1. Gestão de Sistemas Energéticos 2015/2016
Energy Analysis: Input-Output
Prof. Tânia Sousa

2. 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?

3. Input-Output Analysis: Motivation
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

4. Input-Output Analysis: Motivation
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

5. Input-Output Analysis: Motivation
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

6. Input-Output Analysis: Motivation
Building a scenario for the economy in a consistent way is difficult because of the interdependence within the economic system

7. Input-Output Analysis: Motivation
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
Refinery
Power Plant
Chemical Industry
Coal Mine

8. Input-Output Analysis: Motivation
Portuguese Scenarios for 2050:

9. 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 1936 and applied to US national accounts in the 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.

10. Input-Output Portugal
Input-Output matrix Portugal (2008)
PRODUCTS (CPA*64)
R01
R02
R03 RB
R10_12
Products of agriculture, hunting and related services
954,9
18,4
0,0
4275,2
Products of forestry, logging and related services
103,4
Fish and other fishing products; aquaculture products; support services to fishing
38,4
40,5
Mining and quarrying
0,5
152,7
10,6
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
4,0
5,3
1,2
R16
Wood and of products of wood and cork, except furniture; articles of straw and plaiting materials
30,4
1,8
58,5
R17
Paper and paper products
8,2
1,3
2,2
304,3
R18
Printing and recording services
0,3
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
12,1

11. 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
Individual
Consumers
Tire Factory
Automobile
Factory

12. Input-Output: Basics 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
Individual
Consumers
Tire Factory
Automobile
Factory

13. Input-Output: Basics
For the Electricity Sector: xi= zi1+ zi2+… + zii+… + zin+ fi

14. Input-Output: Basics
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
Individual
Consumers
Electricity Sector
Automobile
Factory

15. Input-Output: Basics
What is the meaning of this?
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
Individual
Consumers
Electricity Sector
Automobile
Factory

16. Input-Output: Basics
Electricity consumed within the electricity sector: hydraulic pumping & electric consumption at the power plants & losses in distribution
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
Individual
Consumers
Electricity Sector
Automobile
Factory

17. Input-Output: Basics 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)

18. Input-Output: Basics 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?

19. Input-Output: Basics For all sectors:
i is a column vector of 1´s with the correct dimension
Lower case bold letters for column vectors
Upper case bold letters for matrices

20. 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

21. Input-Output: Matrix A of technical coefficients
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

22. Input-Output: Matrix A of technical coefficients
Rewritting the system of equations using aij:

23. Input-Output: Matrix A of technical coefficients
Rewritting the system of equations using aij:
How can it be written in a matrix form?

24. Input-Output: Matrix A of technical coefficients
Rewritting the system of equations using aij:
In a matrix form:

25. Input-Output: Matrix A of technical coefficients
The meaning of matrix of technical coefficients A:

26. Input-Output: Matrix A of technical coefficients
The meaning of matrix of technical coefficients A:
What is the meaning of this column?

27. Input-Output: Matrix A of technical coefficients
The meaning of matrix of technical coefficients A:
Column i represents the inputs to sector i
Inputs to sector 1

28. Input-Output: Matrix A of technical coefficients
The meaning of matrix of technical coefficients A:
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

29. 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
Cobb-Douglas Production Function
Linear Production Function

30. Production Functions: a review
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?
Cobb-Douglas Production Function
Linear Production Function

31. Production Functions: a review
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?
Cobb-Douglas and Linear production functions
Cobb-Douglas Production Function
Linear Production Function

32. Production Functions: a review
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 scale economies?
Cobb-Douglas Production Function
Linear Production Function

33. Production Functions: a review
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 scale economies?
Cobb-Douglas (if b+c >1)
Cobb-Douglas Production Function
Linear Production Function

34. Input-Output: Matrix A of technical coefficients
The meaning of matrix of technical coefficients A:
Production function assumed in the Input-Output Technique
Sector 1 produces X11 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

35. Input-Output: Matrix A of technical coefficients
The meaning of matrix of technical coefficients A:
Production function assumed in the Input-Output Technique
Sector 1 produces X11 units (money) using X1 a11 units of sector 1, X1 a21 units of sector 2, … , X1 an1 units of sector n
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

