Free elective 2

oblem 1 Consider an open production model having # industries with > > 1. In order to produce $1 of its own output, the jth industry must spend $ (1 / >) for the output of the ith industry (for all i # /), but the jth industry (for all j = 1, 2, 3. ... >) spends nothing for its own output. Construct the consumption matrix C', show that it is productive, and determine an expression for (], - C.,) _ In determining an expression for (/, - C,) , use a computer to study the cases when , = 2, 3, 4, and 5; then make a conjecture and prove your conjecture to be true. [Hint: IF,, = [1], (Le., the y x x matrix with every entry equal to 1), first show that F, = MF and then express your value of (/, - C.) in terms of n. 1, and F,.]