energy management: 2014/2015 energy analysis: input-output class # 5 prof. tânia sousa...

Energy Management: 2014/2015

Energy Analysis: Input-OutputClass # 5

Prof. Tânia [email protected]

Input-Output Analysis: Motivation

• Energy is needed in all production processes• Different products have different embodied energies

or specific energy consumptions – How can we compute these?


• Energy is needed in all production processes• Process Analysis Methodology

– To compute embodied energies or specific energy consumptions of different products

– To compute the impact of energy efficiency measures in the specific energy consumptions of a product

• Input-Output Methodology


• Energy is needed in all production processes• Process Analysis Methodology

– To compute embodied energies or specific energy consumptions of different products

– To compute the impact of energy efficiency measures in the specific energy consumptions of a product

• Input-Output Methodology– To compute the embodied energies for all products/sectors in

an economy simultaneously (no need to consider specific consumption of inputs equal to zero)

– To compute the impact of energy efficiency measures across the economy


• Input-Output Methodology– To compute energy needs for different economic scenarios

because it allow us to build scenarios for the economy in a consistent way


• Building a scenario for the economy in a consistent way is difficult because of the interdependence within the economic system


• Building a scenario for the economy in a consistent way is difficult because of the interdependence within the economic system– a change in demand of a product has direct and indirect

effects that are hard to quantify – Example:

– To increase the output of chemical industry there is a direct & indirect (electr. & refined oil products) increase in demand for coal

Chemical Industry Power Plant

Coal Mine

Refinery


• Portuguese Scenarios for 2050: http://www.cenariosportugal.com/

Input-Output Analysis: Basics

• Input-Output Technique– A tool to estimate (empirically) the direct and indirect change

in demand for inputs (e.g. energy) resulting from a change in demand of the final good

– Developed by Wassily Leontief in 1936and applied to US national accounts inthe 40’s

– It is based on an Input-output table which is a matrix whose entries represent:

• the transactions occurring during 1 year between all sectors;• the transactions between sectors and final demand;• factor payments and imports.

Input-Output Portugal

• Input-Output matrix Portugal (2008)

PRODUCTS (CPA*64) R01 R02 R03 RB R10_12

R01 Products of agriculture, hunting and related services 954,9 18,4 0,0 0,0 4275,2

R02 Products of forestry, logging and related services 0,0 103,4 0,0 0,0 0,0

R03Fish and other fishing products; aquaculture products; support services to fishing

0,0 0,0 38,4 0,0 40,5

RB Mining and quarrying 0,5 0,0 0,0 152,7 10,6

R10_12 Food products, beverages and tobacco products 1284,7 0,1 3,9 1,1 3012,0

R13_15 Textiles, wearing apparel and leather products 21,1 0,0 4,0 5,3 1,2

R16Wood and of products of wood and cork, except furniture; articles of straw and plaiting materials

30,4 0,0 0,0 1,8 58,5

R17 Paper and paper products 8,2 0,0 1,3 2,2 304,3

R18 Printing and recording services 4,0 0,3 1,8 4,3 49,5

R19 Coke and refined petroleum products 224,8 14,3 38,6 144,3 99,4

R20 Chemicals and chemical products 225,9 10,2 0,8 31,8 106,5

R21 Basic pharmaceutical products and pharmaceutical preparations 6,3 0,0 0,0 0,1 12,1

Input-Output Portugal

• DPP (Departamento de Prospectiva e Planeamento e Relações Internacionais) that belongs to the MAOT developed an input-output model MODEM1 which has been used to evaluate the macroeconomic, sectorial and regional impacts of public policies

• O DPP has online the input-output matrix for 2008 with 64 64 sectors

• World Input-Output Database for some countries from 1995 onwards: http://www.wiod.org/database/nat_suts.htm

http://www.wiod.org/database/nat_suts.htm

http://www.wiod.org/database/nat_suts.htm

Input-Output: Basics

For the “Tire Factory”

Output from sector 1 to sector 2 Output from sector 1 to final demand

Total Production from sector 1

Tire Factory

Automobile Factory

Individual Consumers


For the “Tire Factory”

x1= z11+ z12+… + z1n+ f1

Output from sector 1 to sector 2 Output from sector 1 to final demand

Total Production from sector 1

Tire Factory

Automobile Factory



For the Electricity Sector:

xi= zi1+ zi2+… + zii+… + zin+ fi




Output from sector i to sector 2

Output from sector i to final demand

Total production from sector i

Electricity Sector

Automobile Factory








Electricity Sector

Automobile Factory


What is the meaning of this?







