1. Building an IO Model l Form Input-Output Transactions Table which represents the flow of purchases between sectors. l Constructed from ‘Make’ and ‘Use’ Table Data – purchases and sales of particular sectors.

2. Building an IO Model l Sum of Value Added (non-interindustry purchases) and Final Demand is GDP. l Transactions include intermediate product purchases and row sum to Total Demand. l From the IO Transactions table, form the Technical Requirements matrix by dividing each column by total sector input – matrix D. Entries represent direct inter-industry purchases per dollar of output.

3. Transactions Table X ij + F i = X i ; X i = X j ;using A ij = X ij / X j (A ij *X j ) + F i = X i in vector/matrix notation: A*X + F = X => F = [I - A]*X or X = [I - A] -1 *F

4. Two Sector Numerical Example l Reading across: Sector 1 provides $150 of output to sector 1, $500 of output to sector 2, and $350 of output to consumers. l Reading down: Sector 1 purchases $150 of output from sector 1, $200 of output from sector 2, and adds $650 of value to produce its output l Transaction Flows ($) are at right. 12Final Demand 1150500350 22001001700 Value Added 65014002050

5. Complete Transactions Matrix Sector 1Sector 2Final Demand Total Output Sector 11505003501000 Sector 220010017002000 Value Added 6501400GDP 2050 Total Input 10002000

6. Requirements Matrix l Creating the A matrix l A ij = X ij / X j l So, to make $1 of output from sector 1 requires $0.15 of output from the same sector. Sector 1Sector 2 Sector 1150/1000 = 0.15 500/2000 =.25 Sector 2200/1000 = 0.2 100/2000 =.05

7. Production of Good 1 in our Two Sector Model Sector 1 Sector 2 $ 1 Good 1 $0.2/$ Good 2 $ 0.15/$ Good 1 To produce $1 of output from sector one requires $0.15 of goods from the sector itself, plus $0.2 of goods from sector 2.

8. Production of Good 2 in our Two Sector Model Sector 1 Sector 2 $ 1 Good 2 $0.25/$ Good 2 $ 0.05/$ Good 2 To produce $1 of output from sector two requires $0.05 of goods from the sector itself, plus $0.25 of goods from sector 1.

9. Leontief Inverse l [I – A] l [I – A] -1 or X = [I - A] -1 *F

10. Add Final Demand l Determine the effects of $100 additional demand from Sector 1 l X = [I – A] -1 F l Total Outputs: $125.4 of Sector 1 and $26.4 of Sector 2, or $ 151.8 Total. l Direct intermediate inputs: $15 of 1 and $20 of 2 for $100 output of 1 (or $ 135)

11. Add Environmental Effects l Add sector-level environmental impact coefficient matrices (R) »[effect/$ output from sector] l Example: Hazardous Waste Generation (R) »R 1 = 100 grams/$ in Sector 1 »R 2 = 5 grams/$ in Sector 2

12. Production of Waste in our Two Sector Model Sector 1 Sector 2 $ 1 Good 1 Haz. Waste 100 gm/$ Good 1 Haz Waste 5 gm/$ Good 2 $0.2/$ Good 2 $ 0.15/$ Good 1

13. Sector 1 Sector 2 $ 1 Good 2 Haz. Waste 100 gm/$ Good 1 Haz Waste 5 gm/$ Good 2 $0.25/$ Good 2 $ 0.05/$ Good 2 Production of Waste in our Two Sector Model

14. l B = R*X l 12,540 grams of hazardous waste generated by sector 1 l 132 grams of hazardous waste generated by sector 2 l Total of 12672 grams hazardous waste generated