10

The Circuit of Capital

Paulo L. dos Santos and Duncan K. Foley

Introduction

The Circuit of Capital is a conceptual tool first advanced by Marx (1893) to analyze the process of capitalist accumulation, its requirements, and potential contradictions. It is founded on consideration of the characteristic motion or metamorphoses experienced by capital value as it seeks self-expansion through the exploitation of wage-labor, which Marx schematized as,

$M-C(lp,mp)\dots P\dots C\prime -M\prime$ (1)

The circuit is opened as capital value in monetary form M is advanced as capital outlays that purchase input commodities C, including labor power and means of production. Those inputs are combined in productive processes P that result in the completion of output commodities C′. The circuit is closed as output commodities are sold, typically generating revenues M′ that exceed the original capital outlay and realize capitalist profits. Those profits are grounded on the appropriation of surplus value, made possible by the fact that employed labor-power can typically contribute more value to output commodities than its own value. The capitalization of fractions of profits to support growth in the scale of the circuit is taken as the most general foundation for the accumulation of capital—i.e., economic growth.

Marx emphasized the significance of the fact that the movement of capital value through the various phases of (1) took place over concrete, historical time. Mobilized inputs only yield output commodities gradually, giving rise to what may be termed a production lag. Output commodities are sold over time, defining a realization lag. Earnings retained by capitalist enterprises are only gradually recommitted to capital outlays, defining a finance lag. The existence of time lags also ensures three different stocks of capital value accumulate in the circuit. The production lag ensures there are stocks of input commodities tied up in production; the realization lag ensures there are inventory stocks of unsold output; and the finance lag ensures there are stocks of capital in monetary form awaiting recommitment to the circuit.

Aggregate social capital is composed of myriad pulses of value traversing the circuit, so that at any given time a certain measure of value is engaged in each stage of the process. The demand and supply for commodities may be considered in relation to individual circuits, resulting in a dynamic macroeconomic framework defined by the necessary relationships between time lags and the stocks and flows of capital value. Marx sought to use this broad approach to cast light onto issues like the supply and demand relationships between industries producing consumption and investment goods, the dynamic determinants of profitability in accumulation, and the formation of what is now called aggregate demand.

Foley (1982) codified the Circuit of Capital into a well-specified dynamic model of capitalist accumulation. This resulted in a distinctively broad analytical framework offering a deliberate, stock-flow-consistent account of the dynamic interaction between productive and consumption undertakings. Against this framework, most neoclassical, Keynesian, and Kaleckian aggregative models of accumulation may be understood as special cases of the Circuit of Capital. Foley’s (1982) formalization has also been recently applied and extended to consider a range of important productive and financial developments that dynamically condition growth, profitability, and distribution in contemporary capitalism.¹

The Framework

The Circuit of Capital consists of three flows of value—capital outlays, the value of finished output, and sales—and three stocks of value—productive capital, inventories, and financial or money capital. The flows of value are governed by five parameters—the markup on costs (which is defined by the rate of exploitation and the composition of capital), the proportion of profits recommitted to the circuit (called the rate of capitalization below), and the three time lags in the circuit—the production lag, the realization lag, and the finance lag.

In constructing a mathematical representation of the circuit it is easiest to make the simplifying assumption that the time lags in the circuit are simple delays. Hence, it will be assumed that a dollar advanced as capital stays in the production process for a given time period and then emerges all at once as finished product. A more general, but mathematically more complicated, approach to time lags allows value to flow gradually through different phases in the circuit.²

Let Z_t, P_t, S_t respectively represent flows of capital outlays, finished commodities (valued at cost), and commodity sales during time period t. Similarly, let П_t, N_t, F_t respectively denote the stocks of productive capital; goods in inventory (valued at cost); and financial or monetary capital during that period. The composition of capital will be measured by the fraction k of capital outlays that is taken to purchase labor power. Profits represent a realization of a markup on costs q = kε, where ε measures the rate of exploitation. The production, realization, and financial delays in the circuit will be given by T_p, T_r, T_f. Their sum defines the total turnover time of the circuit and is represented by τ.