Electricity Sector

Automobile Factory


Electricity consumed within the electricity sector: hydraulic pumping & electric consumption at the power plants & losses in distribution


For all sectors:

zij is sales (ouput) from sector i to (input in) sector j (in ? units)

fi is final demand for sector i (in ? units)

xi is total output for sector i (in ? units)


For all sectors:

zij is sales (ouput) from sector i to (input in) sector j (in money units)

fi is final demand for sector i (in money units)

xi is total output for sector i (in money units)

• The common unit in which all these inputs & outputs can be measured is money

• Matrix form?

1 11 12 1

2 21 22 2

1 2

...

...

...n n n n

x z z f

x z z f

x z z f


For all sectors:

1 11 12 1

2 21 22 2

1 2

...

...

...n n n n

x z z f

x z z f

x z z f

x Zi f

i is a column vector of 1´s with the correct dimensionLower case bold letters for column vectorsUpper case bold letters for matrices

vector of sector output

vector of final demand

matrix with intersectorial transactions

x

f

Z

Input-Output: Matrix A of technical coefficients

Let’s define:

• What is the meaning of aij?zij is sales (ouput) from sector i to (input in) sector j

xj is total output for sector j

ijij

j

za

x


Let’s define:

• The meaning of aij:– aij input from sector i (in money) required to produce one

unit (in money) of the product in sector j– aij are the transaction or technical coefficients

ijij

j

za

x


Rewritting the system of equations using aij:

ijij

j

za

x

1 11 12 1

2 21 22 2

1 2

...

...

...n n n n

x z z f

x z z f

x z z f



• How can it be written in a matrix form?

ijij

j

za

x

1 11 1 12 2 1

2 21 1 22 2 2

1 1 2 2

...

...

...n n n n

x a x a x f

x a x a x f

x a x a x f

1 11 12 1

2 21 22 2

1 2

...

...

...n n n n

x z z f

x z z f

x z z f



matrix of technical coefficients

x

f

A



• In a matrix form:

x Ax f

1 11 12 1

2 21 22 2

1 2

...

...

...n n n n

x z z f

x z z f

x z z f

ijij

j

za

x

1 11 1 12 2 1

2 21 1 22 2 2

1 1 2 2

...

...

...n n n n

x a x a x f

x a x a x f

x a x a x f




x

f

A x Zi f


• The meaning of matrix of technical coefficients A:



– What is the meaning of this column?

1 11 12 1 1 1

2 21 22 2 2

1 2

...

... ...

... ... ... ... ... ... ...

...

n

n n n nn n n

x a a a x f

x a a x f

x a a a x f

ijij

j

za

x

1 11 1 12 2 1

2 21 1 22 2 2

1 1 2 2

...

...

...n n n n

x a x a x f

x a x a x f

x a x a x f



– Column i represents the inputs to sector iInputs to sector 1

1 11 12 1 1 1

2 21 22 2 2

1 2

...

... ...

... ... ... ... ... ... ...

...

n

n n n nn n n

x a a a x f

x a a x f

x a a a x f

ijij

j

za

x

1 11 1 12 2 1

2 21 1 22 2 2

1 1 2 2

...

...

...n n n n

x a x a x f

x a x a x f

x a x a x f



– Column i represents the inputs to sector i– The sector i produces goods according to a fixed production

function (recipe)• Sector 1 produces X1 units (money) using a11X1 units of sector 1, a21X1

units of sector 2, … , an1X1 units of sector n

• Sector 1 produces 1 units (money) using a11 units of sector 1, a21 units of sector 2, … , an1 units of sector n

Inputs to sector 1

1 11 12 1 1 1

2 21 22 2 2

1 2

...

