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Energy Management: 2013/2014 Energy Analysis: Input-Output Class # 5 Prof. Tânia Sousa

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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?

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Input-Output Analysis: Motivation Energy is needed in all production processes Block Diagrams 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

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Input-Output Analysis: Motivation Energy is needed in all production processes Block Diagrams 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

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Input-Output Analysis: Motivation Input-Output Methodology –Build scenarios for the economy in a consistent way –To compute energy needs for different economic scenarios

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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.) increase in demand for coal Chemical Industry Power Plant Coal Mine

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Input-Output Analysis: Motivation Portuguese Scenarios for 2050:

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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.

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Input-Output Portugal Input-Output matrix Portugal (2008) PRODUCTS (CPA*64) R01R02R03RBR10_12 R01Products of agriculture, hunting and related services 954,918,40,0 4275,2 R02Products of forestry, logging and related services 0,0103,40,0 R03 Fish and other fishing products; aquaculture products; support services to fishing 0,0 38,40,040,5 RBMining and quarrying 0,50,0 152,710,6 R10_12Food products, beverages and tobacco products 1284,70,13,91,13012,0 R13_15Textiles, wearing apparel and leather products 21,10,04,05,31,2 R16 Wood and of products of wood and cork, except furniture; articles of straw and plaiting materials 30,40,0 1,858,5 R17Paper and paper products 8,20,01,32,2304,3 R18Printing and recording services 4,00,31,84,349,5 R19Coke and refined petroleum products 224,814,338,6144,399,4 R20Chemicals and chemical products 225,910,20,831,8106,5 R21Basic pharmaceutical products and pharmaceutical preparations 6,30,0 0,112,1

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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:

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Input-Output: Basics For the “Tire Factory” x 1 = z 11 + z 12 +… + z 1n + f 1 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

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Input-Output: Basics For the Electricity Sector: x i = z i1 + z i2 +… + z ii +… + z in + f i

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Input-Output: Basics For the Electricity Sector: x i = z i1 + z i2 +… + z ii +… + z in + f i Output from sector i to sector 2 Output from sector i to final demand Total production from sector i Electricity Sector Automobile Factory Individual Consumers

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Input-Output: Basics For the Electricity Sector: x i = z i1 + z i2 +… + z ii +… + z in + f i Output from sector i to sector 2 Output from sector i to final demand Total production from sector i Electricity Sector Automobile Factory Individual Consumers What is the meaning of this?

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Input-Output: Basics For the Electricity Sector: x i = z i1 + z i2 +… + z ii +… + z in + f i Output from sector i to sector 2 Output from sector i to final demand Total production from sector i Electricity Sector Automobile Factory Individual Consumers Electricity consumed within the electricity sector: hydraulic pumping & electric consumption at the power plants & losses in distribution

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Input-Output: Basics For all sectors: z ij is sales (ouput) from sector i to (input in) sector j (in ? units) f i is final demand for sector i (in ? units) x i is total output for sector i (in ? units)

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Input-Output: Basics For all sectors: z ij is sales (ouput) from sector i to (input in) sector j (in money units) f i is final demand for sector i (in money units) x i 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?

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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

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Input-Output: Matrix A of technical coefficients Let’s define: What is the meaning of a ij ? z ij is sales (ouput) from sector i to (input in) sector j x j is total output for sector j

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Input-Output: Matrix A of technical coefficients Let’s define: The meaning of a ij : –a ij input from sector i (in money) required to produce one unit (in money) of the product in sector j –a ij are the transaction or technical coefficients

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Input-Output: Matrix A of technical coefficients Rewritting the system of equations using a ij :

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

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

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

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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

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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 X 1 units (money) using a 11 X 1 units of sector 1, a 21 X 1 units of sector 2, …, a n1 X 1 units of sector n Sector 1 produces 1 units (money) using a 11 units of sector 1, a 21 units of sector 2, …, a n1 units of sector n Inputs to sector 1

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Production Functions: a review Production functions specify the output x of a factory, industry, sector or economy as a function of inputs z 1, z 2, …: Examples: –Produces x units using z 1 units of sector 1, z 2 units of sector 2, …, z n units of sector n Cobb-Douglas Production Function Linear Production Function

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Production Functions: a review Production functions specify the output x of a factory, industry or economy as a function of inputs z 1, z 2, …: Examples: Which of these productions functions allow for substitution between production factors? Cobb-Douglas Production Function Linear Production Function

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Production Functions: a review Production functions specify the output x of a factory, industry or economy as a function of inputs z 1, z 2, …: 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

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Production Functions: a review Production functions specify the output x of a factory, industry or economy as a function of inputs z 1, z 2, …: Examples: Which of these productions functions allow for scale economies? Cobb-Douglas Production Function Linear Production Function

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Production Functions: a review Production functions specify the output x of a factory, industry or economy as a function of inputs z 1, z 2, …: Examples: Which of these productions functions allow for scale economies? Cobb-Douglas (if b+c >1) Cobb-Douglas Production Function Linear Production Function

