The Genuine Meaning of Keynes’ Multiplier*
By Ezra Davar
This paper shows that Keynes’ investment multiplier and Kahn’s employment multiplier are different: (1) Kahn’s approach is compatible with the second phase of the investment process, when fixed capital (investment) is determinant; while Keynes’ approach is compatible with the first phasewhen investment (saving) is determinate; (2) The source of an additional increment of investment in Kahn’s approach is exogenous, whilst in Keynes’ approach is endogenous.
Also, Keynes’ investment “multiplier” is a reciprocal of the marginal propensity to invest (save); therefore, its genuine meaning is that of a requirement, which indicates the quantity of national income required to realize one unit of investment (saving).
Keywords: Multiplier, Requirement, Walras, Keynes, Kahn, General Equilibrium Theory
JEL Classifications: B, D5, and E2
Author: Dr, Ezra Davar, Ben-GurionUniversity of the Negev
Yehuda Hanasi St. 15/17
* The paper waswritten to the 2003 UK HET Conference, Leeds, 3-5 September
The Genuine Meaning of Keynes’ Multiplier
By Ezra Davar
“The traditional analysis has been aware that saving depends on income but it has overlooked the fact that income depends on investment, in such fashion that, when investment changes, income must necessarily change in just that degree which is necessary to make the change in saving equal to the change in investment.” Keynes, The General Theory, p.184
The multiplier is one of the main tools for establishing a relationship between income, investment, consumption and employment developed by Keynes in his “The General Theory”. Since its very first appearance, the attitude towards the multiplier has been ambiguous. One group of economists (mainly Keynes’ followers) state that the Keynesian multiplier is a new paradigm in economic theory and that it is a milestone in the development of macroeconomic theory. Blaug writes (p.189): ‘The principal novel prediction of Keynesian economics is that the value of the instantaneous multiplier is greater than unity’ (see also Pasinetti, p.40). Yet, some scholars stated that "This is, no doubt, in a general way, correct" (Pigou, 1936). And "In order to avoid any possible misunderstanding, let me conclude this paper by emphasizing that there can be no doubt about the importance of Kahn's 1931 multiplier article in the history of the development of macroeconomic theory. Nor can there be any doubt that his multiplier formula is logically equivalent to the theory of effective demand" (Patinkin, pp.324-5). But at the same time, there were economists who indicated doubt regarding the multiplier "... it seems to me doubtful whether, for the analysis of a fluctuating world, the "multiplier" constitutes much advance over more crudely "monetary" weapons of thought".(Robertson, 1936); Another group posed serious doubts concerning the multiplier’s correctness (Ahiakpor, 2001; Hazlitt, 1959). There are authors who considered multiplier as a dynamic phenomenon (process) (Goodwin, 1947; Hansen, 1953) and V. Chick claims that Keynes’ multiplier has two views: equilibrium and dynamic (Chick, 1983). Many arguments were raised against it, such as: the multiplier is severely static (Schumpeter, p.1174) unrealistic, characterized by instability, and so forth.Keynes’ followers have been attempting to "improve" the theory (multiplier) of Keynes in order to silence such critics. A central argument, often used by them, is that the multiplier has rests on a solid mathematical foundation (Minsky, 1975). In addition, several papers show that ‘the balanced-budget expenditure has a multiplier of exactly one;’ (Samuelson, 1966; see also Samuelson, 1974; Salant, 1974 (1942); Haavelmo, 1943; Turvey, 1953 and so on). But this “discovery” does not solve the problem because according to Keynes’ theoretical definition and practical estimation of multiplier, the “indicator’s” magnitude is strongly greater than one and, investment does not produce income itself (vide infra). Recent debate between Ahiakpor (2000) and Dimand (2000) and Darity and Young (2000) have been showing continuing controversial interpretation of the multiplier and how much the solution of this problem is required. Yet, this unresolved argument has serious implications, such as its continued presence in textbooks despite its unresolved status. Nevertheless, "Like many other tools of economic theory, the multiplier must be used with care, but there is no case for its demise. It remains a very important relationship in post-Keynesian monetary macroeconomics" (Gilbert, 1982). It is necessary to stress that Keynes himself in the letter to Beveridge claimed that “The theory of the multiplier. You write here as though this was a matter on which I had only dogmatized and not discussed. But not only have I given a long chapter expressly to this subject, but about half the book is really about it.” (Keynes, 1973, p.57)