... ...

... ... ... ... ... ... ...

...

n

n n n nn n n

x a a a x f

x a a x f

x a a a x f

ijij

j

za

x

1 11 1 12 2 1

2 21 1 22 2 2

1 1 2 2

...

...

...n n n n

x a x a x f

x a x a x f

x a x a x f

Production Functions: a review

• Production functions specify the output x of a factory, industry, sector or economy as a function of inputs z1, z2, …:

• Examples:

– Produces x units using z1 units of sector 1, z2 units of sector 2, … , zn units of sector n

1 2( , ,...)x f z z

1 2 ....b cx az z

1 2 ....x a bz cz

Cobb-Douglas Production Function

Linear Production Function

1 2( , ,...)x z z


• Production functions specify the output x of a factory, industry or economy as a function of inputs z1, z2, …:

• Examples:

• Which of these productions functions allow for substitution between production factors?



1 2( , ,...)x f z z

1 2 ....b cx az z

1 2 ....x a bz cz



• Examples:

• Which of these productions functions allow for substitution between production factors?• Cobb-Douglas and Linear production functions



1 2( , ,...)x f z z

1 2 ....b cx az z

1 2 ....x a bz cz

11 2 1 2

2

0.8 with 1 0.2bz

x a bz cz a b z c dz dcz



• Examples:

• Which of these productions functions allow for scale economies?



1 2( , ,...)x f z z

1 2 ....b cx az z

1 2 ....x a bz cz



• Examples:

• Which of these productions functions allow for scale economies?• Cobb-Douglas (if b+c >1)



1 2( , ,...)x f z z

1 2 ....b cx az z

1 2 ....x a bz cz

1 2 1 22 2 2 2 2 if 1b c b cb c b ca z z a z z x x b c

1 11 12 1 1 1

2 21 22 2 2

1 2

...

... ...

... ... ... ... ... ... ...

...

n

n n n nn n n

x a a a x f

x a a x f

x a a a x f



– Production function assumed in the Input-Output Technique• Sector 1 produces X11 units (money) using X1 a11 units of sector 1, X1

a21 units of sector 2, … , X1 an1 units of sector n

• Is there substitution between production factors?• Are scale economies possible?

Inputs to sector 1

1 11 1 12 2 1

2 21 1 22 2 2

1 1 2 2

...

...

...n n n n

x a x a x f

x a x a x f

x a x a x f

ijij

j

za

x

1 11 12 1 1 1

2 21 22 2 2

1 2

...

... ...

... ... ... ... ... ... ...

...

n

n n n nn n n

x a a a x f

x a a x f

x a a a x f





• Leontief which does 1) not allow for substitution between production factors and 2) not allow for scale economies

Inputs to sector 1

Leontief Production Function

1 11 1 12 2 1

2 21 1 22 2 2

1 1 2 2

...

...

...n n n n

x a x a x f

x a x a x f

x a x a x f

ijij

j

za

x

1 11 11 21 21min , ,....x z a z a





• Leontief which does not allow for 1) substitution between production factors or 2) scale economies

• Matrix A is valid only for short periods (~5 years)

Inputs to sector 1

1 11 12 1 1 1

2 21 22 2 2

1 2

...

... ...

... ... ... ... ... ... ...

...

n

n n n nn n n

x a a a x f

x a a x f

x a a a x f

1 11 1 12 2 1

2 21 1 22 2 2

1 1 2 2

...

...