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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 X 1 1 units (money) using X 1 a 11 units of sector 1, X 1 a 21 units of sector 2, …, X 1 a n1 units of sector n Is there substitution between production factors? Are scale economies possible? Inputs to sector 1

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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 X 1 1 units (money) using X 1 a 11 units of sector 1, X 1 a 21 units of sector 2, …, X 1 a n1 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

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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 X 1 1 units (money) using X 1 a 11 units of sector 1, X 1 a 21 units of sector 2, …, X 1 a n1 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

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

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

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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 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

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

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

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Input-Output Analysis: Leontief inverse matrix How to relate final demand to production? Leontief inverse matrix which can be obtained as:

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Input-Output Analysis: Leontief inverse or total requirements matrix can be used to answer: –If final demand in sector i, f i, (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? 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) – 1 st indirect effects –A[Af] accounts for the intersectorial needs to produce Af (e.g. coal to produce the steel) – 2 nd indirect effects

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

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Input-Output: Multipliers Total output is: ? ?

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Input-Output: Multipliers Total output is: –l ij represents the production of good i, x i, that is directly and indirectly needed for each unit of final demand of good j, f j –What about l ii ? x 1 needed for one unit of f 1 x n needed for one unit of f 1

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Input-Output: Multipliers Total output is: –l ij represents the production of good i, x i, that is directly and indirectly needed for each unit of final demand of good j, f j –l ii > 1 represents the production of good i, x i, that is directly and indirectly needed for each unit of final demand of good i, f i x 1 needed for one unit of f 1 x n needed for one unit of f 1

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Input-Output: Multipliers Total output is: –l ij represents the production of good I, x i, that is directly and indirectly needed for each unit of final demand of good j, f j –What is the meaning of the i column sum? x 1 needed for one unit of f 1 x n needed for one unit of f 1

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Input-Output: Multipliers Total output is: –l ij represents the production of good I, x i, that is directly and indirectly needed for each unit of final demand of good j, f j Multiplier of sector i: the impact that an increase in final demand f i has on total production (not on GDP) x 1 needed for one unit of f 1 x n needed for one unit of f 1

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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

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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:

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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:

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Input-Output: Primary Inputs Relevance:

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

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

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

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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

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

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Exercise Matrix of technical coefficients: Compute the Leontief inverse matrix: What is the meaning of this? x 1 =l 11 f 1 +l 12 f 2 +…

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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

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Exercise Matrix of technical coefficients: Compute the Leontief inverse matrix: What is the meaning of this? x 1 =l 11 f 1 +l 12 f 2 +… x 2 =l 21 f 1 +l 22 f 2 +… x 3 =l 31 f 1 +l 32 f 2 +…

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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

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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?

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Exercise If final demand in sector 1 (e.g. agriculture) is to increase 10% –What will be necessary changes in the final outputs of agriculture, industry and services?

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Exercise If final demand in sector 1 (e.g. agriculture) is to increase 10% –What will be necessary changes in the final outputs of agriculture, industry and services? Initial x

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Exercise If final demand in sector 1 (e.g. agriculture) is to increase 10% –What will be necessary changes in the final outputs of agriculture, industry and services? –What will be the new sales of industry to agriculture?

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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 z 21 =20

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Exercise What is the new added value?

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

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Imports A C B 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?

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Exercise Matrix: Input- Output Model:

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Imports A C B Final Demand Exercise 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.

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Exercise Matrix: Input- Output Model: Matrix L=I+A

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

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Input-Output Application to the energy sector?

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Input-Output Energy needs for different economic scenarios –Using the input-output analysis to build a consistent economic scenarios and then combining that information with the Energetic Balance –Using the input-output analysis where one or more sectors define the energy sector

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Input-Output Analysis: Embodied Energy The input-ouput model Intermediate Inputs (square matrix) Primary Energy Inputs Total Energy in Inputs Embodied Energy in Final Demand Total Energy in outputs Outputs Inputs Sectors

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Input-Output Analysis: Embodied Energy Embodied energy intensity, CE i, in outputs from sector i to final demand or to other sectors is constant, i.e., The energy sector 1 receives (direct + indirect) energy which is distributed to its intended output m 1 S 1

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Input-Output Analysis: Embodied Energy Simplifying per unit of mass:

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Input-Output Analysis: Embodied Energy Simplifying per unit of mass: We can compute the embodied energy intensities for all sectors CE i because we have n equations with n unknowns –We must know mass flows, residue formation factors and direct energies intensities

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Input-Output Analysis: Embodied Energy Simplifying per unit of mass: We can compute the change in embodied energy intensities for all sectors with the change in direct energy intensities

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Input-Output Analysis To compute embodied “something”, e.g., energy or CO 2, 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

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Input-Output Analysis: Motivation Direct and indirect carbon emissions

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