The Keynesian multiplier

This emphasis on the importance of aggregate demand suggests a multiplier relationship. In Keynesian terms, the aggregate demand for capital goods produced by Department 1 can be defined as investment demand. Since this demand provides for future expansion of means of production, in the current period of production it can reasonably be assumed to be exogenous, not dependent upon any current parameters or constraints. The multiplier provides a possible way of capturing the structural relationship between investment demand and the aggregate income of the economy. 

In the large body of work that has explored the relationship between the systems of Marx and Keynes,5 there is no established understanding of the role played by the multiplier. This can be illustrated by some of the more recent attempts to interpret the multiplier from a Marxian perspective. Two main topics of concern are (1) the role of the multiplier in the reproduction schema and (2) the way in which Marx s category of surplus value relates to the structure of the multiplier. The following brief consideration of this recent literature provides the backdrop to a full critique, in which some of its limitations will be addressed. 

Lianos (1979) provides an accessible insight into how the multiplier can be located in the reproduction schema. By focusing specifically upon Department 1 he states, it is convenient to assume a one sector economy (ibid. 407). Only information from Department 1 of the example used by Marx (Table 2.2) is included in the Lianos reproduction schema, as shown in Table 2.3. The key modification which enables a translation to Keynesian economic categories is to interpret all value added, variable capital plus surplus value, as net income (T,) for Department 1. Assuming away for the moment the problems associated with Adam Smith s dogma, this income is net of constant capital. The net income of the one-good economy is 2,000, consisting of 1,000 units of variable capital and 1,000 units of surplus value. 

A distinction is also made between the current period of production (period 1) and the subsequent period of production (period 2). The aggregate investment demand of 500 is explicitly shown as relating to the expansion of means of production in period 2. This is net investment, additional to the replacement of means of production used up in period 1. 

An analytical leap can now be made that provides the cornerstone of the rest of this book. Located in this reproduction schema is a Keynesian multiplier that enables a relationship to be specified between net investment and net income. The intuition runs as follows. Capitalists anticipate that they will expand their constant capital by 500 in the next period of production. There is therefore a net investment demand for 500 emits of output to be produced in the current period.6 Workers are hired to produce this 

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The main problem with this decomposition of the multiplier is that it is restricted to a one-good model. A contribution which relates the Keynesian multiplier to a two-good model, along the lines of Marx s reproduction schema, has been provided by Hartwig (2004). As a starting point, net income in the two departments is captured by the identities... 

Under Marx s assumption, in Capital, volume 2, that prices and values are identical, and hence 1 of output is equal to an hour of labour time, this equation captures both an income and multiplier relationship. The equivalence between prices and values is embodied in the identity p = v such that the total employment of labour units (vQ) is equal to total money net income (pQ). Similarly, vF the total number of labour emits required to produce final demand, is equal to total money final demand (pF). Hence, the expression 1/1 — vh is an income/employment multiplier, in which the scalar vh represents the propensity to consume b, derived from the two-department schema.10 We shall refer to this as the Keyensian scalar multiplier, since although it is somewhat unusually defined according to worker consumption it retains the l/l h structure that is so common to economics textbooks. The simplicity of the Keynesian multiplier is retained in a two-department setting. 

The role of Marx s category of surplus value can therefore be identified in a macro scalar multiplier without the restrictive assumption of a one-good model. This scalar multiplier captures the inter-departmental structure of the reproduction schema without constant capital being assumed away. A formal model of aggregate demand in the reproduction schema is developed, which retains the simplicity of the Keynesian multiplier together with Marx s value categories. 

Since profits consist of total capitalist consumption and investment, (3.8) could be employed as the scalar for final demand /in (3.4). Substituting (3.8) into (3.4), the Keynesian multiplier takes the form... 

The Keynesian multiplier has as its constituent elements the Marxian term representing the share of surplus value e and the Kalecki multiplier 1/1 A. 

The starting point for this analysis is the Keynesian multiplier... 

Following the analysis carried out in Chapter 3, the Keynesian multiplier can also be synthesized with the Kalecki multiplier. By again redefining the share of surplus value as e, the expression (3.9) can be re-written as8... 

Trigg, A.B. (2002) Surplus value and the Kalecki principle in Marx s reproduction schema , History of Economics Review, 35 104-14. Trigg, A.B. (2002) Surplus value and the Keynesian multiplier , Review of Radical Political Economics, 34(1) 55-65. 

Hartwig (2004 323) modifies his structural multiplier to incorporate constant capital. However, the simplicity of the b/1 —b structure is not retained. His modification requires new elements in the numerator and denominator. My objective is to incorporate constant capital in the Keynesian 1/1 — b multiplier, without losing its simplicity. Although the main purpose of this analysis is to develop the multisectoral structure of the Keynesian multiplier, by implication a contribution can also be made to generalizing the foundations of its structural counterpart. 