The equations of the framework simply record the assumptions made about time lags and accounting conventions. The flow of finished output during a point in time will be equal to capital outlays undertaken T_p periods earlier,

$P_t=Z_{t-T_p}$ (2)

Along similar lines, sales taking place during a time period correspond to the output commodities completed T_r periods earlier. Sales generate revenues that represent both the recovery of production costs and profits,

$S_t=(1+q)P_{t-T_r}$ (3)

The fraction of total sales representing the recovery of production costs, and the fraction representing profits are respectively given by,

${S^{\prime }}_t=\frac{1}{1+q}{S}_t$ (4)

$S_t^{\prime }=\frac{q}{1+q}{S}_t$ (5)

A fraction 1 – p of profits is spent in capitalist consumption, ensuring p is a propensity to save profit income by the capitalist sector. If capital outlays draw exclusively on own funds, capital outlays will be,

$Z_t=S_{t-T_f}^{\prime }+p{S}_{t-T_f}^{″}$ (6)

The accounting rules relating balance sheets and income statements establish the laws governing changes in the stocks of value in the Circuit of Capital. For instance, the stock of productive capital is increased by capital outlays, which mobilize means of production and labor-power, and is decreased as finished output emerges from production. Using ${\dot{\text{Q}}}_{\text{t}}$ to denote the time rate of change of any stock Q_t, we have,

${\dot{\Pi }}_t=Z_t-P_t$ (7)

In a similar fashion, inventories are increased by finished output flows and decreased by production costs recovered by sales, while the stock of financial or monetary capital is increased by sales revenues and decreased by capitalist consumption and capital outlays,

${\dot{N}}_t=P_t-S_t^{\prime }$ (8)

${\dot{F}}_t=S_t-(1-p)S_t^{″}-Z_t=(1+pq)S_t^{\prime }-Z_t$ (9)

Equations (2)–(9) constitute the basic model of the Circuit of Capital.

Simple Reproduction

The simplest case of the model developed above to examine is the simple setting where all profits are consumed, leaving no funds to increase the scale of reproduction. Marx termed this case simple reproduction. As no profit capitalization takes place, enterprises only retain revenues corresponding to the recovery of production costs, ensuring that the scale of capital outlays (and of accumulation) is constant,

$Z_t=P_t=S_t^{\prime }$ (10)

The model cannot establish how large these flows will be; all it can establish is that they will stay at whatever level they have once the economy “starts.” It also establishes that capitalists consume the totality of profits, given by $q{S}_t^{\prime }$.

The identities contained in (10) also ensure that the stocks of capital value described by (7)–(9) do not change along this accumulation path. As the length of time it takes value to flow through each one of these stocks is given by the respective fixed delays, it is possible to establish how large balance-sheet stocks must be. Since it takes exactly T_p units of time for value committed by capital outlays to production to emerge as finished output, the total stock of productive capital must be equal to Z_tT_p. By the same reasoning, and (10), it can be established that,

${\Pi }_t=Z_t{T}_p$ (11)

$N_t=P_t{T}_r=Z_t{T}_r$ (12)

$F_t=S_t^{\prime }{T}_f=Z_t{T}_f$ (13)

Total capital value in circulation X_t, which consists of the sum of these three stocks, is given by,

$X_t=\tau Z_t,$ (14)

It is now possible to turn formally to the dynamic determinants of growth, profitability, and distribution in simple reproduction. Obviously growth will be zero. The rate of profit ρ is given by the ratio of profit flows to total capital value in circulation. Formally,

${\rho }^{\underset{\_}{\underset{\_}{\text{def}}}}\frac{S_t^{″}}{X_t}=\frac{q{S}_t^{\prime }}{\tau Z_t}=\frac{q}{\tau }$ (15)

Marx put considerable weight on this relationship, which helps highlight oft under-appreciated dynamic determinants of the aggregate profitability of capital. Relationship (15) states that the rate of profit is determined by the input-cost markup and by the circuit’s turnover time. The mark-up rate measures how much a unit of value expands in a single turnover in the circuit. The turnover time establishes how many turnovers take place during any given unit of time. The ratio in (15) thus measures by how much value committed to the circuit expands per unit of time—a natural dynamic measure of profitability. All factors determining the paces at which value travels through each phase of the circuit will thus directly condition profitability, alongside the rate of exploitation and the composition of capital.

