Let us consider the general case in which several techniques for the production of one or more of the products are available. Our object is to study which one from amongst the alternative techniques will be chosen in the final equilibrium.
IT IS therefore necessary to define the technique of producing a given product and to distinguish it from the description of the product itself. In particular, it is important to note that the proportions which the raw material ingredients bear to one another (apart from quality variations of a statistical nature) define the product, not the technique of producing it. Any change in these proportions changes the product. On the other hand, a different technique of production will be identified only if it involves the use in different proportions of the 'agents of production' i.e. of the types of machines and of labour required to process the raw materials into the finished product.
To be sure, a change in the type of machinery will usually impose the requirements of working inputs specific to it, e.g. electricity in place of human or animal power. Yet, if a comparison between different techniques of production is to be possible without the interfering influences from changes in the nature of the product itself, the technical properties of the product must be assumed to remain the same, irrespective of the technique used to produce it. And this means that the ingredients of the product must be assumed to remain the same when a comparison is to be made between the techniques of production.
The distinction of the technique of production from the specification of the product is thus seen to hinge upon the distinction between the agents of production and the ingredients of the product; the former do not undergo any change in their physical shape in the course of production, whilst the latter are, usually irreversibly, transformed into the product. Thus, in a system with exclusive use of working inputs and one kind of labour the choice of technique problem is trivial. For, in these conditions different techniques will be identified only by the distinct quantities of labour required by each of them for a given level of output. And the technique that uses the least quantity of labour per unit of output will obviously be chosen as the most profitable. It is only when different types of machines are involved with different types of labour that the problem of choice comes to deserve more detailed consideration.
If this line of reasoning is accepted we are led to infer that if the raw material ingredients change, with or without a change in the machines and labour required, the resulting product itself changes. There will then be a change in the Engels' coefficients relevant to the changed products. Such products will have their own prices which will not be directly comparable with the price of any commodity and would therefore be considered in relation to those of the others. With these qualifications in view we can proceed to illustrate the procedure for the general solution. Accordingly, we set up two systems of equations 1 and 2, which, although identical in all other respects, differ only in one, viz, that the price equation for commodity A is represented in system I by the equation of technique I and in system II, by that of technique II.
Next, we compare the equilibrium solutions of each system and select the system that yields a higher rate of profit.An identical procedure holds in the general case in which the several techniques of production for the various commodities differ in any one or more of the following respects; the quantities and types of machines used, their durabilities, the quantities and types of labour required, the quantities of the technique specific working inputs, or the wastages of raw materials characteristic to them.It is possible, of course, to avoid rummaging through all the systems of equations if the purpose is only to know which technique will be selected rather to know what rate of profit it will earn in the new equilibrium.
This is facilitated by Sraffa's criterion for selection, viz, the technique which produces at the lowest unit cost, the cost being evaluated at the ruling (equilibrium) levels of the rate of profit, prices and the real wage, is the most profitable technique. In the light of the procedure for the general solution this implies that the adoption of the technique which meets this criterion will raise the rate of profit of the entire economy. The criterion can be readily applied to a number of stylized examples. We can, in like manner, deal with the other possible differences between the techniques.
Thus, for example, the wage cost of the different types of labour will appear on the respective sides of the cost equations of the techniques. Similarly, the costs of technique-specific working inputs (energy, maintenance etc.) if any, can also be accommodated. Finally, if the wastages of raw materials differ as between the techniques, their net benefit/cost can be included as well.The procedure of the general solution described above conceals the details of the dynamic process observed in the actual economy when a more efficient new technique supplants an existing one. The general solution only tells us which technique will be selected.
In fact, however, when a new technique (provided it is more efficient by the criterion explained above) is introduced it supplants the old technique in steps.Thus suppose that a new machine substitutes an old one in the production of commodity j. This will have two effects. The first effect is that all expansions of new plant and the replacement of old plant will now embody the new technique. The second is that the size of the industry producing the old machine will shrink because the demand for its product from industry j ceases altogether.In the years to come the demand for the new machine originating from industry j will rise rapidly in steps determined by the standard multipliers which characterize the equilibrium age-distribution of the existing stock of machines of the old type in industry j.
There will thus be a prolonged boom for the industry producing the new machine which will last for producing the new machine which will last for s years, i.e. for the duration of the life of old machine. Thereafter, a growth cycle will be observed around the new equilibrium growth path.