Matrix's and consumption
Ok so I have this study question that really has me stumped, I cant, find anything in the textbook to help me and I am really stuck.
The question says there is an economy that has 3 manu, agricult, indust, labour.
$1 ag = 0.5 Ag, 0.20 Manu, and 1.00 Labour
$1 manu = 0.8 manu and 0.4 labour
$1 labour = 0.25 agri and 0.10 manu.
It first asks what the consuption matrix C is. Now I assume that it would simply be matrixing this out so it would be like, this I am not sure on though.
ag ma la
ag 0.5 0.2 1
ma 0 0.8 0.4
la 0.25 0.10 0
Then it says to find a production schedual that satisfies a demand of 100$ for agriculture, 500$ for manufacturing and 700$ for labor.
(This part I have no idea, I think you multiply a 100 500 700 matrix by your consumption matrix, but I dont know what that means or does, I am probely wrong)
It asks which industries are profitable and if the economy is productive exc.
I assume that to find productivity I simply go (I-E)P=0 and solve for P (E being the consumption matrix i made above, I being an identity matrix of the same size exc) and then figure it out from there. (based on the values I get for each thing)
Am I on the right track? You see I have spent a loong time on this question but there is absolutely no similar example in my textbook as well as no outside help so I really don't know if I am close or way off or thinking in the right direction but doing something wrong, could someone explain what needs to be done for a question like this . It would be greatly appreciated, I have spent many hours looking this over only to be stumped, the textbook I have does not show any similar questions at all and I don't have much to reference too.
Would be greatly appreciated for help.