Finally, the functional distribution of income may be measured by the ratio of profits to wages, denoted by ψ. In simple reproduction, this ratio will be given by,

${\psi }^{\underset{\_}{\underset{\_}{\text{def}}}}\frac{S_t^{″}}{k{Z}_t}=\epsilon \frac{S_t^{\prime }}{Z_t}=\epsilon$ (16)

As with profitability, the class distribution of income is shown here to have important dynamic determinants in the accumulation of capital. Distribution is obviously shaped by the rate of exploitation, given by the ratio of average unpaid to paid labor time in production. It is also conditioned by the ratio of the present, cost-accounted value of commodity sales and present capital outlays. This ratio conditions distribution because, as Marx was at pains to emphasize, profits and wages do not represent a sharing of output. Wages logically pertain to the opening of the circuit—the capitalist decision to produce. Profits pertain to the closing of the circuit—as output commodities are sold and their value, including surplus value, is realized.

The ratio in (16) has an intuitive interpretation as a measure of capitalist “animal spirits.” Cost-accounted sales measure the past capital outlays that opened the individual circuits being presently closed by the sale of their outputs. The ratio thus provides a natural measure of the extent to which capitalist enterprises are effectively expanding the scale of the aggregate circuit. In simple reproduction this ratio will be one, ensuring that the rate of exploitation describes exhaustively the ratio of aggregate profits to aggregate wage flows. As is taken up below, this is not generally the case in the process of accumulation.

Expanded Reproduction with Say’s Law

It is possible to relax the assumption that no capitalization of profits is taking place. This allows consideration of expanded reproduction, in which accumulation takes place at growing scales. For now, the assumption made above of a given realization lag will be maintained, ensuring that aggregate demand consistently allows the timely sale of output—i.e., that Say’s Law holds. Instrumentally, expanded reproduction implies all flows and stocks are increasing at the same, unknown, exponential rate g. Along such evolutions, all stocks and flows Q_t will evolve according to Q_t = Q₀e^gt. Note also that this means that Q_t–x = Q_te^–gx. This ensures that ratios between any two stocks or flows remain constant along these evolutions. Exponential, expanded-reproduction evolutions may thus be interpreted as evolutions with commodity-market and monetary equilibrium, in the sense that aggregate ratios of sales to inventories, sales to productive capacity, and of financial and real holdings to total assets, remain constant.

A few substitutions involving the system outlined in section two make it possible to investigate the properties of expanded-reproduction evolutions of this kind. Because current sales depend on past production, and because past production depends on even earlier capital outlays, current sales may be related to the capital outlays that financed the production of commodities being currently sold. Formally, (2) and (3) ensure that,

$S_t=(1+q)Z_{t-(T_p+T_r)}$ (17)

Present capital outlays are in turn financed by past retained earnings. By (4)–(6), this dependence may be expressed as,

$Z_t=(1+pq)S_{t-T_f}^{\prime }$ (18)

From (4), (17), and (18), it is possible to relate present capital outlays to their past values, casting light onto the dynamic evolution of the circuit,

$Z_t=(1+pq)Z_{t-\tau }$ (19)

Since capital-outlay flows are assumed to evolve exponentially, this may be expressed as,

$Z_0{e}^{gt}=(1+pq)Z_0{e}^{g(t-\tau )}$ (20)

Simple manipulation yields the system’s rate of growth,

$g=\frac{1}{\tau }ln[1+pq]$ (21)

A number of important insights about expanded reproduction in capitalist economies are contained in this equation. Both the markup and capitalization rates condition the rate of expansion of a capitalist economy. The expression 1 + pq measures the rate at which a unit of capital value self-augments during one turnover of the Circuit of Capital. It is conditioned by the extent to which social relations and the development of productive forces permit the exploitation of wage labor, and the measure to which the resulting surplus is effectively used to expand the scale of reproduction. As expected, the rate of growth of capital value in historical time is fully described by this measure divided by the circuit’s turnover time.