...n n n n

x a x a x f

x a x a x f

x a x a x f

ijij

j

za

x

• Intermediate inputs: intersector and intrasector inputs

• Final Demand: exports & consumption from households and government & investment

Input-Output Analysis: The model

• The input-ouput model

IntermediateInputs

(square matrix)

Fina

l Dem

and

Tota

l out

put

Outputs

Inpu

ts

Sectors

Sec

tors

Z

ij ij jz a x f x



• Primary inputs: payments (wages, rents, interest) for primary factors of production (labour, land, capital) & taxes & imports



IntermediateInputs

(square matrix)

Primary Inputs

Fina

l Dem

and

Tota

l out

put

Outputs

Inpu

ts

Sectors

Sec

tors

Z

ij ij jz a x f x






IntermediateInputs

(square matrix)

Primary Inputs

Total Inputs or Total Costs

Fina

l Dem

and

Tota

l out

put

Outputs

Inpu

ts

Sectors

Sec

tors

Z

ij ij jz a x f x

pi



IntermediateInputs

(square matrix)

Primary Inputs


Fina

l Dem

and

Tota

l out

put

Outputs

Inpu

ts

Sectors

Sec

tors

1 1

1 1

n n

ij i i ij jj i

n n

ij i i i i ij j jj i

z f x z pi

z c g e inv z av i

xf

Z

pi



Lines & columns are related by:

IntermediateInputs

(square matrix)

Primary Inputs


Fina

l Dem

and

Tota

l out

put

Outputs

Inpu

ts

Sectors

Sec

tors

xf

Z

pi

´ Zi f pi i Z

Ax f x

1ˆ

Ax Zi

A Zx

1 1

1 1

n n

ij i i ij jj i

n n

ij i i i i ij j jj i

z f x z pi

z c g e inv z av i

Input-Output Analysis: Leontief inverse matrix

• How to relate final demand to production?

Ax f x vector of sector output



x

f

A



• is useful for which types of questions?

1

Ax f x

f x Ax

f I A x

I A f x

Lf x

1




Leontief inverse matrix

x

f

A

I A

x Lf



• is useful for which types of questions?– If final demand in sector i, fi, (e.g. agriculture) is to increase

10% next year how much output from each of the sectors would be necessary to supply this final demand?

1

Ax f x

f x Ax

f I A x

I A f x

Lf x

1




Leontief inverse matrix

x

f

A

I A

x Lf

Input-Output Analysis: Leontief inverse or total requirements matrix

Direct effectscars for final demand

1st Indirect effectsintersectorial needs to produce these cars

2nd Indirect effectsintersectorial needs to produce the following intersectorial needs


• Leontief inverse matrix which can be obtained as:

• Total Output is:

– If accounts for the final demand in total output (e.g. cars consumed by households) – direct effects

– Af accounts for the intersectorial needs to produce If (e.g. steel to produce the cars) – 1st indirect effects

– A[Af] accounts for the intersectorial needs to produce Af (e.g. coal to produce the steel) – 2nd indirect effects

1 2 3 ... x I A f I A A A f

1 2 3

0

... j

j

I A I A A A A


• Impacts in output from marginal increases in final demand from f to fnew:

1 1 11 1 1 1

1

1 11 1 1

1

...

... ... ... ... ...

...

...

... ... ... ... ...

...

new new

n

n n n nn n n

n

n n nn n

x x l l f f

x x l l f f

x l l f

x l l f

x Lf

x L f

Input-Output: Multipliers

• Total output is:

1 11 1 1

1

...

... ... ... ... ...

...

n

n n nn n

x l l f

x l l f

x Lf1 11 1 12 2

1 1 2 2

...

...n n n

x l f l f

x l f l f

iij

j

xl

f

If sector 1 is paints and sector 2 is cars what is the meaning of l12?



1 11 1 1

1

...

... ... ... ... ...

...

n

n n nn n

x l l f

x l l f

x Lf1 11 1 12 2

1 1 2 2

...

...n n n

x l f l f

x l f l f

iij

j

xl

f

Total production of paints

Production of paints required directly and indirectly for 1 unit of final demand of cars



– lij represents the production of good i, xi, that is directly and indirectly needed for each unit of final demand of good j, fj

– What about lii?

x1 needed for one unit of f2

xn needed for one unit of f1

1 11 1 1

1

...

... ... ... ... ...

...

n

n n nn n

x l l f

x l l f

x Lf1 11 1 12 2

1 1 2 2

...