De Angelis, M. (2000) Social relations and the Keynesian multiplier , Review of Radical Political Economics, 32(1) 80-103. 

Moore, B.J. (1984) The demise of the Keynesian multiplier , Journal of Post Keynesian Economics, 17(1) 121-33. 

Having nested the multiplier in the reproduction schema, some attention can be given to its structure. As a starting point, the Keynesian income multiplier takes the form... 

On this interpretation b represents the labour-output ratio (L/y) multiplied by the consumption per unit of labour ratio (B/L).7 This expression, it can be argued, represents the value of labour power - the labour embodied in the commodity bundle required to reproduce each unit of labour. Since the propensity to consume is a pure number (money/money), decomposition makes it possible to show that it is identical to the value of labour power (labour/labour), which is also a pure number. An examination of equation (2.1), therefore, reveals that the value of labour power itself (not its monetary expression) appears as the core component of the Keynesian income multiplier. This represents a more revealing insight into the structure of class relationships, with Marx s theory of surplus value directly represented in the denominator of the multiplier. Since the component b is the value of labour power, the denominator —b is the share of surplus value, the proportion of labour time extracted as surplus value. This interpretation of the multiplier penetrates beneath the surface of monetary economic categories as considered by De Angelis, to the Marxian labour categories. 

Since y = B + I, it follows that the traditional Keynesian multiplier (see equation 2.1) can be derived from (2.13) as... 

This demonstrates that the scalar Keynesian multiplier relationship can in principle be derived from a two-sector model. As it stands, however, since (2.14) is defined using net income, no account is taken of the constituent role of constant capital in the production process.9 In embracing Keynes to model aggregate demand, a Marxian response is required to the charge that the scalar multiplier falls prey to Smith s dogma. 

Following the analysis of Chapter 2 (equations 2.15-2.24), the simple Keynesian multiplier... 

What is more, these equally valid ways of defining value are consistent with a macroeconomic interpretation of the autonomous role of money. Since under the Kalecki principle capitalists earn what they spend, the social validation of the market, led by capitalist investment and consumption, is the starting point for economic activity. Commodities are only produced, labour is only employed, if capitalists cast into circulation the money required for sales to be realized - for labour embodied in commodities to become socially necessary. Since money, with its specific role in a capitalist economy, is so central to the Kalecki principle, a possible synthesis can be suggested with the value-form approach without, that is, compromising the use of a Leontief/Keynesian multiplier framework together with embodied labour categories. 

A marked degree of clarity and accessibility is therefore offered by this application of the simple Keynesian multiplier to the circulation of money in a macro economy. In addition, Appendix 4 shows that the interindustry foundations of this model are consistent with Marx s value categories and his definition of investment. As a basis for future research, this macro monetary model is offered as a way of potentially improving communication between the Franco-Italian circuit school and the Marxian and Post Keynesian traditions. 

It should be noted, however, that our application of the new interpretation does not imply that the traditional labour embodied definition of value should be completely abandoned. Foley (2000 30) is open to the possibility that there may be a role for both the new and traditional interpretations of the value of labour power. As Appendix 4 shows, the labour embodied definition of the value of labour power is nested in the input-output model of the circulation of money between departments of production, regardless of how prices are defined. The deviation of prices from values does not modify the constituent role of the labour embodied measure in the interindustry monetary circuit. It is only when a macroeconomic aggregation is developed under price-value deviations, and in the derivation of the scalar Keynesian multiplier, that a switch to the value-form definition is required. 

The result, obtained in Chapter 2, that Marx s category of surplus value can be identified as a constituent element of the Keynesian scalar multiplier, can also be derived for the Leontief matrix multiplier. Starting with the input-output identity... 

Capitalists in Department 2 use this multiplier to anticipate how much consumption goods they need to produce in order to respond to the investment decisions of Department 1. Hartwig (2004) provides a particular interpretation of the methodology employed by Keynes, in which entrepreneurs use the multiplier to plan their outputs at the start of each production period. A key advantage of this multiplier, in comparison to a one-good Keynesian model, is that it embodies the requirement of proportionality between departments of production. 

There is a logical equivalence between this structural multiplier and the more traditional Keynesian variant. By writing (2.11) as... 

Schmitt (1996 123) also argues against the narrow Keynesian specification of the multiplier as a model of impacts between the investment sector and the consumption sector . This is the approach taken by Nell (2004). Following Marx s definition of investment as increments in constant and variable capital, the multiplier in equation (4.23) is exempt from this criticism, locating increments in both sectors. 

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