This paper will present and discuss the arguments made by both sides, and also present a third, new perspective on the Keynes’ multiplier. It will be shown that Keynes’ investment multiplier and Kahn’s employment multiplier are different not only as regards their theoretical meaning, but also with respect their practical magnitude because of the following reasons: (1) Kahn’s approach is compatible with the second phase of the investment process, when fixed capital (investment) is determinant; therefore, the calculation of Kahn’s multiplier is a dynamic process, albeit though the time-lag is not taking into account; while in Keynes’ approach, when investment (saving) is determinate, is compatible with the first phase of the investment process, therefore, the calculation is static; (2) The source of an additional increment of investment in Kahn’s approach is exogenous, whilst in Keynes’ approach is endogenous; (3) Kahn’s multiplier is a technological-economic phenomenon, while Keynes’ multiplier is a psychological phenomenon.
Also, it will be shown that Keynes’ investment “multiplier” is a reciprocal of the marginal propensity to invest (save); therefore, its genuine meaning is that of a requirement, which indicates the quantity of national income required to realize one unit of investment (saving).
The paper consists of five sections. Following the introduction, the second section describes a commonly used general equilibrium theory approach and discusses two possibilities to income increases: endogenous and exogenous. In the third section, Kahn’s original definition of multiplier is presented. The forth section reviews Keynes’ definition of the multiplier. In the final section the genuine meaning of Keynes’ multiplier will be presented, followed by conclusions.
2. Produced Income and Used Income
For the reasons of convenience, general equilibrium theories state that in an equilibrium position the total value of all employed services (employed quantities of services multiplied by their according prices) equals the total value of demand (consumption) of all commodities (demanded quantities of commodities multiplied by their according prices). The first is known as produced (created) national income or national income in terms of factors’ (services’) prices Yp, while the latter is known as used (consumed) national income or national income in terms of commodities’ market prices Y.This statement is known as Walras’ law,which all schools of thought of economics recognize and, in addition, and something which is very important – it is compatible with empirical accounts of national income. At the same time, it is necessary to point out that there is a difference between Walras’ own law and the post-Walrasian version of this law. Walras’ law means that the law is only satisfied for equilibrium prices established for each goods and services separately in the condition that the total demand is equal to the total supply for services and the cost of production (the supply price) is equal to the demand prices for goods. In addition,prices are strongly positive even someservices are underemployed in equilibrium state. The Walras followers’ law is satisfied for any prices and if there is unemployed service, then its price is equal zero.Therefore, the post-Walras’ law is a by-product of his original law, but Walras’ own law is compatible to economical reality, whilst the post-Walras’ law is incompatible with reality, whereas this law is fundamental to the post-Walrasian approach (Davar, 1994). Hence, the Walras’ law can be presented as
pi–is equilibrium price of service i;
Oi – is equilibrium employed (required) quantity of service i, which is either equal to or less than its available (existence) quantity Qi, i.e., OiQi;
j – is equilibrium price of commodity j;
Dj – is equilibrium demanded quantities of commodity j.
For the following discussing there are two things must be pointed out: (1) the employed (required) quantities of services are obtained on the basis of inverse coefficients of factors (Walras, 1954, pp.240-1; Leontief, 1986, pp.394-5; Davar, 1994, pp.17-8), which means that they include the direct and indirect inputs of services.So, these required (employed) quantities of services include the total (direct plus indirect) quantities of services required for the production of demand goods; (2) the list of demand commodities in general include all kinds of commodities, “public work”. If there are some commodities that are not included in the list of demand commodities, it has to be added and required quantities for its production would be obtained according to the previous note.