...n n n

x l f l f

x l f l f

iij

j

xl

f




– lii > 1 represents the production of good i, xi, that is directly and indirectly needed for each unit of final demand of good i, fi



1 11 1 1

1

...

... ... ... ... ...

...

n

n n nn n

x l l f

x l l f

x Lf1 11 1 12 2

1 1 2 2

...

...n n n

x l f l f

x l f l f

iij

j

xl

f




– What is the meaning of the i column sum?



1 11 1 12 2

1 1 2 2

...

...n n n

x l f l f

x l f l f

iij

j

xl

f

1 11 1 1

1

...

... ... ... ... ...

...

n

n n nn n

x l l f

x l l f

x Lf




• Multiplier of sector i: the impact that an increase in final demand fi has on total production (not on GDP)



1 11 1 12 2

1 1 2 2

...

...n n n

x l f l f

x l f l f

iij

j

xl

f

1 11 1 1

1

...

... ... ... ... ...

...

n

n n nn n

x l l f

x l l f

x Lf


• Multipliers change over time and over regions because they depend on:– the economy structure, size, the way exports and sectors are

linked to each other and technology

1 11 1 1

1

...

... ... ... ... ...

...

n

n n nn n

x l l f

x l l f

x Lf


• Multipliers change over time and over regions because they depend on:– the economy structure, size, the way exports and sectors are

linked to each other and technology

• Where do you expect the multiplier of the wind energy sector to be higher: in a country that imports the wind turbines or in a country that develops and produces wind turbines?

1 11 1 1

1

...

... ... ... ... ...

...

n

n n nn n

x l l f

x l l f

x Lf

• Considere the following Economy:

Exercise


Exercise

• Considere the following Economy:

• Compute the matrix A of the technical coeficients:

Sales of Agric. to Indus. orInputs from Agriculture to Industry

Exercise

• Matrix of technical coefficients:

ijij

j

za

x


Exercise


• What happens to the matrix of technical coefficients with time? Why?

The amount of agriculture products (in money) needed to produce 1 unit worth of industry products

ijij

j

za

x

Exercise


• Compute the Leontief inverse matrix:

ijij

j

Za

X

1

0,

j

j

I A A

Exercise



1

0,

j

j

I A A

What is the meaning of this?x1=l11f1+l12f2+… L i

ijj

xl

f

Exercise



1

0,

j

j

I A A

the quantity of agriculture products directly and indirectly needed for each unit of final demand of industry products

L

Exercise



1

0,

j

j

I A A

the quantity of agriculture products directly and indirectly needed for each unit of final demand of industry products

L

?

Exercise



1

0,

j

j

I A A

What is the meaning of this?x1=l11f1+l12f2+…x2=l21f1+l22f2+…x3=l31f1+l32f2+…

L

Exercise



1

0,

j

j

I A A

Multiplier of the industry sector: the total output needed for each unit of final demand of industrial products L

Exercise



1

0,

j

j

I A A

What is the sector whose increase in final demand has the highest impact on the production of the economy? L

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 Private Cons. Final Demand Final Demand

20 30 50 55

30 40 70 70

10 30 40 40

L

Exercise


agriculture, industry and services?

1

2

3

55 80.8

70 122

40 101.6

x

x

x

Initial x


20 30 50 55

30 40 70 70

10 30 40 40

x Lf

Exercise


agriculture, industry and services?

– What will be the new sales of industry to agriculture?

1

2

3

5 5.8

0 2

0 1.6

x

x

x


20 30 50 55

30 40 70 70

10 30 40 40

x Lf

Exercise

• If final demand in sector 1 (e.g. agriculture) is to increase 10% – What will be the new sales of industry to agriculture?

21 21 1 21.6z a x Initial z21=20



Input-Output Analysis: Primary Inputs


IntermediateInputs

(square matrix)

Primary Inputs

Inpu

ts

Sectors

Sec

tors

Z

pi

Input-Output: Primary Inputs

• Primary inputs:

• For the transactions between sectors we defined:

– The inputs of sector j per unit of production of sector i are assumed to be constant

11 1 12 2 11 12 1

21 22

1 1 2 2 1 2

... ... ...

