Download Primary Inputs

Gestão de Sistemas Energéticos
2015/2016
Energy Analysis: Input-Output
Prof. Tânia Sousa
[email protected]
Exercise
• Considere the following Economy:
What is the meaning of this?
Exercise
• Considere the following Economy:
Sales of Agric. to Indus. or
Inputs from Agriculture to
Industry
• Compute the matrix A of the technical coeficients:
Exercise
• Matrix of technical coefficients:
What is the meaning of this?
aij 
zij
xj
Exercise
• Matrix of technical coefficients:
aij 
zij
xj
The amount of agriculture products (in money)
needed to produce 1 unit worth of industry products
• What happens to the matrix of technical coefficients
with time? Why?
Exercise
• Matrix of technical coefficients:
aij 
• Compute the Leontief inverse matrix:
I  A
1


j 0,
Aj
Z ij
Xj
Exercise
• Matrix of technical coefficients:
I  A
1


Aj
j 0,
• Compute the Leontief inverse matrix:
 L
What is the meaning of this?
x1=l11f1+l12f2+…
xi
lij 
f j
Exercise
• Matrix of technical coefficients:
 I  A
1


Aj
j 0,
• Compute the Leontief inverse matrix:
 L
the quantity of agriculture products
directly and indirectly needed for each
unit of final demand of industry products
Exercise
• Matrix of technical coefficients:
?
 I  A
1


Aj
j 0,
• Compute the Leontief inverse matrix:
 L
the quantity of agriculture products
directly and indirectly needed for each
unit of final demand of industry products
Exercise
• Matrix of technical coefficients:
 I  A
1


Aj
j 0,
• Compute the Leontief inverse matrix:
 L
What is the meaning of this?
x1=l11f1+l12f2+…
x2=l21f1+l22f2+…
x3=l31f1+l32f2+…
Exercise
• Matrix of technical coefficients:
 I  A
1


Aj
j 0,
• Compute the Leontief inverse matrix:
 L
Multiplier of the industry sector: the total
output needed for each unit of final
demand of industrial products
Exercise
• Matrix of technical coefficients:
 I  A
1


Aj
j 0,
• Compute the Leontief inverse matrix:
 L
What is the sector whose increase in
final demand has the highest impact on
the production of the economy?
Exercise
• If final demand in sector 1 (e.g. agriculture) is to
increase 10%
– What will be necessary changes in the total outputs of
agriculture, industry and services?
x  Lf
 Exports
 20

30

10
 L 
Private Cons.  Final Demand   Final Demand 
 
 

30
50
55



 
 

40
70
70
 
 

30
40
40
 
 

Exercise
• If final demand in sector 1 (e.g. agriculture) is to
increase 10%
– What will be necessary changes in the total outputs of
agriculture, industry and services?
x  Lf
 Exports
 20

30

10
 x1 
x  
 2
 x3 
Private Cons.  Final Demand   Final Demand 
 
 

30
50
55



 
 

40
70
70
 
 

30
40
40
 
 

55   80.8 
70    122 
  

 40 101.6
Initial x
Exercise
• If final demand in sector 1 (e.g. agriculture) is to
increase 10%
– What will be necessary changes in the total outputs of
agriculture, industry and services?
x  Lf
 Exports
 20

30

10
 x1 
 x  
 2
 x3 
Private Cons.  Final Demand   Final Demand 
 
 

30
50
55



 
 

40
70
70
 
 

30
40
40
 
 

5 5.8
0    2 
   
0 1.6 
– What will be the new sales of industry to agriculture?
Exercise
• If final demand in sector 1 (e.g. agriculture) is to
increase 10%
– What will be the new sales of industry to agriculture?
z21  a21 x1  21.6
Initial z21=20
Input-Output Analysis: Primary Inputs
• The input-ouput model
•
Z
Inputs
Sectors
Sectors
Intermediate
Inputs
•
(square matrix)
Primary Inputs
pi
Intermediate inputs: intersector
and intrasector inputs
Primary inputs: payments (wages,
rents, interest) for primary factors
of production (labour, land,
capital) & taxes & imports
Input-Output: Primary Inputs
• Primary inputs:
va´  va1 ... van 
m´  m1 ... mn 
• For the transactions between sectors we defined:
 z11 x1 z12 x2 ... ...  a11 a12 ... a1n 
 ...
...
... ...  a21 a22 ... ... 


A
...
... ...  ... ... ... ... 
 ...

