Multiplier, The

BIBLIOGRAPHY

In macroeconomics, the multiplier is the ratio of a change in the equilibrium level of national income (or of aggregate employment) to the change in autonomous spending (or in employment on public-works projects) that brought it about. As early as Walter Bagehot’s Lombard Street in 1871 and Alfred and Mary Marshall’s Economics of Industry in 1879 (and arguably even in an oration by Pericles, as reported by Plutarch), it has been recognized that an initial round of spending in one sector caused successive rounds of spending as the recipients of each round of income spent that increase in their income in ways that created more income for others.

John Maynard Keynes and Hubert Henderson invoked this long-held belief in their 1929 pamphlet Can Lloyd George Do It?, in which they endorsed the pledge by Liberal leader (and former prime minister) David Lloyd George to eliminate Britain’s interwar unemployment through public-works spending that would indirectly generate more jobs than just the direct employment on public works. The problem with winning acceptance for that argument was that it was unclear why the process would be finite, why employing one person on public works would not push the whole economy to full employment. The crucial advance was not recognition of successive rounds of spending but the analysis of the leakages from each round of spending that led to the multiplier having a finite value. If a fraction of each round of income is not spent on domestic output, the geometric series of rounds of spending sums to a finite value (just as, about the same time, it was shown that in a fractional-reserve banking system, a change in the monetary base leads to a finite change in the money supply because of leakages into currency and required reserves).

The successive contributions to this analysis by Ralph G. Hawtrey, Lyndhurst F. Giblin, Richard Kahn, Jens Warming, J. M. Keynes, Michal Kalecki, and John Maurice Clark from 1928 to 1935 are reprinted in Dimand (2002) (see Hegeland 1954; Wright 1956; Davis 1980; Kahn 1984; Dimand 1988, 1994). Keynes’s 1933 pamphlet The Means to Prosperity and his General Theory (1936), crediting Kahn (1931), used such a finite-valued spending multiplier to analyze how expansionary fiscal policy could increase output and employment in an economy operating below full employment, with the difference that while Kahn (1931) analyzed successive rounds of employment, Keynes (1933, 1936) considered successive rounds of spending. Davis (1980) argues that, in addition to the influence of Kahn (1931), Keynes was also influenced by correspondence with Hawtrey. Translated from changes in income and autonomous spending to their levels, the multiplier analysis led to the IS goods market equilibrium condition of the IS-LM model. However, understanding of the multiplier process and the goods market equilibrium condition need not imply support for activist fiscal policy. Hawtrey, the British Treasury economist who provided early numerical examples and algebraic analysis of the finite-valued multiplier, held that fiscal expansion would simply crowd out private investment because he considered the demand for money not responsive to the interest rate (in later terminology, a vertical LM curve).

The Keynesian spending multiplier k represents the change in equilibrium income and expenditure (Y ) resulting from a change in autonomous investment (I ) or government spending (G ), Δ Y = k Δ I or Δ Y = k Δ G, assuming that the price level, money wage rate, and interest rate do not change. It can thus be best viewed as the amount by which the IS curve (the goods market equilibrium condition) shifts horizontally at a given interest rate in the Hicks-Hansen IS-LM diagram (which is drawn for given prices and money wages) rather than as a change in the ultimate equilibrium of a complete model. The aggregate demand curve, on an aggregate demand/aggregate supply diagram with the price level and income on the two axes, would shift by as much as the IS/LM intersection shifted. In a footnote at the start of the very first multiplier article, Kahn (1931) promised a second article showing the results carried through even if fiscal expansion increased money wages, but that article never appeared and the footnote is not in the reprint in Kahn (1972). The Keynesian spending multiplier k, long the workhorse of introductory macroeconomics courses, is 1/(1 – z ), where z is the marginal propensity to spend. If there were no taxes or imports, the marginal propensity to spend would equal the marginal propensity to consume out of disposable income, c. With an income tax rate, t, and a marginal propensity to import, m, the marginal propensity to spend z = (1 – t ) c – m. Since the marginal propensities to consume and save out of disposable income add to 1 (s + c = 1), the denominator of the multiplier, 1 – z, is equal to s (1 – t ) + t + m. The larger the leakages from spending on domestic output into taxes, saving, and imports, the smaller the multiplier for a small open economy. (The multiplier for a large open economy would have to recognize that an increase in imports has a multiplier effect on equilibrium income in the rest of the world, which causes the rest of the world to import more from the home country.)

Because a change in taxes affects disposable income rather than spending in the first round, its effect will be proportionally smaller than that of a change in government spending. If there were only lump-sum taxes, with (for simplicity) no proportional taxes and no marginal propensity to import, the multiplier for a change in government spending would be 1/(1 – c ) and that for a change in taxes would be c /(1 – c ). Notice that for a balanced budget increase in government spending, with lump-sum taxes increased by as much as government spending, the balanced budget multiplier would (1 – c )/(1 – c ), which is 1.

The empirical importance of the simple Keynesian multiplier was diminished by the permanent income and life-cycle theories of consumption, which argued that the marginal propensity to consume out of a change in current income (and hence also the value of the multiplier) is much smaller than had been assumed. The importance, and presumed size, of the multiplier was further diminished by the theory of Ricardian equivalence or debt neutrality, which argued that a deficit-financed increase in government spending causes consumers to save in anticipation of the future tax liabilities implied by the government borrowing, so that any change in government spending, whether financed by current taxes or by borrowing against future taxes, will only shift the IS curve by the amount of the balanced budget multiplier effect. The multiplier continues to be a central feature of introductory macroeconomics courses but in more advanced courses is subsumed in the goods market equilibrium condition represented by the IS curve. The multiplier is used in regional and urban policy analysis to analyze the effects on a local economy of a public-works project such as a new sports stadium.

SEE ALSO Economic Growth; Economics, Keynesian; Full Employment; Involuntary Unemployment; Kahn, Richard F.; Keynes, John Maynard; Macroeconomics; Propensity to Consume, Marginal; Propensity to Import, Marginal; Underemployment; Unemployment

BIBLIOGRAPHY

Davis, Eric G. 1980. The Correspondence between R. G. Hawtrey and J. M. Keynes on the Treatise : The Genesis of Output Adjustment Models. Canadian Journal of Economics 13: 716–724.

Dimand, Robert W. 1988. The Origins of the Keynesian Revolution. Aldershot, U.K.: Edward Elgar, and Stanford, CA: Stanford University Press.

Dimand, Robert W. 1994. Mr. Meade’s Relation, Kahn’s Multiplier, and the Chronology of the General Theory. Economic Journal 104: 1139–1142.

Dimand, Robert W., ed. 2002. The Origins of Macroeconomics, 10 vols. London and New York: Routledge.

Hegeland, Hugo. 1954. The Multiplier Theory. New York: Augustus M. Kelley Reprints of Economic Classics, 1966.

Kahn, Richard F. 1931. The Relation of Home Investment to Unemployment. Economic Journal 41: 173–198.

Kahn, Richard F. 1972. Selected Essays on Employment and Growth. Cambridge, U.K.: Cambridge University Press.

Kahn, Richard F. 1984. The Making of Keynes’s General Theory. Cambridge, U.K.: Cambridge University Press.

Keynes, John Maynard. 1936. The General Theory of Employment, Interest and Money. London: Macmillan.

Wright, A. Llewellyn. 1956. The Genesis of the Multiplier Theory. Oxford Economic Papers, n.s. 8: 181–193.

Robert W. Dimand