Thread: Consumption matrix

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.

its not that hard. You don't even have to find out if it's productive or not. That's really just a remedial step.I'm not mistaken, I think you just need to do this for b

b)
|0.1 0.2 0.05| |10|
|0.25 0.45 0.10| |15|
|0.35 0.15 0.15| * |20|
(multiply your consumption matrix by the vector 10,15,20)

c) I'm not sure, I'll have to look at my notes. I'm also taking this class right now

d)

subtract from the identity matrix

|1 0 0|
|0 1 0| - |your consumption matrix|
|0 0 1|

then augment your new matrix with 30,50 and 40 in the last column

after that, just put the matirx in reduced row echelon form, that will give you the gross production for x,y and z.

thanks for the reply mate, but i figured it all out weeks ago , thanks again

Originally Posted by sterps

thanks for the reply mate, but i figured it all out weeks ago , thanks again

If you had clicked on the Solved option in the Thread Tools dropdown menu or posted that you'd solved it then whatsmath might not have wasted his time replying. Just a thought .....