02 office furniture. $1 of office furniture
requires: $.04 of bolts, $.05 of office furniture.
Construct a consumption matrix for this
company.
B
From
B
F
To
F
 .03 .04 


 .02 .05 
The Leontief Input-Output Method, Part 1
Example 2: If the company produces $300
worth of bolts, what input of bolts and office
furniture does it require?
B
From
B
F
To
F
 .03 .04 


 .02 .05 
The Leontief Input-Output Method, Part 1
Example 2: If the company produces $300
worth of bolts, what input of bolts and office
furniture does it require?
Bolts: 300(.03) = $9
Office Furniture: 300(.02) = $6
B
From
B
F
To
F
 .03 .04 


 .02 .05 
The Leontief Input-Output Method, Part 1
Example 2: If the company receives an order
for $400 worth of bolts, what value of bolts
must it produce to fill the order?
B
From
B
F
To
F
 .03 .04 


 .02 .05 
The Leontief Input-Output Method, Part 1
Example 2: If the company receives an order
for $400 worth of bolts, what value of bolts
must it produce to fill the order?
400 = P - .03P = .97P
P = $412.37
B
From
B
F
To
F
 .03 .04 


 .02 .05 
The Leontief Input-Output Method, Part 1
Exercise 1:
Total
Production
Units
500
900
Units Used
Internally
.05(500) =
Units for External
Sales
500 - .05(500) =
100
250
2,375
7,125
P