Input-Output Approach in an Allocation System

An input-output transaction matrix may be conceived in terms of an equilibrium position of two sets of interacting forces. The broadest way in which we can define them is 'to denote one set of forces as technical factors expressed through production functions and the other set as market factors expressed through allocation functions. Though technical factors influence production, it is widely recognised that there are various alternative technical combinations in any economy and under different market situations different combinations are actually taken up. An input-output matrix then represents an equilibrium solution for two sets of equations somewhat analogous to demand and supply functions. Under a competitive market and non-scarce resources allocation functions will play a minor role in the set up, and special conditions may be formulated under which production coefficients will determine the equilibrium. But under a monopolistic market with scarce resources allocation functions will determine which among a large group of alternative processes and combinations will be taken up by any particular sector. That is, production functions are forced to play a minor role. We can in this sense associate with an input-output matrix two sets of coefficients. One of these sets has been familiarised by Leontief as production coefficients, or, technical coefficients. They express the relationship xjj =ccjX5 where x, is the output of the ith sector sold to the jth sector and Xi is the output of the jth sector. We can similarly also assume the' existence under different circumstances of the relation xi, =A jXi where xi, is as before the output of the ith industry going to the jth sector and Xi is the output of the ith sector. According as supply or demand conditions predominate either of the relations may approximate reality or neither of these simplified situations may actually approximate reality at all. Leontief has formulated an idealised situation where the set oc, is assumed fixed and the set Ail is allowed to change freely with any change in the final demand. Such conditions may be assumed to hold approximately so long as there is no scarce factor and so long as suppliers are able to offer more of any commodity at the existing price. Leontief's formulation thus takes up for consideration a situation where there is even in the short period a large unused capacity in most sectors such that any change in the final demands do not set