10. Some Continuity Properties of a Reformulated Sraffa Model

In this chapter we provide some continuity results for Sraffa price system which include subsistence consumption in the matrix of intermediate inputs, but which allow for wage level fluctuations around the subsistence wage level, assuming thereby ex post wage payments only with respect to this deviation from the subsistence wage level. These continuity results all concern a neighborhood of the maximum rate of profit R derived from the subsistence wage situation. An economic consequence of theses mathematical results is that the concept of ‘basic commodities’ needs reformulation from the empirical point of view, since it may (on the physical level) include basics of very minor importance (‘pencils’). These types of commodities must in some way or another be classified as non-basics. They should also not be considered as giving rise to switches of techniques when ball-pens are replacing pencils, in case this latter commodity is no longer available. From a broader perspective, these observation again suggest that the basic/non-basic distinction cannot be meaningfully applied to the highest level of disaggregation (the physical level), but must be reconsidered in its usefulness after some aggregation for appropriately chosen aggregated sets of commodities and aggregated methods of production. This again suggests that an input–output oriented approach as in Bródy (1970), concerning fixed capital, semi-finished products, and now also the notion of basic commodities will be the better choice compared to the physical one that was chosen by Sraffa and his followers.