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
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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