... ... ... ... ... ...

... ... ... ... ... ... ... ...

... ... ...

n

n n n n nn

z x z x a a a

a a

z x z x a a a

A

1

1

´ ...

´ ...

n

n

va va

m m

va

m


• For the primary inputs we define the coefficients:

– 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:

– The inputs of sector j per unit of production of sector i are assumed to be constant

1 1 1

1 1 1

´ ... ...

´ ... ...

c n n c cn

c n n c cn

va x va x va va

m x m x m m

va

m

11 1 12 2 11 12 1

21 22

1 1 2 2 1 2

... ... ...

... ... ... ... ... ...

... ... ... ... ... ... ... ...

... ... ...

n

n n n n nn

z x z x a a a

a a

z x z x a a a

A




• How to compute new values for added value or imports?

1 1 1

1 1 1

´ ... ...

´ ... ...

c n n c cn

c n n c cn

va x va x va va

m x m x m m

va

m




• To compute new values for added value or imports:

1 1

...

newnewc

new

newcn n

va x

va x

va

1 1 1

1 1 1

´ ... ...

´ ... ...

c n n c cn

c n n c cn

va x va x va va

m x m x m m

va

m




• To compute new values for added value or imports:

1 1 1 10 0

... 0 ... 0 ...

0 0

new newc c

new new new

new newcn n cn n

new new

va x va x

va x va x

c c

c

va va x va Lf

m m Lf

1 1 1

1 1 1

´ ... ...

´ ... ...

c n n c cn

c n n c cn

va x va x va va

m x m x m m

va

m


• Relevance:GDP= Added Values

Final consumption Exports ImportsGDP

Exercise

• What is the new added value?

1

2

3

80.8

122

101.6

new

new

newx

x

x

Exercise

• What is the new added value?

• GDP increased by 3%

1 2 3

20 40 30; ;

75 120 10080.8

20 40 30122 92.69

75 120 100101.6

c c cva va va

va

Imports

A

C

B

20

5

30 3

5

2

6

2

5

95

65

150

120

500

Final Demand

Exercise

• Consider na economy based in 3 sectors, A, B e C.

• Write the matrix with the intersectorial flows and the input-output model.

• Which is the sector with the highest added value?

Exercise

• Matrix:

• Input- Output Model:

A B C

A 5 30 6

B 2 3 2

C 5 20 5

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

• Consider na economy based in 3 sectors, A, B e C.

• 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.

Imports

A

C

B

20

5

30 3

5

2

6

2

5

95

65

150

120

500

Final Demand

Exercise

Exercise

• Matrix:

• Input- Output Model:

• Matrix L=I+A

A B C

A 5 30 6

B 2 3 2

C 5 20 5

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

0.031 0.191 0.011 R= 1.031 0.191 0.011

0.012 0.019 0.004 0.012 1.019 0.004

0.031 0.127 0.009 0.031 0.127 1.009

1 im=IM i /X i = 0.404 0.000 0.179

1

1

L

Exercise

• For each vector of final demand we compute the change in total output and the change in imports:

PF={1,0,0} PF={0,1,0} PF={0,0,1}

X IM X IM X IM

1.031 0.416 0.191 0.000 0.011 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

x L f

0.031 0.191 0.011 R= 1.031 0.191 0.011

0.012 0.019 0.004 0.012 1.019 0.004

0.031 0.127 0.009 0.031 0.127 1.009

1 im=IM i /X i = 0.404 0.000 0.179

1

1

L

Ti

´ 1 0 0 f ´ 0 1 0 f ´ 0 0 1 f

c cm m x m L f

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


IntermediateInputs

(square matrix)

Primary Energy Inputs

Total Energy in Inputs

Embo

died

Ene

rgy

in

Fina

l Dem

and

Tota

l Ene

rgy

in o

utpu

ts

Outputs

Inpu

ts

Sectors

Sec

tors

=n×1 vector of embodied energy in final demandEf

=n×n matrix of intersectorial transactions of embodied energyEZ

=1×n vector of direct energy inputs

(embodied energy in primary inputs, e.g,

direct primary energy consumption &

embodied energy in imports )

