Scissor crises, value-prices, and the movement
of value-prices under technical change
Francis Seton *
Emeritus Fellow Nuffield College,3 Sta6erton Road,Oxford OX2 6XH, UK
Accepted 5 October 1999
Abstract
The paper defines and exemplifies scissor crises as untoward price movements and their social effects and looks for possible causes in historical developments and for the effects of differential movements in sectoral efficiencies on an important type of ‘rational’ prices. It establishes the parallelism of these price movements with what might be expected to occur in the realm of market prices in the same conditions and investigates the relative speed of causes and effects. The emphasis throughout is on the link between efficiencies and changes in values and thus on the link between physical phenomena and their social effects as mediated by values and prices, effects which in extreme cases could result in the trauma of scissor crises. © 2000 Elsevier Science B.V. All rights reserved.
JEL classification:B14; B24; C67
Keywords:Scissor crises; Shadow prices; Value prices
1. The Russian experience
The world suffered the most telling impact of a scissor crisis in the Soviet Union during Lenin’s New Economic Policy in the mid-twenties of this century. Agricul-tural prices had fallen precipitously from their post-war high to a woefully inadequate level, while industrial prices had cut this declining curve in a powerful upward trend from below at a point corresponding to what was considered traditionally acceptable, thus producing a time-graph in the shape of the scissors which had given the crisis its name. Why crisis? With the terms of trade having
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turned radically against agricultural producers, the peasants, so disastrously disad-vantaged by the market, were sorely tempted to turn away from it and retreat into a primitive form of self-sufficiency, to which, after all, they had long been accustomed under serfdom and even during the subsequent emancipation. If they could not obtain their clothes, shoes, blankets, and other industrial goods on reasonable terms with money obtained from selling their food to the towns at acceptable prices, they would refuse to sell any food at all, consume it all themselves, and make these other products by hand in their own cottages, leaving the towns to starve. In more developed countries this would not be a threat since agricultural producers, long removed from self-sufficiency, would be too dependent on the market ever to contemplate ‘withdrawing from it’. But in a still underdevel-oped economy, such as the Soviet Union was at the time, it was a dire threat indeed, a threat to the urban population and with it to the regime itself and to the success of the Revolution.
The concept of a ‘scissor crisis’ and the term itself probably had their origin in Trotsky’s report to the twelfth party congress in April 1923 in which he produced a diagram showing two ‘blades’ of the price scissors representing industrial and agricultural price levels, respectively, intersecting at the fulcrum of the scissors whose nature was not explained in any detail beyond the fact that it represented the conventional or traditional relative level which had proved acceptable for a historical period. Extensive though the subsequent debate proved to be, the nature of the phenomenon has never to my knowledge been analysed in general terms, probably being too country- and time-specific to arouse the interest of economists as opposed to historians or political analysts.
The cause of the particular Soviet scissor-like movements in market prices, however, was not far to seek. The high post-war agricultural prices induced by war-time scarcities were quickly brought down by recovering agricultural produc-tion as returning soldiers swelled the rural labour force, and neglected, but still fertile land was retaken into cultivation. By contrast industrial prices, at first kept low by what was known as ‘razbazarovanie’ or ‘squandering’, (the competitive scramble to obtain industrial working capital by cut-price sales of raw material and even equipment) experienced a rapid rise as industrial managers realised their mistake and formed enterprise trusts and syndicates with monopolistic intent and effect1.
2. Potential scissor crises
Have we seen the last of scissor crises? Not necessarily. A modern version of the phenomenon may well make its appearance due to the new-found concern with environmental issues. When zealous observers spot a threat to the food chain caused by excessive use of fertilizers or pesticides or by outbreaks of epidemic
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.
2A left-hand eigenvector p% of a matrix W is mathematically defined as a row-vector whose
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 creatcollaborat-ing 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 (p%W) in the production sectors, any value-element remaining over and above these (p%−p%W) can only be explained as an undifferentiated and therefore uniform force acting in supplementation of them, i.e. p%−p%W=kp%W. This immediately establishes the value-pricesp% as the elements of a left-hand eigenvector of the matrix W.
