Energy Management: 2013/2014

1. Energy Management: 2013/2014 EnergyAnalysis: Input-OutputClass # 5 Prof. Tânia Sousataniasousa@ist.utl.pt

2. Input-Output Analysis: Motivation • Energyisneeded in allproduction processes • Differentproductshavedifferentembodiedenergiesorspecificenergyconsumptions • How can we compute these?

3. Input-Output Analysis: Motivation • Energyisneeded in allproduction processes • BlockDiagramsMethodology • To compute embodiedenergiesorspecificenergyconsumptionsofdifferentproducts • To compute theimpactofenergyefficiencymeasures in thespecificenergyconsumptionsofa product • Input-Output Methodology

4. Input-Output Analysis: Motivation • Energyisneeded in allproduction processes • BlockDiagramsMethodology • To compute embodiedenergiesorspecificenergyconsumptionsofdifferentproducts • To compute theimpactofenergyefficiencymeasures in thespecificenergyconsumptionsofa product • Input-Output Methodology • To compute theembodiedenergies for allproducts/sectors in aneconomysimultaneously (no need to considerspecificconsumptionof inputs equal to zero) • To compute theimpactofenergyefficiencymeasuresacrosstheeconomy

5. Input-Output Analysis: Motivation • Input-Output Methodology • Build scenarios for the economy in a consistent way • To compute energyneeds for differenteconomicscenarios

6. Input-Output Analysis: Motivation • Building a scenario for the economy in a consistent wayis 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 increasethe output ofchemicalindustrythereis a direct & indirect (electr.) increase in demand for coal PowerPlant ChemicalIndustry Coal Mine

7. Input-Output Analysis: Motivation • Portuguese Scenariosfor 2050: http://www.cenariosportugal.com/

8. 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.

9. Input-Output Portugal • Input-Output matrix Portugal (2008)

10. Input-Output Portugal • DPP (Departamento de Prospectiva e Planeamento e Relações Internacionais) thatbelongs to the MAOT developedaninput-outputmodel MODEM1 whichhasbeenused to evaluatethemacroeconomic, sectorial and regional impactsofpublic 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

11. 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 Productionfrom sector 1 Individual Consumers Tire Factory Automobile Factory

12. Input-Output: Basics For theElectricity Sector: xi= zi1+zi2+… + zii+… + zin+ fi

13. Input-Output: Basics For theElectricity Sector: xi= zi1+zi2+… + zii+… + zin+ fi Output from sector i to sector 2 Output from sector i to final demand Total productionfrom sector i Individual Consumers Electricity Sector Automobile Factory

14. Input-Output: Basics Whatisthemeaningofthis? For theElectricity Sector: xi= zi1+zi2+… + zii+… + zin+ fi Output from sector i to sector 2 Output from sector i to final demand Total productionfrom sector i Individual Consumers Electricity Sector Automobile Factory

15. Input-Output: Basics Electricityconsumedwithintheelectricity sector: hydraulicpumping & electricconsumptionatthepowerplants & losses in distribution For theElectricity Sector: xi= zi1+zi2+… + zii+… + zin+ fi Output from sector i to sector 2 Output from sector i to final demand Total productionfrom sector i Individual Consumers Electricity Sector Automobile Factory

16. Input-Output: Basics For allsectors: zijis sales (ouput) from sector i to (input in) sector j (in ?units) fiisfinal demand for sector i (in ?units) xiistotal output for sector i (in ?units)

17. Input-Output: Basics For allsectors: zijis sales (ouput) from sector i to (input in) sector j (in moneyunits) fiisfinal demand for sector i (in moneyunits) xiistotal output for sector i (in moneyunits) • Thecommonunit in whichallthese inputs & outputs can bemeasuredismoney • Matrixform?

18. Input-Output: Basics For allsectors: iis a column vector of 1´s withthecorrectdimension Lower case bold letters for columnvectors Upper case bold letters for matrices

19. Input-Output: Matrix A of technical coefficients Let’s define: • Whatisthemeaningofaij? zijis sales (ouput) from sector i to (input in) sector j xjis total output for sector j

20. Input-Output: Matrix A of technical coefficients Let’s define: • Themeaningofaij: • aij input from sector i (in money)required to produceoneunit(in money) oftheproduct in sector j • aijare thetransactionortechnicalcoefficients

21. Input-Output: Matrix A of technical coefficients Rewrittingthesystemofequationsusingaij:

22. Input-Output: Matrix A of technical coefficients Rewrittingthesystemofequationsusingaij: • How can itbewritten in a matrixform?

