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Leontief’s Input-Output Model

Leontief’s Input-Output Model. Andrew Blythe Peter Whitley. Economics in the Model. A matrix representation to predict the effect of changes in one industry on others

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Leontief’s Input-Output Model

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  1. Leontief’s Input-Output Model Andrew Blythe Peter Whitley

  2. Economics in the Model • A matrix representation to predict the effect of changes in one industry on others • Considers inter-industry relations in an economy: an output in one industry goes to another industry as an input creating dependent industries

  3. Restrictions • Each industry only produces one homogenous good • Industry uses fixed ratio of inputs to outputs • Every industry has constant returns to scale

  4. = 1 =1 =1 0.3 +0.3 +0.3 0.4 +0.1 +0.5 0.3 +0.6 +0.2

  5. Variables in the Closed Model • Economy consisting of n interdependent industries, S1,…,Sn • mij : percentage of units produced by industry Sithat are consumed by industry Sj • pk: production level of industry Sk • mij pj : number of units produced by industry Si that are consumed by industry Sj • p1mi1+p2mi2+…+pnmin : total number of units produced by Si

  6. AP = P

  7. AP=P ( A-I)P = 0 P= Null Space of A-I - = 0

  8. A – I augmented Matrix = Reff(A) =

  9. Open Model • Open Model P=AP+d d = • di : demand for ith commodity from outside the economy

  10. Solve For P in Open Model AP + d=P (I-A)P=d P=(I-A)-1*d

  11. * =

  12. NAFTA • P = [y1,y2,y3] • y1 =Price US charges for all its goods • y2 =Price Canada charges for all its goods • y3 =Price Mexico charges for all its goods • a11y1 + a12y2 + a13y3 = Monetary sum of goods bought in US • a21y1 + a22y2 + a23y3 same for Canada • a31y1 + a32y2 + a33y3 same for Mexico

  13. NAFTA • A= p0 = original p P = [y1,y2,y3] • AP = p • If AP ≠ p • P(k) = how p changes after k months • p(k+1) = Ap(k) - find • p(k) = Akp0for long run equilibrium

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