4. The general n-sector case
The starting point is the ‘generator matrix’ a square matrix of order n (the number of sectors) such as
W= Á Ã Ã Ã Ä
a1 b1 ... n1
a2 b2 ... n2 . . ... .
an bn ... nn
 à à à Å
where the elementsa,b, etc., may be termed the ‘generators’, being, as it were, the seed-corn of the left-hand eigenvector of W. The generator in position ij of W
measures the physical input of productior any other cost item involving the use of
iper unit outputi.3
The left-hand eigenvector of such a matrix, sayp%, is defined by the equationp%w=pWand will therefore satisfy the equation
p%(W−wI)p%W0 =0 (1)
wherew is the dominant eigenvalue ofW which makes the characteristic determi-nant W−wI=W0 vanish. It follows that p% will be proportional to the set of first-column cofactors of the characteristic matrix W0 , say A%=[A1, A2, …, An], since A%a is the expansion of W0 by its first column and must therefore vanish, while at the same time the product of A with all other columns of W0 must also vanish since they are the expansions ofW0 by ‘alien’ cofactors. The same holds of all other columns ofW0 , since by virtue of their mutual proportionality, ensured by
3Throughout this paper the matrixWis assumed to be strictly positive and non singular. Nor is this
their derivation from a singular matrix, they will all give the same proportional results as A%a, thus all obeying Eq. (1) which establishes proportionality with p%. This fact may be expressed more concisely by the equation
p%=k(i%r)W0 (2)
implying relativities p1/p2=Ar/As, where k is a proportionality factor, i%r, the rth
row of the unit vector, and rmay be any number from 1 to n. Eq. (2) enables us to convert the market prices of all commodities and of any indicator or aggregate derived from them into the equivalent measure in value prices, but does so only up to a proportionality factor. To establish an absolute conversion we must in addition ‘scale’ the elements of p% to ensure the invariance of any chosen indicator or aggregate in the face of this conversion. The most convenient aggregate from this point of view would seem to be the national income p%y, where y is the column vector of deliveries to final purposes, requiringkof Eq. (2) to be derived from the supplementary equation
ki%rW0 y=y (3)
This ensures that the weighted average of the conversion factors inp%is equal to unity, and therefore any element of it greater/smaller than unity can justifiably be interpreted as the undervaluation/overvaluation of the corresponding commodity by the market.
5. Technological change
We now wish to enquire how the relative value-pricepi/pjor 6ijwill be affected
by technical progress or some change which will bring about changes in all generators, thus transforming the matrix W into a new matrix
V= Á Ã Ã Ã Ä
a1 b1 ... g1 a2 b2 ... g2 . . ... . an bn ... gn
 à à à Å
with eigenvalue v and left-hand eigenvector p. The use of Greek symbols corre-sponding to the Latin parameters ofW saves us from the tedium of repeating the previous derivation and enables us to write the new relative value pricespby simple analogy as
pr/ps=yrs=Fr/Fs (4)
a1=a1/e1, a2=a2/e1, a3=a3/e1, etc.,
b1=b1/e2, b2=b2/e2, b3=b3/e2, etc., and v=w/y (5)
or, in terms of reciprocal efficiencies o1 and h
a1=a1/o1, a2=a2/o1, etc.,
b1=b1/o2, b2=b2/o2, etc., and v=wh
In general, therefore, when efficiency changes vary between sectors and their input utilisation, each element of the co-factorsA and f will grow at a different rate, thus producing changes in relative value-prices which are crucially dependent-on the exact cdependent-onfiguratidependent-on of sizes within W in relation to these rates. The most that can be said about these changes, therefore, is that they are encapsulated in the formula
prps}pr/ps=Fr/Fs}Ar/As (6)
where theAs andFs are, respectively, the first-column co-factors of the generator matrices Wand V before and after the efficiency gains, i.e.
W=
The growth factors of the price relatives (Eq. (6)) are in fact measured by the elements of what may concisely be described as the ‘Hadamard Ratio’4 of the adjoining characteristics of the generators. It can be seen from Eq. (6) that in a world of n sectors the results will be of a degree of complexity and irregularity which does not allow any intuitively helpful statement to emerge, and to that extent the changes in technological efficiency cannot be said to carry any general implica-tions for movements in value-prices, scissor-like or otherwise, unless the precise nature of the generator matrix is specified, though some conclusions may be possible in the case of radically reduced or highly aggregated models. As a theoretical boundary condition it is perhaps worth mentioning that in the
hypothet-4The expression is here introduced by analogy with the ‘Hadamard product’ of two matrices, say
V
ical and obviously unrealisable situation where changes in efficiency are uniform in all sectors, say e6, and equal to the overall efficiency gain h, the co-factors, being determinants of ordern−1 in which each element is multiplied by o, would imply that all value-prices would increase by a factor ofon−1, i.e. reduced in the uniform proportionen−1, in fact that relative value-prices would remain unaffected by the efficiency gains as defined in Eq. (5).