The left side expression of (2-1) is national income in terms of factors’ (services’) prices Yp(produced income) and if we take into account the results of the individuals model’ solution it have dividedinto two components: commodities for consumption (Cd) and saving (S). The right side expression is national income in terms of commodities prices (used income) and it is also combined by twocomponents: commodities for consumption (Cd) and new capital goods (investment - I). So, in the equilibrium situation there are:
Yp = Oipi = Cd + S, (2-2)
Y = Dii = Cd + I, (2-3)
Yp = Y and Cd + S = Cd + I, therefore S = I, (2-4)
Equation (2-4) indicates that in an equilibrium situation saving equals investment. But, individuals who save differ from individuals who invest. This means saving may differ from investment.Therefore, in order to establish equilibrium, saving must be equal to investment by means of changing the interest rate (Chick, 1997, p.174; Sawyer, p.52).
In addition, it has been shown that the classical and the Walrasian approach -- as well as Keynes approach -- assumes that in an equilibrium position, might be unemployed services (including labor) (Davar, 1994), It is necessary to stress that there is a difference between Walras’ and Keynes’ unemployment albeit that they are interwoven. The former is observed as voluntary unemployment,while the latter as involuntary underemployment (Davar, 2002). If the unemployed share of services is considerable, it will be desirable to attempt to shiftequilibrium position,if it is possible, in order to decrease unemployment and, consequently to increase income (investment).
2.1 Investment (Saving) as Determinate and Fixed Capital (Investment) as Determinant
Keynes stated that ‘Thus the traditional analysis is faulty because it has failed to isolate correctly the independent variables of the system. Saving and Investment are the determinates of the system, not the determinants. They are the twin results of the system’s determinants, namely, the propensity to consume, the schedule of the marginal efficiency of capital and the rate of interest (Keynes, 1936, pp.183-4).’ This is a very important statement, which is based on Walras’ theory, but Keynes destroyed it in the multiplier theory, where investment becomes a determinant (vide infra).
For the following discussion it is necessary to make clear whether new capital goods (investment) produced in a certain period (year) transform services (fixed capital) either in that year or the next year.It is, in general, assumed that new capital goods produced during a certain year become services the next year. One of the central assumptions of Keynes’ analysis is ‘the existing quality and quantity of available equipment, the existing technique,’ (Keynes, 1936, p.245). This means that new capital goods do not create (produce) national income in the year when they are produced. So in this case there is no direct connection between investment and the creating of national income. There is a connection between them in such way so as to produce new capital goods (invest) so that according national income must be created.This is the first phase of the whole process of investment, i.e. when investment is created, therefore, in this phase, investment (saving) is determinate. It must be stressed that investment might be increased without any changes of created income, and moreover it might be increased if created income is decreased, by decreasing of the value of consumers’ commodities (vide infra). Even if assuming that new capital goods (investment) became services in the same year when they are produced, then created income might be increased according the magnitude of its employment and according to the required employed quantities of other services (especially labour) determined by the current technology.
In the second phase, investment is transformed into fixed capital and produces income in combination with other services (labour, land, money) according to the technology of the sector (industry) where fixed capital (investment) is planned. So, in this phase fixed capital (investment) is determinant. The first round of producing income continues over the number of years that the fixed capital might be served (5 years in our case). The income produced, in turn, makes up investment according to the marginal propensity to consume (invest) (vide infra) in each year. The latter produces new income in the second round and continues on the serving years of fixed capital (investment). This process continues infinitely (see Appendix 1, where we confine ourselves to describing only three rounds) (see also Sawyer, p.52). There are two things to be noted: (1) starting from the second round (beginning from second year) income has a cumulative character. The same is true for investment from the third round (beginning from third year); (2) It is assumed, for all rounds (years), that the new fixed capital will be fully employed and required quantities of other factors (labour, land, money) will be satisfied accordingly.