23. Input-Output: Matrix A of technical coefficients Rewrittingthesystemofequationsusingaij: • In a matrixform:

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

25. 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

26. 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

27. ProductionFunctions: a review • Productionfunctionsspecifythe output xof a factory, industry, sector oreconomy as a functionof inputs z1, z2, …: • Examples: • Produces x units using z1units of sector 1, z2units of sector 2, … , znunits of sector n Cobb-Douglas ProductionFunction Linear ProductionFunction

28. ProductionFunctions: a review • Productionfunctionsspecifythe output xof a factory, industryoreconomy as a functionof inputs z1, z2, …: • Examples: • Whichoftheseproductionsfunctionsallow for substitutionbetweenproductionfactors? Cobb-Douglas ProductionFunction Linear ProductionFunction

29. ProductionFunctions: a review • Productionfunctionsspecifythe output xof a factory, industryoreconomy as a functionof inputs z1, z2, …: • Examples: • Whichoftheseproductionsfunctionsallow for substitutionbetweenproductionfactors? • Cobb-Douglas and Linear productionfunctions Cobb-Douglas ProductionFunction Linear ProductionFunction

30. ProductionFunctions: a review • Productionfunctionsspecifythe output xof a factory, industryoreconomy as a functionof inputs z1, z2, …: • Examples: • Whichoftheseproductionsfunctionsallow for scaleeconomies? Cobb-Douglas ProductionFunction Linear ProductionFunction

31. ProductionFunctions: a review • Productionfunctionsspecifythe output xof a factory, industryoreconomy as a functionof inputs z1, z2, …: • Examples: • Whichoftheseproductionsfunctionsallow for scaleeconomies? • Cobb-Douglas (ifb+c >1) Cobb-Douglas ProductionFunction Linear ProductionFunction

32. Input-Output: Matrix A of technical coefficients • The meaning of matrix of technical coefficients A: • Production functionassumed in the Input-Output Technique • Sector 1 produces X11 units (money) using X1 a11units of sector 1, X1 a21units of sector 2, … , X1 an1units of sector n • Is there substitution between production factors? • Are scale economies possible? Inputs to sector 1

33. Input-Output: Matrix A of technical coefficients • The meaning of matrix of technical coefficients A: • Production functionassumed in the Input-Output Technique • Sector 1 produces X11 units (money) using X1 a11units of sector 1, X1 a21units of sector 2, … , X1 an1units 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 LeontiefProductionFunction

34. Input-Output: Matrix A of technical coefficients • The meaning of matrix of technical coefficients A: • Production functionassumed in the Input-Output Technique • Sector 1 produces X11 units (money) using X1 a11units of sector 1, X1 a21units of sector 2, … , X1 an1units 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

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

36. Sectors Intermediate Inputs(square matrix) Outputs Total output Final Demand Sectors Inputs Primary Inputs Input-Output Analysis: Themodel • 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-ouputmodel

37. Sectors Intermediate Inputs(square matrix) Outputs Total output Final Demand Sectors Inputs Primary Inputs Total Inputs or Total Costs Input-Output Analysis: Themodel • 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-ouputmodel

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

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

40. Input-Output Analysis: Leontiefinversematrix • How to relate final demand to production? • Leontiefinversematrixwhich can beobtained as:

41. Input-Output Analysis: Leontiefinverseor total requirementsmatrix • can beused to answer: • Iffinal demand in sector i, fi, (e.g. agriculture) is to increase 10% nextyearhowmuch output fromeachofthesectorswouldbenecessary to supplythis final demand? • Total Output is: • Ifaccounts for the final demand in total output (e.g. carsconsumedbyhouseholds) – 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 intersectorialneeds to produce Af(e.g. coal to produce the steel) – 2nd indirect effects

42. Input-Output Analysis: Leontiefinverseor total requirementsmatrix • Impacts in output from marginal increases in final demandfromf to fnew:

43. Input-Output: Multipliers • Total output is: ? ?

44. Input-Output: Multipliers • Total output is: • lijrepresents 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? x1needed for oneunitof f1 xnneeded for oneunitof f1

45. Input-Output: Multipliers • Total output is: • lijrepresents 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 x1needed for oneunitof f1 xnneeded for oneunitof f1

46. Input-Output: Multipliers • Total output is: • lijrepresents the production of good I, xi,that is directly and indirectly needed for each unit of final demand of good j, fj • Whatisthemeaningoftheicolumn sum? x1needed for oneunitof f1 xnneeded for oneunitof f1

47. Input-Output: Multipliers • Total output is: • lijrepresents the production of good I, xi,that is directly and indirectly needed for each unit of final demand of good j, fj • Multiplierof sector i: theimpactthatanincrease in final demandfihason total production(not on GDP) x1needed for oneunitof f1 xnneeded for oneunitof f1

48. 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

49. Input-Output: Primary Inputs • For theprimary inputs we define thecoefficients: • Theaddedvalueof sector j per unitofproductionorimportsof sector j per unitofproductionare assumed to beconstant • For thetransactionsbetweensectors:

50. Input-Output: Primary Inputs • For theprimary inputs we define thecoefficients: • Theaddedvalueof sector j per unitofproductionorimportsof sector j per unitofproductionare assumed to beconstant • To compute newvalues for addedvalueorimports: