The long-period theory of demand-led output: synthesising Keynes’ theory of output with Sraffa’s theory of value

Without the acceptance of the marginalist methods of thought, The General Theory would not have had the enormous and relative quick impact that it had on the thinking of mainstream economists.

HERBERT A. SIMON

In revisiting the Sraffa-Keynes synthesis, this essay proffers a hitherto unexplored avenue through which a long-period theory of demand-led output can be fashioned. The main proposition is that Keynes’ theory of output is incomplete insofar as it does not fully account for three issues in value and distribution: investment, competition, and gravitation. It is held that, taken together, these themes are underpinned by the Lakatosian ‘core’ of the Keynesian programme, namely, effective demand and underemployment equilibrium. Sraffa’s pricing theory, it is argued, situates these themes in a broader context that complements the General Theory’s determination of output by completing it. In exploring investment and the interdependence it fosters between capital, demand and uncertainty, the paper demonstrates how the Sraffian interpretation of the surplus approach allows the General Theory to incorporate asset and price transformation without it having to rely on the marginal efficiency of capital or Tobin’s q-theory. The relationship between competition and accumulation in Keynes’ General Theory is then discussed, before turning to the long-period method of gravitation. The paper concludes with a consideration of how Sraffa’s conception of distribution underlies an important resonance with Keynes’ policy prescriptions and helps clarify them, before offering an appraisal of the Sraffa-Keynes synthesis and directions forward.

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Pierro Sraffa (left), Keynes (seated, centre), Dennis Robertson (right); location Tilton, ca. 1927. Reproduced by permission of Dr Milo Keynes. Source: https://doi.org/10.1093/oxfordjournals.cje.a035051

Its prominently open-ended style of analysis granted, it remains a well-known fact of the history of economic thought that J.M. Keynes’ General Theory is incomplete, and conspicuously so. While this opens Keynes’ system to attack, it also affords us the opportunity to draw out some useful connections with the classical political economists which even Keynes may not have perhaps given thought to, had he completed his theory of the political economy definitively and alone. The purpose of this essay is to contribute to the literature by showing how the Sraffian variation of the surplus approach complements Keynes’ determination of output with respect to three important themes: investment (encompassing capitalism’s inherent instability), competition (entailing a theory of accumulation), and gravitation (involving a long-period theory of natural prices). The main proposition is that Keynes’ presentation of these ideas is incomplete and requires complementation. The paper considers how Sraffa’s conception of distribution underlies an important resonance with Keynes’ policy prescriptions and helps clarify them, before concluding with an appraisal of the Sraffa-Keynes synthesis and directions forward.

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Keynes’ Babylonian theory of output is animated by a foundation that does not found. From the peculiarities of human spontaneity, uncertainty and expectations, emerge the real value of the economy’s expected demand for goods and services, Z (Figure 1), which firms use in modelling their production money outlays, PY(Z), a function of ‘the proceeds which entrepreneurs expect to receive from the employment of N men’ (Keynes [1936] 2016: 22). The direction of causality, therefore, runs from demand to supply, and is equilibrated at the point of effective demand, E (Figure 1).[1] However, it is also useful to examine these dynamics in neo-Keynesian (or dynamicised) terms (Figure 2), for if planned output, Y, is below potential output, Y*, unexpectedly lower realised output will aggravate the economy’s contraction, but only ‘in so far as they influence the ensuing expectations in the next production period’ (Keynes 1973: 179). Because a double whammy of this kind is rare, just one setback—lower expected proceeds—is common. To be sure, assuming planned investment is of the form

I = f(r, ΔY, q)

where r denotes the real interest rate, Y, domestic output, and q, Tobin’s market-capital-replacement ratio (Lindenberg & Ross 1981: 3), and disposable consumption, Cd, takes the form

Screen Shot 2018-10-14 at 6.50.23 pm

where  refers to exogenous consumption, c(Y T) to endogenous consumption, and c to the MPC (satisfying the condition that c Î [0, 1]), then we can surmise that if actual investment is equal to planned investment, and actual consumption relates to the individual’s marginal propensity to consume in correct proportion to income, there is nothing to suggest the equilibrium in which we find ourselves is one of full employment, owing to a surplus concomitant with underconsumption. The premise implicit in this chain of reasoning concerns first and foremost the issue of the instability of capital: in particular, the theory of liquidity preference and its special bearing over the real economy, including the role of profitability in adjusting quasi-rents and directing the (often volatile) reproduction of capital.

However, this account is incomplete[2] and conspicuously so, for a demand function of investment cannot, in the first instance, be feasibly established: capital cannot be quantified in physical units, nor aggregated independently of the rate of interest.[3] While Keynes never embraced the aggregate production function[4] his reappraisal of the marginal efficiency of capital permits the extrapolation of neoclassical conclusions from its underlying structure. Secondly, Keynes’ portfolio analysis of investment, elucidated above, requires the addition of Tobin’s q-theory to guarantee internal consistency with the claim that a buoyant stock market ‘inevitably exert[s] a decisive influence on the rate of current investment’ because new projects can be ‘floated off on the Stock Exchange at an immediate profit’ (Keynes [1936] 2016: 151). However, the account of competition and accumulation implicit here does not fully capture the one presented in Chapter 17 of the General Theory, where it is held that a fall in the rate of interest will lower servicing costs and lead to a higher real wage, ensuring that the rate of profit will move in the same direction as, and by a magnitude proportional to, the change in the rate of interest (Keynes [1936] 2016: 229-230).

The third issue, consisting in the long-period conception of gravitation, is also given an unsatisfactory appraisal in the General Theory. While Keynes acknowledges that the economy rounds ‘an intermediate position appreciably below full employment’, and that we must not ‘conclude that the position thus determined by “natural tendencies” … [are], therefore, established by laws of necessity’ (Keynes [1936] 2016: 254) these ‘centres of gravitation’ presuppose a steady growth path featuring disembodied technical progress, in order that they be consistent with an elastic schedule given by the MEC, yet this belies the disruptive nature of investment, which features prominently in Keynes’ analysis.

Taken together, these three dimensions of effective demand and underemployment equilibrium—namely, investment, competition, and gravitation—are incomplete as they appear in the General Theory because the system is set in a Marshallian short period.  reswitching and reversal, the aggregate production function, Tobin’s q-theory and the elastic MEC schedule all pose complications for Keynes’ determination of output because he embraced the marginalist short period. Eatwell (1983: 122) has suggested that, in addressing these concerns, dispensing with a monotonic inverse relationship between the rate of interest and the volume of investment (Figure 3) is required, while Garegnani (1979: 79) has argued for a total overhaul of the system’s microfoundations. These two approaches, however, imply an ex ante trend of the long-period (Nell in which investment does not have a disruptive influence because the long-period level of employment serves as a centre of gravitation for actual values.

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A more fruitful approach, incorporating asset and price transformation into the General Theory via Sraffa’s theory of value, can be found in Rosser’s (2013: 133) ‘eccentric reswitching’ model, presented in Figure 5, where a complex systems schedule maps the implications of capital reversal on the best practice coefficient, embodied in a wage-profit envelope which traces the combinations between the rate of the wage, W, and profits, r (Asada 2009: 92) emerging from a selected from a selected joint-production fixed capital network given by Sraffa’s systems of equations.

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The associated wage-profit frontier[5], shown in Figure 6, graphs a situation in which the final technique, given by a wage rate on the unprofitable side of the midpoint of the frontier, will induce the rates of profit and wages, including the value of capital per worker, to leap over the intermediate zone as the growth rate and consumption per capita approach, asymptotically, the final steady state. However, unlike traditional syntheses where investment forms a part of the movement toward the long-period position, here it stimulates discontinuities in the trajectory, with the rates of return on capital and the wage determined simultaneously. While the Sraffian wage-profit dynamics implicit in the foregoing analysis provides a clear account of the destabilising nature of investment, it also brings to light the General Theory’s failure to account for the causation between the rates of profit and interest underlying these changes and techniques.

The relationship between the rate of interest and the rate of profit features prominently in Keynes’ determination of output (Nell 2005: 293), for it establishes, via investment, the dominant and persistent presence of underemployment equilibrium. Yet the account given in Chapter 17 of the General Theory concerning this issue is incomplete (Nell 1988: 265). Keynes sets out an ‘own-rates’ theory of interest in which various Sraffian-like commodity-rates of interest are measured in terms of themselves as the standard of intertemporal value, therein providing the benchmark against which the rate of a capital-asset must attain if it is to be newly produced (Keynes [1936] 2016: 202). The crucial role of the reward for parting with liquidity in regulating investment is thus asserted. However, Keynes defines the ‘shifting equilibrium’ of the asset market as equating, for all i, all money own rates with the money rate itself, so that the money own-rate, rm, is given by

Screen Shot 2018-10-14 at 6.50.44 pm

where  denotes the commodity own-rate and a^i, the appreciation own-rate (Lawlor 2006: 256), without an explanation of the dynamics underlying the uniformity of profit in the long-period. This ambiguity arises from the absence of any underlying account of competition. In contrast to Keynes’ approach where capital arbitrage and speculation form the means by which the spot and future prices of the stock of assets outstanding on the market are discounted (Perelman 1989: 81), Sraffa looks to the smooth mobility of capital flowing between industries as the dominant and persistent force underlying the equalisation of profits, calculated on a simultaneous basis. The surplus approach allows us in this way to understand why the prevailing ‘natural’ or ‘normal’ rate of interest in Keynes’ analysis will be associated with that profit rate entailing sustained underemployment: when the rate of interest falls, so do normal costs, and following Sraffa’s (1960: 62) key insight, the real wage also, given it is a residual variable. As accumulation gains pace, class conflict and the tendentially regulated market come to interact in a complex iterative process in which the principle of effective demand assumes a central role in shaping the point about which the long-period ultimately gravitates.

