Why are the columns of any reasonable consumption matrix alw

Solution

let C be the consumption matrix the output from industry is i which is needed to produce one unit of output of industry j.

If industry j wants to produce one unit of its own product it needs to consume Cij units of the output of the industry i.

we have n industries producing Xi units each The production vector p is p =x1

                                                                                                             x2

The consumption by industries will be Cp. and p-Cp=(1-C)p is the amount available for external use.

The demand matrix d from outside of the system id d= d1

                                                                                d2

where di shows the demand for the output of the industry i.

from this we conclude that consumption is zero the deman will be 1 and vice verse therefore the consumption adds upto atleast 0ne