‘Surplus-levelling’ prices Directory UMM :Data Elmu:jurnal:S:Structural Change and Economic Dynamics:Vol11.Issue1-2.Jul2000:

disease in livestock, the loss of confidence by consumers in important agricultural products and consequent fall in demand may drive down agricultural prices quite sharply in relation to the prices of industry which may be rising sharply at the same time due to the costs of pollution control in cities. In some countries, particularly in underdeveloped regions, this might pose a threat of crisis dimensions quite different in kind from the Russian one, as the already acute process of landflight is accelerated with impoverished peasants flocking into towns in increasing numbers, aggravating conditions in shanty towns with urban misery and disease, not to speak of possible shortages of home-grown produce and the consequent need for costly imports, international borrowing and mounting debt. All this might replicate the Soviet situation of the 1920s with very different causes and different effects. The environ- mental impact of the 20th and 21st centuries may well ensure that scissor crises re-emerge in various guises for a long time to come. It may not be idle therefore to enquire how the relative values of the two major sectors of an economy, those shadow prices constructed by economists to mimic a ‘rational’ price system independent of the vagaries of the market, might be affected by various physical changes; in particular we want to investigate whether the value equilibrium might not be under constant threat from universal, non country-specific developments like the cost effects of technological progress, always to be expected, the more so since, contrary to observed market prices, these effects may be formally implicit in the price models if suitably simplified for all to see. We shall refer to these shadow prices as ‘value-prices’ as opposed to market prices in the rest of this paper, and investigate a more general problem of which scissor crises may be a particular though important sub-species. Even though firm conclusions as regards scissor crises will turn out to be impossible in the general case, it may be useful to establish general rules on the impact of efficiency gains in various sectors on the movement of value-prices, for application to conclusions on scissor prices in specific cases where this is possible.

3. ‘Surplus-levelling’ prices

The link between physical and ‘value’ dynamics which forms the subject of the rest of this paper must of course vary with the precise definition of the value concept adopted, but can be exemplified most clearly and generally with reference to the largest class of value-prices proposed. I have in mind the popular and ever-expanding tribe of value-prices which emerge as the left-hand latent vectors or ‘eigenvectors’ of theoretically defined matrices, their ‘generator matrices’ 2 . 2 A left-hand eigenvector p of a matrix W is mathematically defined as a row-vector whose post-multiplication by the matrix results in a simple scalar product of that same vector, i.e. pw, where the scalar w is known as the ‘eigenvalue’ of W, in fact pW = wp or equivalently where the characteristic determinant wI−W vanishes. The concept of such vectors is intuitively satisfying in that they transform a structure of costs or cost-indicators linearly into sectoral unit-costs which allow prices to exceed costs by a uniform profit- or surplus-margin in every sector, as befits the notion of a residual after all factors explanatory of cost differentials have been allowed for. Such value-prices may be described as ‘surplus-levelling’. They are themselves members of a much larger tribe which might be described as ‘bi-polar’ in that they offer a twofold explanation of value, whereby the main element of it is traced to a set of enumerated production factors exerting their power individually by ‘absorp- tion’, and a secondary constituent, the ‘surplus’, ascribed to all factors collaborat- ing conjointly in creating a value-element in addition to these. To the extent that production factors may be defined as the only sectoral unit cost-indicators dis- played in the matrix W which can account for differential values pW in the production sectors, any value-element remaining over and above these p − pW can only be explained as an undifferentiated and therefore uniform force acting in supplementation of them, i.e. p − pW = kpW. This immediately establishes the value-prices p as the elements of a left-hand eigenvector of the matrix W.

4. The general n-sector case