The General Theory provides an incomplete description of the long-period tendencies of the economy. In particular, it is unclear where, in the long-period, the economy gravitates given the possibility inherent in Keynes’ model of the establishment of a full-employment rate of interest. This complication arises from the fact Keynes had refuted the ‘monetary route’ to effective demand but not the symmetrical ‘real way’ of the orthodoxy (Garegnani 1983: 69). Sraffa’s theory of value and distribution provides a means of complementing Keynes’ determination of output in the long-period with respect to this real way. The first point to note is that the ‘centre of gravitation’ is inconstant, for

If, for any reason, the supply and demand for a commodity are not in equilibrium … its spot and forward prices diverge, and the ‘natural’ rate of interest on that commodity diverges from the ‘natural’ rates on other commodities. … [T]his divergence of rates is as essential to the effecting of the transition [to a new equilibrium] as is the divergence of prices from the costs of production; it is, in fact, another aspect of the same thing

Sraffa (1932: 50)

The vision of a circular, socially contingent process of production underpinning this appraisal of the long-period path dependency of savings on decisions to invest finds its analytic expression in the supermultiplier relation, first devised by Hicks (1950: 62) and reformulated by Serrano (1995: 79), typically given by

screen-shot-2018-10-14-at-6-50-58-pm.png

where Q denotes the social product; G, normal government expenditure; X, normal exports; zs, the leakage coefficient; k, the mark-up; t, the terms of trade; b1 and b2, the import coefficients; and (g + d)v the gross investment-output ratio, or I/Q, where d represents the fraction of the normal capital stock annually replaced; and v denotes the normal capital coefficient K/Q. Here, an inverse relationship exists between normal output, Q, and the property share in income, 1 – (1/k), determined by zs, the leakage share. It can be demonstrated that the centre of gravitation, although dynamic, rests on an involuntary unemployment outcome. Because unemployment implies the saving-income ratio, ss[1 – (1/k)], exceeds the investment-output ratio, (g + d)v, the higher leakage out of income associated with this level must be replenished with private and/or public consumption, entailing the redistribution of the surplus to normal wage share, 1/k. However, assuming public spending boosts consumption, the tax rate, ts, will rise, and thereby precipitate a fall in the saving coefficient, ss, implying a return to involuntary unemployment (although not in the mechanical sense). While this long-period apparatus precludes functional relationships, it lends credence to Keynes’ intuition that ‘measures for the redistribution of incomes in a way likely to raise the propensity to consume may prove positively favourable to the growth of capital’ (1936 [2016]: 372), an insight that underlies an important resonance between Sraffa’s conception of distribution and Keynes’ policy prescriptions.

In discussing how Sraffa’s theory of value and distribution completes Keynes’ determination of output with respect to investment, competition, and gravitation, a clear picture emerges of the complementarities between the two theories on the effectiveness of fiscal and monetary policies in managing the economy. To this end, the issue of the redistribution of income is a defining theme (Wells 1987: 508). Keynes’ view that for every value of N there exists a ‘corresponding marginal productivity of labour in the wage-goods industries’ and that this ‘determines the real wage’ (1936 [2016]: 29) implies a stable relationship between monetary policy and the distribution of income. However, discounting this marginalist postulate as a view which enabled the analysis leads us to the conclusion that the monetary transmission mechanism channels real changes to key distributive variables in virtue of the endogenous nature of money. That the supply of money is ‘horizontal’ implies in turn that interest-rate determination is not constrained by a natural rate of profitability regulated by the MEC (Pivetti 2001: 115). The relationship between the money rate of interest, therefore, governs instead the ratio of money prices to the money wage, that is, the real wage (Sraffa 1960: 33). In taking into account industrial fluctuations and wage differentials, then, the monetary authority can effect a higher real wage, thereby demarcating what Bortis (2013: 75) terms the ‘market-equilibrium’ of Marshall from the ‘system equilibrium’ of Marx, consistent with Keynes’ insight that the distribution between real wages and profits underpin the equality between savings and investment. However, the associated supermultiplier relation motivates Sraffa’s relatively conservative disposition to fiscal affairs. Because investment represents derived demand in the long-period, profligate deficit expenditure may affect perversely the level of effective demand as consumption is curtailed by tax increases. Accordingly, Sraffa’s budgetary perspective safeguards the efficacy of the ‘socialisation of investment’ championed by Keynes.

