1. Gestão de Sistemas Energéticos 2016/2017
Energy Analysis: Input-Output
Prof. Tânia Sousa

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

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

4. 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?

5. 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

6. Input-Output Analysis: Leontief inverse or total requirements matrix
Leontief inverse matrix which can be obtained as:
Total Output is:

7. 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

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

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

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

11. 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

12. 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

13. 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

14. 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

15. 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.

16. 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.

17. Exercise
Considere the following Economy:
What is the meaning of this?

18. Exercise Considere the following Economy:
Compute the matrix A of the technical coeficients:
Sales of Agric. to Indus. or
Inputs from Agriculture to Industry

19. Exercise Matrix of technical coefficients:
What is the meaning of this?

20. Exercise Matrix of technical coefficients:
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

21. Exercise Matrix of technical coefficients:
Compute the Leontief inverse matrix:

22. Exercise Matrix of technical coefficients:
Compute the Leontief inverse matrix:
What is the meaning of this?
x1=l11f1+l12f2+…

23. Exercise Matrix of technical coefficients:
Compute the Leontief inverse matrix:
the quantity of agriculture products directly and indirectly needed for each unit of final demand of industry products

24. Exercise ? Matrix of technical coefficients:
Compute the Leontief inverse matrix: ?
the quantity of agriculture products directly and indirectly needed for each unit of final demand of industry products

25. Exercise Matrix of technical coefficients:
Compute the Leontief inverse matrix:
What is the meaning of this?
x1=l11f1+l12f2+…
x2=l21f1+l22f2+…
x3=l31f1+l32f2+…

26. Exercise Matrix of technical coefficients:
Compute the Leontief inverse matrix:
Multiplier of the industry sector: the total output needed for each unit of final demand of industrial products

27. Exercise Matrix of technical coefficients:
Compute the Leontief inverse matrix:
What is the sector whose increase in final demand has the highest impact on the production of the economy?

28. 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?

29. 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?
Initial x

30. 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?
What will be the new sales of industry to agriculture?

31. Exercise
If final demand in sector 1 (e.g. agriculture) is to increase 10%
What will be the new sales of industry to agriculture?
Initial z21=20

32. Input-Output Analysis: Primary Inputs
Intermediate inputs: intersector and intrasector inputs
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
Inputs
Sectors

33. Input-Output: 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

34. Input-Output: Primary Inputs
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:

35. Input-Output: Primary Inputs
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
How to compute new values for added value or imports?

36. Input-Output: Primary Inputs
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
To compute new values for added value or imports:

37. Input-Output: Primary Inputs
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
To compute new values for added value or imports:

38. Input-Output: Primary Inputs
Relevance:

39. Exercise
What is the new added value?

40. Exercise
What is the new added value?
GDP increased by 3%