The Static Input-Output Model without Substitution

Abstract

We begin with a somewhat selective treatment of Input Output analysis. We assume an economy with n producible goods. In order to produce one unit of good j the economy needs a_ij units of good i (for i=1,…n) as input. Thus if industry j (which produces good j) wants to produce x_j units of output it must receive a_1j x_j units as inputs from industry 1, a_2j x_j units as inputs from industry 2 and so on. The set of input-output ratios a_ij form an n times n matrix which we call A. All a_ij are nonnegative, quite a few of them will probably be zero. There is one additional commodity, called “labour”. It’s specific characteristic is that it cannot be produced in the usual sense of the word. We assign the index zero to this commodity. Thus for every j we have an input output ratio a_oj which tells us how much labour per unit of output is necessary in industry j. The vector (a_o1, a_o2, … a_on) is denoted by a_o.