2.2Endogenous and Exogenous Increment of Investment
Let us to point out, firstly, that the problem of investment increment is compatible with the first phase of investment process, when investment (saving) is determinate.
There are two sources for increasing investment: endogenous and exogenous. Let us to start with the first - endogenous source. On the basis of (2.3) we can conclude that there are three possibilities for investment increasing: 1) when value of consumption is decreased and income does not change; 2) value of consumption is constant (no change) and investment increase by increasing income; 3) both, consumption and investment, are increased by increasing income,either they are increased with variable marginal propensity to consume, as Keynes assumed in the General Theory (Keynes, 1936, p.114, see also Hawtrey, p.179n) or they are increased by constant marginal propensity to consume. Instead of that, Keynes considered the first version of investment increasing with others ‘Assuming that the decisions to invest become effective, they must in doing so either curtail consumption or expand income. Thus the act of investment in itself cannot help causing the residual or margin, which we call saving, to increase by a corresponding amount.’ (Keynes, 1936, p.64)let us discuss only two latter cases, because not only the first happens very rarely in reality, but also Keynes discussed only the following. Assume that the value of the consumption and investment commodities are increased, so that Cd1 (>Cd) and I1 (>I).Assume also that there is a possibility to achieve the next state of equilibrium according for this new data. Hence, for this case we also have
Cd1 + S1 = Cd1 + I1, (2-5)
Comparing (2-2) and (2-5) we obtain
∆Cd + ∆S = ∆Cd +∆I, (2-6)
From this condition to hold we must conclude that an increment in demand for commodities, either consumption or investment or both has occurred, i.e., the increment of used income stipulates an increment in produced income of the same magnitude, and vice versa. In other words the increment in investment or consumption must be financed by equivalent increment in produced income (increment in value by the additional employed services). In addition, the increment in investment must be equal the increment of saving. The relationship between consumption and investment (marginal propensity to consume) does not influence this conclusion. The latter influences only on the magnitude of the increasein income (vide infra). So, we can conclude that in all cases where the increment in investment (income) is a result of endogenous sources, the magnitude of the increment of consumed (used) income equals the magnitude of produced income and vice versa (Negishi, 1979, p.182; Samuelson, 1948 and 1974; Salant, 1974 (1942 and 1964); Haavelmo, 1943; Turvey, 1953).
The second source for increasing investment - exogenous - means that the increment is obtained by means of borrowing from either domestic sources (banks and other similar institutions) or foreign sources (governments and banks), or both of them. In the case of exogenous increment of investment, the calculation of the national income created and the additional (produced) investment, generally, is divided into to stages: (1) this is the same as was described for the second phase of the investment process i.e., in the next year investment is transformed into fixed capital, and starts the infinite process of income and investment creation (see 2.1, p.7); (2) because of this, the source of increment of investment is exogenous in the year of the investment, also create national income in the branches where capital products are produced; and the quantity of income created is equal to the value of investment minus the intermediate input of goods. But this additional produced income is not used to finance additional consumption and investment in the year of the investment as in the previous case, just because its source is exogenous. So, the additional produced income is “free” and might be use for the new additional purchase of commodities for consumption and investment. Thus, this created income divided between consumption and investment in according to propensity to consume (save) and following the calculation of additional income and investment, is the same as the previous cases.
In addition to the two notes (see p.7) there is one more note, namely, the question of the efficiency of borrowing and the problem of loan repayment are not discussed here. Despite these obstacles, we can conclude that in the case of an exogenous increment in used investment, the increase of desirable produced income is to be greater than the increment in used income. In other words, here, the coefficient of produced income increment might be more than one, whereas in the case of an endogenous increment of investment, the coefficient always equals one.