Epi

´E E E E Z i f pi i Z



Direct Energy Use

A

C

B Final Demand



Direct Energy Use

A

C

B Final Demand

1 11 1 12 1 13 1 1

2 21 2 22 2 23 2 2

3 31 3 32 3 33 3 3

1 1 1A A

B B

C C

E CE m CE m CE m CE m S





• We can compute the embodied energy intensities for all sectors CEi because we have n equations with n unknowns

Direct Energy Use

A

C

B Final Demand

1 11 1 12 1 13 1 1

2 21 2 22 2 23 2 2

3 31 3 32 3 33 3 3

1 1 1A A

B B

C C




Input-Output Analysis

• To compute embodied “something”, e.g., energy or CO2, that is distributed with productive mass flows use:– x is the vector with specific embodied “CO2” for all outputs

assuming that outputs from the same operation have the same specific embodied value

– f is the vector with specific direct emissions of “CO2” for each operation

– S is the diagonal matrix with the residue formation factors for each operation

– A is 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

•

– Nº equations: 7– Nº unknonws: 7

•

1ˆ ´ S A x f x


• Direct and indirect carbon emissions


• Embodied energy intensity, CEi, in outputs from sector i is constant, i.e.,

• Sector 1 receives (direct + indirect) energy which is distributed to its intended output m1S1

11 1

21

1

1 11 1 1

2 21

1

... ...

... ... ... ...1 1 ... 1

... ... ... ... ...

... ...

... ...

... ... ... ...1 1 ... 1

... ... ... ... ...

... ...

E EA n

E

E En n nn

A n

n n n n nn

pi z z

z

pi z z

pi CE m CE m

CE m

pi CE m CE m

1 1

2 2

...

A

B

n n n

CE m S

CE m S

CE m S

´E E E E E Z i f pi i Z x


• Simplifying per unit of mass:

1 1 1 1 1 1 11 1 1

1

1 ... 0 0 1 ... 0 0 ... ...1

0 ... ... ... ... 0 ... ... ... ... ... ... ...1

0 0 ... ... ... 0 0 ... ... ... ... ... ......

0 ... ... 1 0 ... ... 1 ... .1

T

n

n n n n n n n

m S PI m S CE m CE m

m S PI m S CE m

1

2

...

.. n nn n

CE

CE

CE m CE

1,11 1 1 1 1

2,2 2

,1 1

... ...

... ... ... ...

...... ... ... ... ... ...

... ...

T

dirn n

dir

n dirn nn n n n

CEf S f S CE CE

CECE CE

CEf S f S CE CE

1 11 1 1 1 1 1 1

2

1

1 ... 0 0 ... ...

0 ... ... ... ... ... ... ... ... ...

0 0 ... ... ... ... ... ... ... ... ...

0 ... ... 1 ... ...

T

n

n n nn n n n n n

S f f CE PI m S CE

CE

S f f CE PI m S CE



• 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

1,11 1 1 1 1

2,2 2

,1 1

... ...

... ... ... ...

...... ... ... ... ... ...

... ...

T

dirn n

dir

n dirn nn n n n

CEf S f S CE CE

CECE CE

CEf S f S CE CE

1, 1 1 1

2,

,

...

... ...

dir

dir

n dir n n n

CE pi m S

CE

CE pi m S



• We can compute the change in embodied energy intensities for all sectors with the change in direct energy intensities

1,11 1 1 1 1

2,2 2

,1 1

... ...

... ... ... ...

...... ... ... ... ... ...

... ...

T

dirn n

dir

n dirn nn n n n

CEf S f S CE CE

CECE CE

CEf S f S CE CE

1

´

´

dir

dir dir

dir

A* ce ce ce

ce I A* ce L*ce

ce L* ce

x Ax f

x Lf

x L f1ˆ´ ´A* ce S A ce

energy management: 2014/2015 energy analysis: input-output class # 5 prof. tânia sousa...

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