Transcript Project Control - EIO-LCA

Building an IO Model
Form Input-Output Transactions Table
which represents the flow of purchases
between sectors.
 Constructed from ‘Make’ and ‘Use’ Table
Data – purchases and sales of particular
sectors.

Building an IO Model
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
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Sum of Value Added (non-interindustry
purchases) and Final Demand is GDP.
Transactions include intermediate product
purchases and row sum to Total Demand.
From the IO Transactions table, form the
Technical Requirements matrix by dividing
each column by total sector input – matrix D.
Entries represent direct inter-industry
purchases per dollar of output.
Transactions Table
Input to sectors
Output from sectors
1
2
3
n
Intermediate input I
Value added V
Total input X
1
X11
X21
X31
Xn1
I1
V1
X1
2
X12
X22
X32
Xn2
I2
V2
X2
3
X13
X23
X33
Xn3
I3
V3
X3
Xi = Xj;
 Xij + Fi = Xi;
 (Aij*Xj) + Fi = Xi
Final
demand F
Total
output X
O1
O2
O3
On
F1
F2
F3
Fn
X1
X2
X3
Xn
using Aij = Xij / Xj
in vector/matrix notation:
A*X + F = X =>
n
X1n
X2n
X3n
Xnn
In
Vn
Xn
Intermediate
output O
F = [I - A]*X
or X = [I - A]-1*F
GDP
Two Sector Numerical Example
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Reading across: Sector 1
provides $150 of output to
sector 1, $500 of output to
sector 2, and $350 of output
to consumers.
Reading down: Sector 1
purchases $150 of output
from sector 1, $200 of output
from sector 2, and adds
$650 of value to produce its
output
Transaction Flows ($) are at
right.
1
2
1 150
Final
Demand
500
350
2 200
100
1700
Value 650 1400
Added
2050
Complete Transactions Matrix
Sector 1 Sector 2 Final
Total
Demand Output
Sector 1
150
500
350
1000
Sector 2
200
100
1700
Value
Added
Total
Input
650
1400
GDP
2050
1000
2000
2000
Requirements Matrix
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Creating the A matrix
Aij = Xij / Xj
Sector 1 Sector 2
So, to make $1 of
output from sector 1 Sector 1 150/1000 500/2000
= 0.15
= .25
requires $0.15 of
output from the same
Sector 2 200/1000 100/2000
sector.
= 0.2
= .05
Production of Good 1 in our
Two Sector Model
$ 0.15/$ Good 1
$ 1 Good 1
Sector 1
$0.2/$ Good 2
Sector 2
To produce $1 of output from sector
one requires $0.15 of goods from the
sector itself, plus $0.2 of goods from
sector 2.
Production of Good 2 in our
Two Sector Model
Sector 1
To produce $1 of output from sector
two requires $0.05 of goods from the
sector itself, plus $0.25 of goods from
sector 1.
$0.25/$ Good 2
$ 0.05/$ Good 2
Sector 2
$ 1 Good 2
Leontief Inverse

[I – A]

[I – A]
1 0
0.15 0.25
0.85  0.25


0 1
0.20 0.05
 0.20 0.95
-1
or X = [I - A]-1*F
0.85  0.25
 0.20 0.95
1
1.254 0.33

0.264 1.122
Add Final Demand
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Determine the effects of
$100 additional demand
from Sector 1
X = [I – A] -1 F
Total Outputs: $125.4 of
Sector 1 and $26.4 of
Sector 2, or $ 151.8 Total.
Direct intermediate inputs:
$15 of 1 and $20 of 2 for
$100 output of 1 (or $ 135)
X
X
1.254 0.33
100
0.264 1.122
125.4
0
26.4
Add Environmental Effects

Add sector-level environmental impact
coefficient matrices (R)
» [effect/$ output from sector]
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Example: Hazardous Waste Generation (R)
» R1 = 100 grams/$ in Sector 1
» R2 = 5 grams/$ in Sector 2
Production of Waste in our
Two Sector Model
$ 0.15/$ Good 1
$ 1 Good 1
Sector 1
Haz. Waste 100 gm/$ Good 1
$0.2/$ Good 2
Haz Waste 5 gm/$ Good 2
Sector 2
Production of Waste in our
Two Sector Model
Sector 1
Haz. Waste 100 gm/$ Good 1
$0.25/$ Good 2
$ 0.05/$ Good 2
Haz Waste 5 gm/$ Good 2
Sector 2
$ 1 Good 2
Production of Waste in our
Two Sector Model
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B = R*X
12,540 grams of
hazardous waste
generated by sector 1
132 grams of
hazardous waste
generated by sector 2
Total of 12672 grams
hazardous waste
generated
100 0
R
0 5

125.4
X
26.4
100 0 125.4
12540
B

0 5 26.4
132
