Hey there, i need help with a question.
Im up to Part a) in this question:
An islands economy is divided into three sectors-tourism, transportation, and services. Suppose
that each dollars worth of tourism output requires inputs of $0.10 from the tourism sector, $0.25
from the transportation sector, and $0.35 from the services sector; each dollars worth of trans-
portation output requires inputs of $0.20 from the tourism sector, $0.45 from the transportation
sector, and $0.15 from the services sector; and each dollars worth of services output requires
inputs of $0.05 from the tourism sector, $0.10 from the transportation sector, and $0.15 from
the services sector.
(a) Write the consumption matrix C for this economy. Show that C is productive.
(b) If the gross production for this economy is $10 million of tourism, $15 million of trans-
portation, and $20 million of services, what is the total value of the inputs consumed by
each sector during the production process?
(c) If the total outputs of the tourism, transportation, and services sectors are $70 million, $50
million, and $60 million, respectively, what is the net production of each sector?
(d) What gross production is required to satisfy exactly a demand for $30 million of tourism,
$50 million of transportation, and $40 million of services?
Im pretty sure the consumption matrix is:
|0.1 0.2 0.05|
|0.25 0.45 0.10|
|0.35 0.15 0.15|
now im stuck on where i have to show that it is productive.
|100| |0.1 0.2 0.05| |0.90 -0.80 -0.95| ^-1
|010| - |0.25 0.45 0.10| = |-0.75 0.55 -0.90|
|001| |0.35 0.15 0.15| |-0.65 -0.85 0.85|
when i take the inverse of this matrix, i get one with negative answers, which means C is not productive..... what am i doing wrong!!
also could someone set me off with the rest of the questions.