6. The two-sector case
A particularly simple and transparent case, which is moreover of immediate relevance to scissor crises, arises when the number of sectors is reduced to two and when, additionally, the nature of sectors and/or variables is redefined to make the elements in the main diagonal of the generator matrix disappear, thus converting the matrixW into
W=
0 b1a2 0
This makes the eigenvalues,wandvdirectly computable from first principles and allows Eq. (2) to be expressed entirely in terms of the generators and efficiency changes. Indeed,w can be immediately shown to bea2b1, the square root of the product of the off-diagonal elements, since the characteristic determinant
à à Ã
a2b1 b1
a2 a2b à à Ã
evidently vanishes. By the same token v will be o1o2a1b1. Hence the ratio v/w emerges aso1o2or e1e2. Accordingly, as Eq. (2) and Eq. (5) teach us, the now unique change in value-price is from w/b1 to v/b1, and the change in the relative value-price of sector 1 becomes
p12/p12=v/b1}w/b1=(v/w)(b1/b1)=e2/e1e2=e2e1 (6a)
This betokens a rise in the relative value-price of sector 1 ife1Be2, i.e. if sector 1 increases its efficiency by less than sector 2. In fact the less dynamic sector (in terms of efficiency) is compensated by an improvement in its terms of trade, just as the more dynamic sector suffers a virtual tax by a deterioration.
Moreover, if the improvement takes the form of a secular growth convertinge1 ande2into exp(g1t) and exp(g2t), respectively, the secular rise in the value-price will be measured byexp(g2t)/exp(g1t) or exp[
1
2(g2−g1)t], in fact by a growth-rate of one half the physical efficiency lag of the sector in question. Conversely the leading sector will suffer a relative price fall of one half its physical efficiency lead. If, on the other hand, the sectoral efficiencies change in opposite directions (e1B1Be2), i.e.g1is equal to a rate of decline,d1, the resulting change in value-price of the growing sector will be exp[1
their arithmetic mean, while the efficiency-gaining sector will be penalised by a loss in its terms of trade of an equal amount.
This result, in spite of the highly stylised form in whichRhas been obtained, may not be without interest, the more so since it applies to any two-fold division of the economy, whether agriculture and industry, heavy and light industry, material production and services traditional and modern sector, or any of the divisions felt to be structurally important to a given economy.
While smooth secular rises in the generators thus produce similarly smooth, but mitigated movements in relative value-prices, other types of movements may produce aggravated, or even explosive movements in them. Suppose for instance the generators show movements of a sinusoidal type through time as instanced by
el=costande2=sint, having values bounded above and below. The corresponding value movements would then besint/cost=tantwhich increases without limit as time approachesp/2, leaving ample scope for disparities in value-prices that could produce opposing movements such as might engender scissor crises.
7. Specific instances of surplus-levelling value-prices
To give flesh and blood to formulae such as Eq. (2) or Eq. (4) we must of course define the nature of the generators on which they are based. This will depend on the kind of ‘price rationality’ from which they are derived, which in the last analysis is a matter of philosophy or ideology, as will be made clear in the following sections. These will be devoted to certain specific value-price models, and can now largely be confined to deriving the generators appropriate to them for subsequent application of the formulae already established.
The instances dealt with here are given to illustrate the wide range covered by some of the better known concepts that have been examined or touched upon in the literature without their functioning or mutual kinship being always recognised. Our justification for including them is above all that they obey the rules of behaviour in the face of technological change derived in this article, but they are far from exhausting all the specimens of the large genus that may have been uncovered, or even devised as yet.