It is possible to find expressions for the value of a few economically significant stock-flow ratios along exponential, expanded-reproduction paths under the present specification. To do this it is useful to normalize the system to the measure of productive capital outlays at time zero, so that Z₀ = 1. From this, (2), and (3) it is possible to establish the relative measure of output-commodity flows, sales and its two constituent parts along exponential, expanded-reproduction paths,

$P_0=e^{-g{T}_p}$ (22)

$S_0=(1+q)e^{-g(T_p+T_r)}$ (23)

$S_t^{\prime }=e^{-g(T_p+T_r)}$ (24)

$S_t^{″}=q{e}^{-g(T_p+T_r)}$ (25)

It is also possible to find the relative magnitude of the three stocks of capital value in the economy. For instance, along exponential evolutions the stock of productive capital must be growing at the same rate as the rest of the system. Thus, П_t = П₀e^gt. But by (7) the time derivative of this must be equal to capital outlays minus commodity-output value flows,

${\dot{\Pi }}_t=g{\Pi }_0{e}^{gt}=(Z_0-P_0)e^{gt}$ (26)

But since we have normalized the system to the steady-state measure of capital outlays, so that Z₀ = 1, and (22) tells us that $P_0=e^{-g{T}_p}$, it follows that the value of productive capital relative to capital outlays is given by,

${\Pi }_0=\frac{1}{g}(1-e^{-gTp})$ (27)

Following the same line of reasoning, it may be shown that,

$N_0=\frac{1}{g}(1-e^{-g{T}_r})e^{-g{T}_p}$ (28)

$F_0=(1+pq)\frac{1}{g}(1-e^{-g{T}_f})e^{-g}{}^{(T_p+T_r)}$ (29)

$X_0=pq\frac{1}{g}{e}^{-g}{}^{(T_p+T_r)}$ (30)

The rate of profit along exponential, expanded-reproduction paths will be given by the relative magnitude of profits divided by the relative measure of total capital value committed by enterprises,

$\rho =\frac{S_0^{″}}{X_0}=g\frac{q{e}^{-g(T_p+T_r)}}{pq{e}^{-g(T_p+T_r)}}=\frac{g}{p}=\frac{1}{p\tau }ln[1+pq]$ (31)

Note that (31) is the Cambridge Equation establishing the equilibrium relationship between the rates of growth, profit, and capitalization. Note further that if pq is sufficiently near zero, this expression will be arbitrarily close to the measure of profitability in simple reproduction,

$\rho \approx \frac{q}{\tau }$ (32)

Finally, it is possible to consider the measure of the class distribution of income provided by the ratio of profits to wages along expanded reproduction paths, which as above is given by,

$\psi =\epsilon \frac{S_0^{\prime }}{Z_0}$ (33)

Unlike simple reproduction, positive growth in the scale accumulation by definition requires ongoing expansion of the scale of capital outlays. This means that at any point in time, present capital outlays are greater than the past capital-outlay commitments being presently recovered through sales. The exact relative measure of these asynchronous capital outlays shapes the aggregate class distribution of income over and above the rate of exploitation. Generally, this measure may be taken to capture the aggregate investment responsiveness of capital to sales.³ In the dynamic, fixed-lag terms of the present Circuit-of-Capital framework, this will be given by,

$\frac{S_0^{\prime }}{Z_0}=e^{-g(T_p+T_r)}=(1+pq)e^{-\frac{T_p+T_r}{\tau }}=(1+pq)e^{\left(\frac{T_f}{\tau }-1\right)}$ (34)

As should be expected, this ratio depends on the per-turnover growth in capital value made possible by the realization of profits and their capitalization. But it also depends on dynamic relationships defined by the three time lags in the circuit; specifically, on the share in total turnover time represented by the finance lag. Along exponential-growth paths, this share dynamically conditions the magnitude of capital outlays relative to sales. Shorter financial lags ensure this magnitude decreases, so that for a given pattern of consumption behavior by wage earners, they result in greater wage shares of aggregate income. Conversely, quicker production and realization lags will result, ceteris paribus, on greater profit shares of aggregate income.⁴

Demand-Driven Growth

Marx (1893) also used his discussions of the Circuit of Capital to investigate the problem of aggregate demand, seeking to locate the source of the money flows that allow the sale and of produced commodities at their value. The first insight this offers is that the money demand for produced commodities arises directly or indirectly from the Circuit of Capital itself. This point is also the basis of Keynes’s analysis of aggregate demand, which can be situated within the analytical terms of the Circuit of Capital. This can be done by extending the framework developed above so that deliberate attention is given to the interactions between production, consumption, and balance-sheet decisions and the formation of aggregate demand. On these bases it is possible to obtain important insights concerning the dynamic relationships conditioning growth, profitability, and distribution in an expanding economy.