 

z
x
z
x
...
...
a
a
...
a
n2
nn 
 n1 1 n 2 2
  n1
– The inputs of sector j per unit of production of sector i are
assumed to be constant
Input-Output: Primary Inputs
• For the primary inputs we define the coefficients:
va´c   va1 x1 ... van xn    vac1 ... vacn 
m´c   m1 x1 ... mn xn    mc1 ... mcn 
– The added value of sector j per unit of production or imports
of sector j per unit of production are assumed to be constant
• For the transactions between sectors we defined:
 z11 x1
 ...
A
 ...

 zn1 x1
z12 x2
...
...
zn 2 x2
...
...
...
...
...  a11 a12
...  a21 a22

...  ... ...
 
...  an1 an 2
... a1n 
... ... 

... ... 

... ann 
Input-Output: Primary Inputs
• For the primary inputs we define the coefficients:
va´c   va1 x1 ... van xn   vac1 ... vacn 
m´c   m1 x1 ... mn xn    mc1 ... mcn 
– The added value of sector j per unit of production or imports
of sector j per unit of production are assumed to be constant
• How to compute new values for added value or
imports?
Input-Output: Primary Inputs
• For the primary inputs we define the coefficients:
va´c   va1 x1 ... van xn   vac1 ... vacn 
m´c   m1 x1 ... mn xn    mc1 ... mcn 
– The added value of sector j per unit of production or imports
of sector j per unit of production are assumed to be constant
• To compute new values for added value or imports:
 va x 


  ... 
vacn xn new 


new
c1 1
va new
new
Input-Output: Primary Inputs
• For the primary inputs we define the coefficients:
va´c   va1 x1 ... van xn   vac1 ... vacn 
m´c   m1 x1 ... mn xn    mc1 ... mcn 
– The added value of sector j per unit of production or imports
of sector j per unit of production are assumed to be constant
• To compute new values for added value or imports:
va new
 vac1 x1new  vac1 0
0   x1new 




  ...    0 ... 0   ...   vac x new  vac Lf new


new
new
vacn xn   0


0
va
x

cn   n



m new  m c Lf new
Input-Output: Primary Inputs
• Relevance:
GDP=  Added Values
GDP   Final consumption   Exports   Imports
Exercise
• What is the new added value?
 x1new   80.8 
 new  

 x2    122 
 new  101.6

 x3  
Exercise
• What is the new added value?
20
40
30
vac1  ; vac 2 
; vac 3 
75
120
100
 80.8 
 20 40 30  
  92.69
va