8. ‘Sraffa prices’
The term is not in common use. I venture to introduce it here in deference to Piero Sraffa because of its evident close kinship with the ‘representative commodity’ or ‘standard commodity’ associated with that famous name.5
5Sraffa’s standard commodity is chiefly valued for its function as a composite numeraire. It was
In the understanding of this author Sraffa rationality may be interpreted as implying a price system which ensures that the factors of production as a whole earn the same reward per unit output in whichever sector they are employed, so that there is no tendency for them to move in search of better rewards. This implies that the structure of total output at these prices must exactly correspond to the structure of value-added in the economy, and therefore also to the structure of material input costs (which are the residual when value-added is subtracted from total output). This requirement implies that wp%=p%A, where A stands for the familiar Leontief matrix of direct input coefficients and represents the ‘generator’a1
b1, in this particular case. This we simplify by interpreting as output only those products which are sold by the producing sector outside itself, thus reducing the generator matrix to
A=
0 b1a1 0
which makes the model precisely conformable to that discussed in the previous section with Eq. (6a) applicable as well as all the subsequent commentary. In particular any time-path of the physical efficienciese1(t) ande2(t) will be reflected in the timepathe2(t)/e1(t) followed by the relative value-price of the first sector.
9. Marxian labour values and production prices
Ever since the publication of Stalin’s Economic Problems of Socialism in the USSR which gave legitimacy to a resumption of research and discussion on the ‘Law of Value’ under Socialism in 1952 Soviet economists have cast about for a new price system to bring order into the chaotic system of administrative, historic, or randomly fixed prices inherited from the past. Their quest was in the Marxist tradition not for a system of ‘functional’ prices which would push the economy in a certain direction, e.g. optimise the allocation of resources, but rather for what I have elsewhere called a ‘diagnostic’ system which would claim to penetrate or see through the veil of actual, adventitious prices to some more illuminating underlying reality, more clearly distilling what was thought to be the essence of the social system, such as the Marxian ‘labour values’ or ‘production prices’ to which we must now turn.
additionally needed to secure each unit of output. In this way the ‘augmented technology matrix’F(=A+E) is formed, which enables us to establish the list of prime costs (for material and labour). The requirement that the surplus generated at these costs be a uniform proportion, saye0, of the wage payments can then be put in the form 6 %(1−F)=e06 %E, or
6 %(1−e0E(1−F)−1)=6 %(1−e
0E0)=0% (7) whereE0(=E(l−F)
−1) will be recognised as the matrix of ‘total’ input coefficients which take account not merely of labour inputs carried by the material products absorbed in production, but also of those inputs necessary to ‘feed’ or sustain the workers of the sector in question by means of (subsistence-) wage-financed con-sumption, thus presenting a higher degree of ‘indirection’ than the ‘full’ coefficients (1−A)−1. The Marxian labour values 6 % are thus shown to be the left-hand eigenvector ofE0, and their generators are the total labour input coefficients in the sense just explained. It is to them that Eq. (6) has to be applied to calculate the changes in value prices in the wake of technological change.
In the Soviet price debates of the 1950s and 1960s one group of economists favoured a switch or transition from the chaotic operative price system to (or towards) the labour values as given by Eq. (7) on the grounds that this would be the system ‘appropriate’ to a socialist economy which had overcome capitalism (with the ‘rate of exploitation’ aptly renamed ‘the rate of withholding’ or some such term). Another group, however, argued that this system would only be appropriate to the ‘full communist’ stage which had not been reached yet, and that the system to be favoured was still a price structure which would equate the rate of profit on prime costs (material plus labour) and therefore of the surplus to the prime cost, sayf0, the system defined as ‘production prices’ in Marxian parlance, say u%, where
u%(I−f0F0)=0%, with F0=F(I−F)
−1 (8)
The generators of these value-prices to which Eq. (6) applies are evidently the total prime cost coefficients per unit output.
10. Eigenprices6
Most of the value-prices proposed in the literature, notably the Marxian prices, of the previous section, are based exclusively on cost elements, neglecting the use values or utilities of commodities and resources. This can be seen most clearly from an alternative definition of the labour values equivalent to Eq. (8) which explains them as the ‘full’ labour coefficients
6 %=l%(I−A)−1 (9)
6Eigenprices are introduced in Seton (1985) and Seton (1992) and put to an empirical test in
wherel% stands for the direct labour-input coefficients. This can be paralleled by a definition of ‘full capital values’, say g%=g%(I−A)−1 or ‘full land values’, say
h%=h%(I−A)−1, (whereg% and h% are the direct requirements of these factors per unit output), or any linear combination of these values weighted at the presumed rental attached to the factors, say r1,r2, r3 or r%B, whereB is the matrix of direct factor requirements per unit output. This yields ‘full costs’ equal tor%C, whereCis the matrix B(I−A)−1 or, when provided with a uniform profit margin, 1/f, the ‘full cost prices’ of commodities.
