The business of production as a whole which is going on in a society at any moment can be dissected in countless ways into distinct partial activities and into sectors where these contributory processes take place. A scheme of analysis which is meant to suggest or guide action should conform in some way to the existing division of production amongst decision-making centres; that is to say, amongst firms or such groups of firms as make broadly similar products. Every such firm or industry stands at the confluence of many streams of products which it buys from other sectors, and itself supplies its product directly to many other sectors and through them to the whole productive organism. Each sector also supplies its product direct to final users, comprising consumers who will use the goods for enjoyment and sustenance, businessmen investing in durable equipment which will not itself be passed on to other firms, and the government. The output of each sector (measured by the value of goods sold and not merely by the value which has been added in the sector) thus goes partly for intermediate use and partly for final use. The involvement of almost all sectors in supplying each other directly and indirectly with means of further production implies that the total quantity annually required of any product, for final and intermediate uses taken together, depends on the respective final use quantities required of all products. To find and express this dependence in quantitative terms by a system of equations is the purpose of input-output analysis. Activity, product and sector are classes so conceived in input-output analysis that they stand in one-to-one correspondence with each other. Each activity is deemed to result in only one product, each product to be made by only one activity. Each activity is carried on in only one sector and each sector has only one activity. To allow every technological, geographical or market distinction to define a separate product would result in a list of millions of products. Practical computation can handle only a few hundreds. Each product in input-output analysis is therefore a bundle of commodities made up to be as meaningful as available statistics and the needs of computation allow. For the reason that products are composite if for no other, direct physical measurement


annual quantities Y i demanded for final use. That is to say, we seek a set of equations in each of which, not Yb but Zb will stand by itself on one side of the 'equals' sign, and the manner in which this Zi is determined will be exhibited on the other side of the 'equals' sign in an expression containing the final use quantity of every one of the products. To get this second form of statement out of the other form, to turn the first kind of equations round, is to solve these equations. The entire sequence of steps, leading from the raw data of annual quantities sold of each product for its various applications, to the solution which enables the respective required total outputs to be calculated from any arbitrarily chosen or given 'bill of goods for final use', is best expressed and carried through in matrix notation.