122
  75 120 100   
101.6 
• GDP increased by 3%
Exercise
• Consider na economy based in 3 sectors, A, B e C.
5
120
65
A
2
30
Imports
5
3
Final Demand
6
B
150
20
2
95
C
500
5
• Write the matrix with the intersectorial flows and the
input-output model.
• Which is the sector with the highest added value?
Exercise
• Matrix:
A
B
C
A
5
30
6
B
2
3
2
C
5
20
5
• Input- Output Model:
A
B
C
P. Final
Total
A
5
30
6
120
161
B
2
3
2
150
157
C
5
20
5
500
530
Importação
65
0
95
Valor acrescentado
84
104
422
Total
161
157
530
Exercise
• Consider na economy based in 3 sectors, A, B e C.
5
120
65
A
2
30
Imports
5
3
Final Demand
6
B
150
20
2
95
C
500
5
• Write the matrix with the intersectorial flows.
• Which is the sector with the highest added value?
• Assuming that L=(I-A)-1=I+A, determine the sector that
has to import more to satisfy his own final demand.
Exercise
• Matrix:
A
B
C
A
5
30
6
B
2
3
2
C
5
20
5
• Input- Output Model:
A
B
C
P. Final
Total
A
5
30
6
120
161
B
2
3
2
150
157
C
5
20
5
500
530
Importação
65
0
95
Valor acrescentado
84
104
422
Total
161
157
530
• Matrix L=I+A
0.031
0.191
0.011
0.012
0.019
0.031
0.127
 LR=
1.031
0.191
0.011
0.004
0.012
1.019
0.004
0.009
0.031
0.127
1.009
0.404
0.000
0.179
1
im=IM i /X i =
1
1
Exercise
• For each vector of final demand we compute the
change in total output and the change in imports:
x  Lf
m  m c x  m c Lf
0.031
0.191
0.011
0.012
0.019
0.031
0.127
 LR=
1.031
0.191
0.011
0.004
0.012
1.019
0.004
0.009
0.031
0.127
1.009
0.404
0.000
0.179
iT
1
im=IM i /X i =
1
1
PF={1,0,0}
f ´ 1 0 0 PF={0,1,0}
f ´  0 1 0 PF={0,0,1}
f ´  0 0 1
X
1.031
IM
0.416
X
0.191
IM
0.000
X
0.011
IM
0.005
0.012
0.000
1.019
0.000
0.004
0.000
0.031
0.006
0.127
0.000
1.009
0.181
Input-Output
• Application to the energy sector?
Input-Output
• Energy needs for different economic scenarios
– Using the input-output analysis to build a consistent
economic scenario and then combining that information with
the Energetic Balance
– Using the input-output analysis where one or more sectors
define the energy sector
– What about embodied energy?
Input-Output Analysis:
Embodied Energy
• The input-ouput model
f E =n×1 vector of embodied energy in final demand
Sectors
(square matrix)
Total Energy in outputs
Intermediate
Inputs
Embodied Energy in
Final Demand
Inputs
Sectors
Outputs
Z E i  f E  pi E  i´Z E
Z E =n×n matrix of intersectorial transactions of embodied energy
Primary Energy Inputs
Total Energy in Inputs
pi E =1×n vector of direct energy inputs
(direct primary energy consumption and
embodied energy in imports )
Input-Output Analysis:
Embodied Energy
• The input-ouput model
A
Direct Energy
Use
B
C
Z E i  f E  pi E  i´Z E
Final Demand
Input-Output Analysis:
Embodied Energy
• The input-ouput model
A
Direct Energy
Use
B
Final Demand
C
𝑬𝑨
𝑬𝑩 + 𝟏
𝑬𝑪
𝑪𝑬𝑶𝑨 𝒎𝑨𝑨
𝟏 𝟏 𝑪𝑬𝑶𝑩 𝒎𝑩𝑨
𝑪𝑬𝑶𝑪 𝒎𝑪𝑨
𝑪𝑬𝑶𝑨 𝒎𝑨𝑩
𝑪𝑬𝑶𝑩 𝒎𝑩𝑩
𝑪𝑬𝑶𝑪 𝒎𝑪𝑩
𝑪𝑬𝑶𝑨 𝒎𝑨𝑪
𝑪𝑬𝑶𝑨 𝒎𝑶𝑨 𝑺𝑨
𝑪𝑬𝑶𝑩 𝒎𝑩𝑪 = 𝑪𝑬𝑶𝑩 𝒎𝑶𝑩 𝑺𝑩
𝑪𝑬𝑶𝑪 𝒎𝑪𝑪
𝑪𝑬𝑶𝑪 𝒎𝑶𝑪 𝑺𝑪
Input-Output Analysis:
Embodied Energy
• The input-ouput model
A
Direct Energy
Use
B
Final Demand
C
𝑬𝑨
𝑬𝑩 + 𝟏
𝑬𝑪
𝑪𝑬𝑶𝑨 𝒎𝑨𝑨
𝟏 𝟏 𝑪𝑬𝑶𝑩 𝒎𝑩𝑨
𝑪𝑬𝑶𝑪 𝒎𝑪𝑨
𝑪𝑬𝑶𝑨 𝒎𝑨𝑩
𝑪𝑬𝑶𝑩 𝒎𝑩𝑩
𝑪𝑬𝑶𝑪 𝒎𝑪𝑩
𝑪𝑬𝑶𝑨 𝒎𝑨𝑪
𝑪𝑬𝑶𝑨 𝒎𝑶𝑨 𝑺𝑨
𝑪𝑬𝑶𝑩 𝒎𝑩𝑪 = 𝑪𝑬𝑶𝑩 𝒎𝑶𝑩 𝑺𝑩
𝑪𝑬𝑶𝑪 𝒎𝑪𝑪
𝑪𝑬𝑶𝑪 𝒎𝑶𝑪 𝑺𝑪
• We can compute the embodied energy intensities for
all sectors CEOi because we have n equations with n
unknowns
Input-Output Analysis
• Can be used to compute embodied “something”, e.g.,
energy or CO2, that is distributed with productive mass
flows knowing:
– (assuming) that outputs from the same operation have the
same specific embodied value
– the vector with specific direct emissions of “CO2” for each
operation
– the diagonal matrix with the residue formation factors for
each operation
– the matrix with the mass fractions
• There are things that should flow with monetary
values instead of mass flows
– Economic causality instead of physical causality
Input-Output Analysis:
Embodied CO2
• The input-ouput model
f E =n×1 vector of embodied CO2 in final demand
Sectors
(square matrix)
Total CO2 in outputs
Intermediate
Inputs
Embodied CO2 in
Final Demand
Inputs
Sectors
Outputs
Z E i  f E  pi E  i´Z E
Z E =n×n matrix of intersectorial transactions of embodied energy
Primary CO2 Inputs
Total CO2 in Inputs
pi E =1×n
(direct CO2 emissions &
embodied CO2 in imports )
Input-Output Analysis: Motivation
• Direct and indirect carbon emissions
Input-Output Analysis:
Embodied Energy
Z E i  f E  pi E  i´Z E  x E
• Embodied energy intensity, CEi, in outputs from sector i
is constant, i.e.,
 z E11 ...
 piA 
 E
 ... 
   1 1 ... 1  z 21 ...
 ... ...
 ... 
 E
 