Aggregate demand in a closed, private economy may be divided into three exhaustive categories: demand by capital for means of production, demand by wage earners for consumption goods, and capitalist demand for consumption goods. While consumption demand may be interpreted to involve time lags between revenues and expenditures (in a manner analogous to the finance lags), analysis is greatly simplified if consumption out of wages is taken, like consumption out of profits above, as a given fraction of wage income.⁵ Aggregate demand will then be,

$D_t=(1-k)Z_t+c^{w}k{Z}_t+(1-p)S_t^{″}=(1-k(1-c^w))Z_t+(1-p)S_t^{″}$ (35)

where c^w is the marginal consumption propensity of workers. Aggregate demand funds sales, which by (4) and (5) may be decomposed into profits and recovered costs,

$D_t=S_t^{\prime }+S_t^{″}$ (36)

Subtracting capitalist consumption from both sides of (36), and assuming that capital outlays are entirely financed from unconsumed capitalist revenues, as described in (18), it follows that,

$(1+pq)S_t^{\prime }=(1+pq)(1-k(1-c^w))S_{t-T_f}^{\prime }$ (37)

Along exponential, expanded-reproduction paths, this condition holds only if,

$g{T}_f=ln[1-k(1-c^w)]$ (38)

Since the finance lag is non-negative, this condition is only satisfied by negative rates of growth if workers save, that is, if c^w < 1. Even if workers consume all of their income, (38) holds only if the rate of growth and or the finance lag are zero. Positive growth sustained by the capitalization of profits appears impossible in this light, unless the finance lag is allowed to vanish to zero—which would correspond to a setting with an infinite velocity of money and arbitrarily illiquid positions for capitalist enterprises. Under a constant, positive finance lag, past retained earnings cannot support the growing scales of capital outlays necessary to ensure growth in the scale of profit capitalization—even before savings by workers are considered.

This apparent predicament for the accumulation of capital drew the attention of Rosa Luxembourg (1913), who based her analysis of imperialism on it. Seeking to provide a systematic, economic foundation in the accumulation of capital for the sharpening inter-imperialist rivalries of her time, Luxembourg argued that a closed capitalist system undergoing accumulation would always run into inadequacies of aggregate demand and as a consequence would be forced to seek external markets to realize its surplus production. Luxembourg was entirely correct in identifying a difference in Marx’s system between aggregate demand and the needs of realization in any setting where a fraction of profits is being capitalized (and or workers save). But her argument that this provided an economic imperative for imperialist expansion which alone could ameliorate the problem was not convincing. Where do the external markets get the money to buy the surplus product of the capitalist system? If they get them from selling something to the capitalist system, they add as much as they subtract from aggregate demand.

Marx himself, at the very end of Volume II of Capital (1893, 522–3), proposes an alternative view, which was taken up by Bukharin’s (1924) critique of Luxemburg. In a commodity monetary system, the monetary commodity does not need to be realized through sale. It is already value in monetary form. In such a setting it is possible to imagine a situation in which the output flows of this sector match exactly the desired “savings” of capitalists and workers. While logical, this argument is contrived. A more convincing argument is already latent in (38), which implies that if wage earners are willing and capable of consuming in excess of their income, positive rates of growth are possible. In such a setting, the demand for the capitalization of profits is ultimately accommodated indebtedness by wage earners.

More broadly, the development of credit systems and credit-monetary forms may be understood to offer a potentially flexible means of mediating the desire to accumulate capital value in monetary form by capitalists and wage earners, and the desire of some enterprises or some wage earners to spend in excess of their present revenues. Suppose that total capital outlays are financed through a combination of past retained earnings and present net borrowing, so that,

$Z_t=(1+v)(1+pq)S_{t-T_f}^{\prime }$ (39)

Where ν offers a measure of leverage supporting capital outlays. Following the same process leading to (37), but using the expression for capital outlays in (39) instead of (18), this yields,

$(1+pq)S_t^{\prime }=(1-k(1-c^w))Z_t$ (40)

The flows in the economy are fully described by (2), (4), (5), (39), and (40). Productive capital and inventories still evolve according to (7) and (8). Two more sets of specifications complete the model. First, characterizations of the evolution of the financial position of each sector are necessary. Under a simple credit-monetary financial system, a sector’s financial position is exhaustively measured by its net monetary position, given by the sum of money holdings and debt obligations. Abstracting from interest flows, wage earners see their net monetary position evolve in line with their savings,

${\dot{M}}_t^w=(1-c^w)k{Z}_t$ (41)

The equivalent position for capital evolves according to retained earnings and capital outlays,

${\dot{M}}_t^c=(1+pq)S_t^{\prime }-Z_t$ (42)

Note that by (40), ${\dot{M}}_t^c=-{\dot{M}}_t^w$, in line with the aggregate source-use identity this economy.