The analysis hitherto presented has sought to locate a synthesis between Sraffa and Keynes with respect to the determination of output found in the General Theory. Three promising routes have been identified. The first, concerning investment, draws upon the theory of distribution implicit in Sraffa’s wage-profit frontier to show that investment in the Keynesian context is destabilising; the second, competition, establishes the underlying prescience of underemployment equilibrium on the basis of Sraffa’s theory of accumulation; and the third, gravitation, demonstrates by means of the supermultiplier why Keynes’ determination of output tends about multiple equilibria the ends of which consist in dynamic growth. The famous controversy between Ricardo and Malthus on the possibility of a general glut of commodities, which had been explained away in the high excitement of marginalist infinitesimals, received with the publication of Sraffa’s Production of Commodities by Means of Commodities its foremost scientific embodiment to date. Yet Keynes’ failure to completely refute the return of full employment at the level of the real economy repelled, in the final analysis, attention away from this important discussion toward one concerning the prices of eggs and cups of tea. It is the task now, then, of Sraffians to respond to Keynes’ ideas in a way that is consistent with his vision, acknowledging that the theory must be recast if not redrawn—and weaved, intricately, as it ought to have been—through the fabric of the classical theory of distribution; the theory from which Keynes and his conclusions supposedly transcended.

References


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Bortis, H. (2013), ‘Piero Sraffa and Shackle’s Years of High Theory: Sraffa’s Significance in the History of Economic Theories’, in E. Levrero, A. Palumbo, & A. Stirati (eds.), Sraffa and the Reconstruction of Economic Theory: Sraffa’s Legacy—Interpretations and Historical Perspectives, vol. 3, Berlin: Springer, pp. 55-83.

Cohen, A.J. (1989), ‘Prices, Capital, and the One-Commodity Model in Neoclassical and Classical Theories’, History of Political Economy, vol. 21, no. 2, pp. 231-251.

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Eatwell, J. (1983), ‘Theories of Value, Output and Employment’, in J. Eatwell and M. Milgate (eds.) Keynes’s Economics and the Theory of Value and Distribution, London: Duckworth, pp. 93-128.

Garegnani, P. (1983), ‘Two Routes to Effective Demand: Comment on Kregel’, in J. Kregel (ed.), Distribution, Effective Demand, and International Economic Relations, London: Macmillan, pp. 69-80.

——(1979), ‘Notes on consumption, investment and effective demand: II’, Cambridge Journal of Economics, vol. 3, no. 1, pp. 63.

Hicks, J. R. (1950), A Contribution to the Theory of the Trade Cycle, Oxford: Clarendon.

Keynes, J.M. (1973), ‘The General Theory and After: Part II, Defence and Development’ in Johnson, E. & Moggridge, J. (eds), Collected Writings, vol. XIV, London: Macmillan.

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Nell, E. (1988), ‘Does the Rate of Interest Determine the Rate of Profit?’, Political Economy: Studies in the Surplus Approach, vol. 4, no. 2, pp. 263-267.

——(2005), Transformational Growth and the Business Cycle, Abingdon: Routledge.

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Pivetti, M. (2001), ‘Money endogeneity and monetary non-neutrality: a Sraffian perspective’, in L. Rochon & M. Vernengo (eds.), Credit, Interest Rates and the Open Economy, Cheltenham: Edward Elgar, pp. 104-19.

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Notes


[1] The determination of effective demand can be modelled as a composite function (Asimakopulos 1985: 40) of the form Y = Ne(PY(Z)), where Y denotes output (or the corresponding value of that stock produced by the equilibrium labour force, Ne), Z denotes estimated (or planned) aggregate demand, PY amounts to planned output, and Ne refers to equilibrium employment, as distinguished from full employment.

[2] Keynes’ system is incomplete, not inconsistent. Anything falling outside the bounds of the core of the General Theory—namely, the existence of a monetary production economy—consist in the microfoundations of the system, and insofar as the pricing theory chosen does not bias the content of the core, it serves as a placeholder for a theory of value and distribution which Keynes perhaps had not the time or inclination to fashion. So his theory—far from being inconsistent—is only incomplete.

[3] At least not in a multi-commodity economy or one featuring heterogenous conditions of production. See Samuelson’s (1962: 204) paper concerning this point or Cohen’s (1989) summary for further discussion.

[4] Typically given by Yt = AtF(Kt, Lt), where Yt denotes the quantity of output at time t; At, the technology level at time t; and Kt and Lt the quantity of capital and labour inputs at time t.

[5] where h denotes the gross growth rate of capital; , the gross rate of return; , the final steady-state growth rate; , the time discount rate, and t, the transversality condition of the relevant phase boundary.

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