 pin 
 z n1 ...
 piA 
 CE1m11
 ... 
CE m
   1 1 ... 1  2 21
 ... 
 ...
 

 pin 
CEn mn1
... z E1n 

... ... 

... ... 

... z E nn 
...
...
...
...
... CE1m1n 
 CE1m1S A 
CE m S 
...
... 
   2 2 B
 ...

...
... 



... CEn mnn 
 CEn mn S n 
• Sector 1 receives (direct + indirect) energy which is
distributed to its intended output m1S1
Input-Output Analysis:
Embodied Energy
• Simplifying per unit of mass:
1





m1S1 ... 0
0
... ...
0
0 ...
0
... ... 1
0   PI1  1
...   ...  


...   ...  

 
mn Sn   PI n  
0   f11
1 S1 ... 0
 0 ... ... ...   ...


 0
0 ... ...   ...


0
...
...
1
S
n   f n1

 f11 S1
 ...

 ...

 f n1 S1
...
...
...
...
...
...
...
...
...
...
...
...
f1n S n 
... 

... 

f nn S n 
T
...
...
...
...
m1S1 ... 0
0
... ...
0
0 ...
0
... ... 1
f1n 
... 

... 

f nn 
T
0  1
...   1 
 
...  ...
 
mn S n   1 
T
 CE1m11
 ...

 ...

CEn mn1
 CE1   PI1 m1S1 
 CE1 
 ...  

CE 
...


   2
 ...  

 ... 
...

 



CE
PI
m
S
CE
 n  n n n
 n
 CE1   CE1,dir   CE1 
CE  CE  CE 
 2    2,dir    2 
 ...   ...   ... 
 

 

CE
CE
CE
n
,
dir
n
n

 

 
...
...
...
...
... CE1m1n 
 CE1 
CE 
...
... 
   2
 ... 
...
... 



... CEn mnn 
CE
 n
Input-Output Analysis:
Embodied Energy
• Simplifying per unit of mass:
 f11 S1
 ...

 ...

 f n1 S1
...
...
...
...
...
...
...
...
f1n S n 
... 

... 

f nn S n 
T
 CE1   CE1,dir   CE1 
CE  CE  CE 
 2    2,dir    2 
 ...   ...   ... 
 

 

CE
CE
CE
n
,
dir
 n 
  n
 CE1,dir   pi1 m1S1 
CE  

...
 2,dir   

 ...  

...

 

CE
pi
m
S
n
,
dir

  n n n
• We can compute the embodied energy intensities for
all sectors CEi because we have n equations with n
unknowns
– We must know mass flows, residue formation factors and
direct energies intensities
Input-Output Analysis:
Embodied Energy
• Simplifying per unit of mass:
 f11 S1
 ...

 ...

 f n1 S1
...
...
...
...
...
...
...
...
f1n S n 
... 

... 

f nn S n 
T
 CE1   CE1,dir   CE1 
CE  CE  CE 
 2    2,dir    2 
 ...   ...   ... 
 

 

CE
CE
CE
n
,
dir
 n 
  n
• We can compute the change in embodied energy
intensities for all sectors with the change in direct
energy intensities
A *´ce  ce  ce
dir
x  Ax  f
x  Lf
x  Lf
ce   I  A *´ ce dir  L * ce dir
1
ce  L * ce dir
A *´ce  Sˆ 1A´ce