An important, second specification relates to the evolution of inventories and the scopes for aggregate demand to determine the economy’s rate of growth. Demand in excess of inventories results in demand-pull inflation, not real output growth. Demand can only determine output or growth in settings where aggregate inventories are positive.

Expanded Reproduction with Demand Determination: Limits and Types

The model just outlined may be solved for exponential, expanded-reproduction paths. Their characteristics offer important insights into the interactions between aggregate demand, commodity production, and balance-sheet behavior that shape a capitalist economy’s rate of growth, aggregate profitability, and income distribution. This includes a few useful conclusions that are unattainable on the basis of most conventional macroeconomic approaches.

As above, equations (39) and (40) define the system’s demand-determined rate of growth,

$g=\frac{1}{T_f}ln[(1-k(1-c^w))(1+v)]$ (43)

Which holds for all exponential evolutions along which inventories are positive, i.e., N_t > 0.

Using the measure of capital outlays to normalize the economy, it is possible to find expressions for the relative measure of all steady-state flows and stocks in the economy. Output flows will be given as in (22). The cost-accounted measure of sales can be established from (40),

$S_0^{\prime }=\frac{1-k(1-c^w)}{1+pq}$ (44)

The stock of productive capital will be as given by (27). In contrast, the measure of inventories is different under demand determination. Their evolution along expanded reproduction follows,

${\dot{N}}_t=e^{-g{T}_p}-\frac{1-k(1-c^w)}{1+pq}$ (45)

Which ensures that the steady-state inventory stock is,

$N_t=\frac{1}{g}\left(e^{-g{T}_p}-\frac{1-k(1-c^w)}{1+pq}\right)$ (46)

The net monetary position of wage labor and capital will in turn be given by,

${\dot{M}}_0^w=\frac{1}{g}k(1-c^w)=-{\dot{M}}_t^c$ (47)

Adding up all assets and liabilities of capitalist enterprises yields their net worth,

$W_0=\frac{1}{g}\left(\frac{pq(1-k(1-c^w))}{1+pq}\right)$ (48)

A number of observations follow from (43)–(48). First, the expression for the economy’s demand-determined rate of growth makes it clear that the “paradox of thrift” holds in the present framework. Lower measures of leverage in capital outlays and lower consumption propensities by wage earners, result, ceteris paribus, in lower rates of growth. In this important sense the present framework echoes one of the central conclusions of Keynesian approaches to the role of demand in setting output and growth. But it does so within analytical terms that explicitly account for the dynamic interplay between aggregate demand and productive undertakings. This helps broaden conclusions drawn on standard Keynesian bases.

This is most readily evident in the recognition that demand can only exert an independent influence on the real measure of output if inventories are positive. Formally, this requirement may be expressed for expanded-reproduction paths by using (46), which yields,⁶

$g\le \frac{1}{T_p}ln\left[\frac{1+pq}{1-k(1-c^w)}\right]$ (49)

This inequality defines the upper-bound for the economy’s rate of growth. This constraint is defined not only by the savings behavior of wage earners, but also by two supply-side constraints—the production lag, which measures the dynamic pace at which inputs can be transformed into outputs, and the rate at which profits are capitalized to finance expansions in the scale of productive investment. Here the Circuit of Capital offers an explicit characterization of the dynamic, productive constraints that define the scopes within which aggregate demand may act as an independent determinant of the pace of economic activity.

The endogenous expression for the economy’s rate of growth in (43) also points to a useful distinction between two broad types of changes that may boost the economy’s rate of growth. Within the limits defined by (43) and (49), growth may be increased either by increasing the aggregate consumption propensity of wage earners, or by increasing leverage and the pace at which retained earnings are recommitted to capital outlays. The first possibility sees growth boosted by increases in measures of consumption by wage earners in the economy. This may be called “consumption-led growth.” In the second possibility growth is boosted by increases in measures of capital outlays, in what may be broadly called “investment-led growth.”