36. Input-Output: Matrix A of technical coefficients
The meaning of matrix of technical coefficients A:
Production function assumed in the Input-Output Technique
Sector 1 produces X11 units (money) using X1 a11 units of sector 1, X1 a21 units of sector 2, … , X1 an1 units of sector n
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

37. Input-Output Analysis: The model
Intermediate inputs: intersector and intrasector inputs
Final Demand: exports & consumption from households and government & investment
The input-ouput model
Intermediate
Inputs (square matrix)
Final Demand
Total output
Outputs
Inputs
Sectors

38. Input-Output Analysis: The model
Intermediate inputs: intersector and intrasector inputs
Final Demand: exports & consumption from households and government & investment
Primary inputs?
The input-ouput model
Intermediate
Inputs (square matrix)
Primary Inputs
Final Demand
Total output
Outputs
Inputs
Sectors

39. Input-Output Analysis: The model
Intermediate inputs: intersector and intrasector inputs
Final Demand: exports & consumption from households and government & investment
Primary inputs: payments (wages, rents, interest) for primary factors of production (labour, land, capital) & taxes & imports
The input-ouput model
Intermediate
Inputs (square matrix)
Primary Inputs
Final Demand
Total output
Outputs
Inputs
Sectors

40. Input-Output Analysis: The model
Intermediate inputs: intersector and intrasector inputs
Final Demand: exports & consumption from households and government & investment
Primary inputs: payments (wages, rents, interest) for primary factors of production (labour, land, capital) & taxes & imports
The input-ouput model
Intermediate
Inputs (square matrix)
Primary Inputs
Total Inputs or
Total Costs
Final Demand
Total output
Outputs
Inputs
Sectors

41. Input-Output Analysis: The model
The input-ouput model
Intermediate
Inputs (square matrix)
Primary Inputs
Total Inputs or
Total Costs
Final Demand
Total output
Outputs
Inputs
Sectors

42. Input-Output Analysis: The model
Lines & columns are related by:
The input-ouput model
Intermediate
Inputs (square matrix)
Primary Inputs
Total Inputs or
Total Costs
Final Demand
Total output
Outputs
Inputs
Sectors

43. Input-Output Analysis: Leontief inverse matrix
How to relate final demand to production?

44. Input-Output Analysis: Leontief inverse matrix
How to relate final demand to production?
is useful for which types of questions?

45. Input-Output Analysis: Leontief inverse matrix
How to relate final demand to production?
is useful for which types of questions?
If final demand in sector i, fi, (e.g. automobile industry) is to increase 10% next year how much output from each of the sectors would be necessary to supply this final demand?

46. Input-Output Analysis: Leontief inverse or total requirements matrix
2nd Indirect effects intersectorial needs to produce the following intersectorial needs
1st Indirect effects intersectorial needs to produce these cars
Direct effects cars for final demand

47. Input-Output Analysis: Leontief inverse or total requirements matrix
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

48. Input-Output Analysis: Leontief inverse or total requirements matrix
Impacts in output from marginal increases in final demand from f to fnew:

49. Input-Output: Multipliers
If sector 1 is paints and sector 2 is cars what is the meaning of l12?
Total output is:

50. Input-Output: Multipliers
Total production of paints
Total output is:
Production of paints required directly and indirectly for 1 unit of final demand of cars

51. Input-Output: Multipliers
Total output is:
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

52. Input-Output: Multipliers
Total output is:
lij represents the production of good i, xi, that is directly and indirectly needed for each unit of final demand of good j, fj
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
x1 needed for one unit of f2
xn needed for one unit of f1

53. Input-Output: Multipliers
Total output is:
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 is the meaning of the i column sum?
x1 needed for one unit of f2
xn needed for one unit of f1

54. Input-Output: Multipliers
Total output is:
lij represents the production of good i, xi, that is directly and indirectly needed for each unit of final demand of good j, fj
Multiplier of sector i: the impact that an increase in final demand fi has on total production (not on GDP)
x1 needed for one unit of f1
xn needed for one unit of f1

55. Input-Output: Multipliers
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
“Ripple effect” - Analogous of the impact of a stone in the water, bigger in the point of entry and smaller outward.

56. Input-Output: Multipliers
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?
“Ripple effect” - Analogous of the impact of a stone in the water, bigger in the point of entry and smaller outward.