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17. For the hypothetical economy of Examples 4.24 and 4.25, the Leontief input-output matrix is Agriculture Manufacturing Power Agriculture 0.40 0.15 0.20 A = Manufacturing 0.15 0.30 0.25 Power 0.20 0.25 0.30 (a) How many dollars' worth of manufacturing output are needed to produce $500 worth of agricultural output? Briefly explain. (b) Compute the inverse matrix (I – A) −¹ . - (c) For each open sector demand vector d, compute the optimal output vector x = (Z - A)¯¹d. 100 100 100 (i) d = 30 ; (ii) d = = 30 ; (iii) d = 60 80 105 90

17. For the hypothetical economy of Examples 4.24 and 4.25, the Leontief input-output matrix is Agriculture Manufacturing Power Agriculture 0.40 0.15 0.20 A = Manufacturing 0.15 0.30 0.25 Power 0.20 0.25 0.30 (a) How many dollars' worth of manufacturing output are needed to produce $500 worth of agricultural output? Briefly explain. (b) Compute the inverse matrix (I – A) −¹ . - (c) For each open sector demand vector d, compute the optimal output vector x = (Z - A)¯¹d. 100 100 100 (i) d = 30 ; (ii) d = = 30 ; (iii) d = 60 80 105 90

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 30E
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17. For the hypothetical economy of Examples 4.24 and 4.25, the Leontief input-output matrix is Agriculture Manufacturing Power Agriculture 0.40 0.15 0.20 A = Manufacturing 0.15 0.30 0.25 Power 0.20 0.25 0.30 (a) How many dollars' worth of manufacturing output are needed to produce $500 worth of agricultural output? Briefly explain. (b) Compute the inverse matrix (I – A) −¹ . - (c) For each open sector demand vector d, compute the optimal output vector x = (Z - A)¯¹d. 100 100 100 (i) d = 30 ; (ii) d = = 30 ; (iii) d = 60 80 105 90
Transcribed Image Text:17. For the hypothetical economy of Examples 4.24 and 4.25, the Leontief input-output matrix is Agriculture Manufacturing Power Agriculture 0.40 0.15 0.20 A = Manufacturing 0.15 0.30 0.25 Power 0.20 0.25 0.30 (a) How many dollars' worth of manufacturing output are needed to produce $500 worth of agricultural output? Briefly explain. (b) Compute the inverse matrix (I – A) −¹ . - (c) For each open sector demand vector d, compute the optimal output vector x = (Z - A)¯¹d. 100 100 100 (i) d = 30 ; (ii) d = = 30 ; (iii) d = 60 80 105 90
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