One important feature of this distinction that is suggested by the analytical terms of the Circuit of Capital is that the two types of growth generally have opposing effects on the distribution of income. In the present setting, the ratio of profits to wages is given by,

$\psi =\epsilon \frac{(1-k(1-c^w))}{1+pq}$ (50)

“Consumption-led” growth defined by comparatively higher consumption propensities by wage earners will exhibit comparatively greater profit shares in aggregate income. Conversely, increases in the relative measure of investment ushered by greater profit capitalization rates will result in comparatively higher wage shares.⁷ In the Circuit of Capital, the relative measure of consumption and productive outlays in aggregate demand directly influences the aggregate distribution of income.

Consumption and investment undertakings will also shape the aggregate profitability of capital in settings of demand determination. Profitability in the present setting may be measured as the return on net worth, given by (44) and (48), from which it follows that,

${\rho }^{\underset{\_}{\underset{\_}{\text{def}}}}\frac{q{S}_0^{\prime }}{W_{\text{0}}}=\frac{g}{p}$ (51)

As above, this is a simple statement of the Cambridge Equation, where growth is given by (43).

The Circuit of Capital distinctively shows that developments like greater leverage in capital outlays, quicker paces of recommitment of enterprise retained earnings to investment, and more aggressive consumption behavior by wage earners, etc. all contribute to growth according to their impact on the measure of aggregate demand—within the limits specified by (49). But each of those developments contributes to the class distribution of income according to its impact on the composition of aggregate demand.

Finally, the present specification points towards the financial or monetary requirements of expanded reproduction. Note that (43) implies that positive growth only takes place when,

$\frac{v}{1+v}>(1-c^w)k$ (52)

In words, borrowing by enterprises must exceed savings by wage earners. Private-sector savings are insufficient to supply the volume of loans necessary to meet growing demand for money holdings. Growth requires a consistent, positive injection of means of purchase into the economy—i.e., monetary expansion. This need may be understood as a primary driver of the development of contemporary credit-monetary systems. The Circuit of Capital offers a distinctively useful basis on which to theorize the development of those systems, the contradictions they may throw up, and their relationship to the process of accumulation. As such, the Circuit of Capital may be usefully applied and extended further to provide systematic accounts of the social and macroeconomic content of contemporary capitalism and its distinctive financial practices and relations.

Notes

1    See Abeles (2013) for an application to the problems of contemporary open economies; Basu (2014) and dos Santos (2011) for consideration of the impacts of credit allocation; Jiang (2014) for a dynamic, agent-based model founded on the Circuit of Capital; and dos Santos (2014, 2015) for applications to the contemporary determinants of the functional distributions of income and wealth. A number of additional, interesting applications by other authors are currently in press.

2    The general, distributed-lag framework was first advanced in Foley (1982) and fully developed in Foley (1986a). Foley (1986b) set out the simplified, time-delay specification grounding the present discussion.

3    The theoretical significance and pertinence of these determinations to contemporary capitalism was first motivated in dos Santos (2014, 2015).

4    It is possible to express these two points in relation to important stock-flow ratios that are defined by the three time lags under consideration. Dynamic evolutions where capital is willing to maintain total asset positions that are less liquid, in that they hold greater measures of productive capital relative to money, will exhibit, ceteris paribus, higher wage shares. Conversely, evolutions with quicker paces of production, higher rates of utilization of fixed capital, and tighter inventories will in turn exhibit comparatively higher profit shares.

5    For the purposes of the present discussion, this involves no loss of generality. For a general approach to Circuit-of-Capital frameworks with dynamic consumption lag processes, see dos Santos (2014).

6    The full expression of this constraint in terms of the exogenous variables under the current parametrization is given by $1+pq>{(1+v)}^{T_p/T_f}{(1-k(1-c^w))}^{1+T_p/T_f}$.

7    In most general settings, cases of “investment-led” growth defined by higher measures of leverage in capital outlays and quicker paces of investment of enterprise retained earnings will also result in comparatively higher wage shares. This is not the case here only because the specification of consumption by wage earners implies that the capital-outlay elasticity of aggregate demand is exactly one. See dos Santos (2014).

References

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