p%=(1/f)r%C (10)
We can now counterpose to the full-cost coefficients in which commodities are traced back to the primary level a set of ‘full use’ coefficients through which commodity outputs are traced forward to some final use or combination of final uses weighted at their presumed use-values (prices), say p%. These are then trans-ferred to the original factors in proportion to their roles in the production of commodities, thus deriving a second transformation formula. However, this time the transformation is from commodity prices to factor ‘norms’ of the type
r%=p%N (11)
whereNis the ‘norm matrix’ derived from the same input-output table asAandB, though its elements are distribution (output) quotas rather than input coefficients. The ‘norms’ nkj, more fully explained in the author’s The Economics of Cost, Use, and Value, measure the use-equivalent of factorkin terms of commodityi, or equivalently, the output of commodityithat would be lost by withdrawing one unit of k from its production. It is then argued on both consistency and substantive economic grounds that the only rational price system would be the one where the prices of commodities implied by factor rentals (as per Eq. (11)) would imply the initially assumed commodity prices (as per Eq. (10)), and similarly in the opposite direction starting out from factor rentals, i.e.
p%=(1/f)p%NC or p%(fI−NC)=0% and
r%=(1/f)r%CN or r%(fI−CN)=0% (12) These ‘rational’ prices, for which the author has suggested the name ‘eigenprices’ are thus the left-hand eigenvectors of the ‘norm-cost’ matrix in the case of commodities and of the ‘cost-norm’ matrix in the case of factor rentals.
Their ‘generators’ in the case of commodities are the ‘norm-costs’ which are composed of products nrkcks, the full cost of commodity s in terms of factor k multiplied by the norm of factorkin terms of commodity r, products which must be summed over all factors to give the generator Snrkcks, a term which measures the cost ofsincurred in terms of commodityrby shifting the necessary complement of factors fromrtosor more succinctly the ‘factor-diversion cost’ in commodityr
11. Summary and future outlook
Our quest for the technological reactions of value-prices has brought us into contact with a number of specimens of the genus whose characteristics could be unified in a relatively simple way. To achieve this we have introduced the notion of a ‘matrix-generator’ showing in each cell the unit cost of the column item in terms of the row commodity, as flowing from the idea of ‘rationality’ underlying the particular value-price being considered. We have shown that the relative value-price of any itemrin terms of the itemswill be the ratio of the corresponding co-factors in any column in the characteristic generator (Eq. (2)).
Once the generator-matrix of a value-price is specified, it will therefore be possible to compute its relative size without invoking first principles, and to deduce its absolute size with the aid of the supplementary Eq. (3). In addition it is possible to gauge the reaction of any value-price to technological change from Eq. (2) in conjunction with Eq. (3). Warning signals and guiding lights could therefore emerge when framing technological policy.
It should be noted that these procedures tell us nothing about market prices. What they clarify, however, is the relationship between concepts of value and the philosophy on which they are based. In comparing market price behaviour with the behaviour of these concepts we may come to some conclusions on the appropriate-ness of the value-prices and the philosophy that gives rise to them.
From this we may take it that an agenda for the future may emerge. Empirical research on the numerical value of various value-prices and their behaviour under technological change can give us valuable clues and should be promoted by any means possible. It is the author’s hope that this paper may provide some encourage-ment to a culture supporting this.
References
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Dietzenbacher, E., Wagener, E.J., 1999. Prices in the two Germanys. J. Comp. Econ. 27, 131 – 149. Seton, F., 1985. Cost, Use and Value; The Evaluation of Performance, Structure, and Prices across
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Sraffa, P., 1960. Production of Commodities by Means of Commodities. Cambridge University Press, Cambridge.
Steenge, A.E., 1997. The Elusive Standard Commodity: Eigenvectors as Standards of Value. In: Simonovits, A., Steenge, A.E. (Eds.), Prices Growth and Cycles. Macmillan, London, pp. 236 – 254.
