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Multiplier-Accelerator Models- Introduction -

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Contents

A) The Samuelson OscillatorB) Metzler Inventory CyclesC) Hicks's Trade CycleD) Duesenberry-Smithies Ratchet EffectsE) Growth Cycles: Duesenberry-PasinettiF) Extensions: Shocks and Money

Roy F. Harrodlaid out the basic tenets of the Oxbridge research programmein his 1936 The Trade Cycle: An essaymuch of it written before Harrod even saw a draft of J.M. Keynes's General Theory. Harrod contended "that by a s

f the interconnexions between the Multiplier and the Relation the secret of the trade cycle may be revealed" (Harr936: p.70). This "Relation" was the acceleration principle of investment.

One ought to note that J.M. Keyneshimself did not have much credence in a deterministic accelerator as employedHarrod and the Oxbridge models. Instead, Keynes had argued that it was expectations dynamics that generated cycly affecting the marginal efficiency of investment and subsequently the multiplier and output (Keynes, 1936: Ch.22

Nevertheless, Keynes left the topic undetailed. Thus, Roy Harrodwent on alone, in his theory of the trade cycle (19

nd later on in his theory of growth(1939, 1948), to explore the relationships between the Keynesian multiplier andccelerator-type investment functions to explain a growing, progressive economy with and without cycles.

he principle of the multiplier, as laid out by R.F. Kahn(1931) and J.M. Keynes(1936) is that if investment increahere will be an increase in output as a result of a "multiplier" relationship between equilibrium output anutonomous components of spending, in this case:

DY = DI/(1-c)

where c is the marginal propensity to consume, Y is output and I is investment. The principle of the accelerator, asut by Albert Aftalion(1913) and John Maurice Clark(1917), was that investment decisions on the part of firms aeast in part dependent upon expectations of future increases in demand, which may, in turn, be extrapolated fromurrent or past increases in aggregate demand or output, e.g.

It= b (Yt- Yt-1)

hus, the multiplier principle implies that investment increases output whereas the acceleration principle impliesncreases in output will themselves induce increases in investment.

Consequently, it would at least seem natural if some bright economist put these two together and examineynamic properties of investment and output as they affect each other, perhaps in generating cycles and/or growth.rst such bright economist was Roy F. Harrod (1936), albeit his analysis was purely verbal and not without

http://cruel.org/econthought/essays/multacc/multacc.htmlhttp://cruel.org/econthought/essays/multacc/samacc.htmlhttp://cruel.org/econthought/essays/multacc/metzinv.htmlhttp://cruel.org/econthought/essays/multacc/metzinv.htmlhttp://cruel.org/econthought/essays/multacc/hicksacc.htmlhttp://cruel.org/econthought/essays/multacc/ratchet.htmlhttp://cruel.org/econthought/essays/multacc/duespas.htmlhttp://cruel.org/econthought/essays/multacc/shocks.htmlhttp://cruel.org/econthought/profiles/harrod.htmlhttp://cruel.org/econthought/essays/multacc/oxbridge.htmlhttp://cruel.org/econthought/profiles/keynes.htmlhttp://cruel.org/econthought/profiles/keynes.htmlhttp://cruel.org/econthought/essays/keynes/general.htmlhttp://cruel.org/econthought/profiles/harrod.htmlhttp://cruel.org/econthought/essays/capital/accelerator.htmlhttp://cruel.org/econthought/profiles/keynes.htmlhttp://cruel.org/econthought/profiles/keynes.htmlhttp://cruel.org/econthought/profiles/harrod.htmlhttp://cruel.org/econthought/essays/growth/keynesgrowth.htmlhttp://cruel.org/econthought/profiles/kahn.htmlhttp://cruel.org/econthought/profiles/keynes.htmlhttp://cruel.org/econthought/essays/capital/accelerator.htmlhttp://cruel.org/econthought/profiles/aftalion.htmlhttp://cruel.org/econthought/profiles/aftalion.htmlhttp://cruel.org/econthought/profiles/maurice.htmlhttp://cruel.org/econthought/profiles/harrod.htmlhttp://cruel.org/econthought/profiles/harrod.htmlhttp://cruel.org/econthought/profiles/maurice.htmlhttp://cruel.org/econthought/profiles/aftalion.htmlhttp://cruel.org/econthought/essays/capital/accelerator.htmlhttp://cruel.org/econthought/profiles/keynes.htmlhttp://cruel.org/econthought/profiles/kahn.htmlhttp://cruel.org/econthought/essays/growth/keynesgrowth.htmlhttp://cruel.org/econthought/profiles/harrod.htmlhttp://cruel.org/econthought/profiles/keynes.htmlhttp://cruel.org/econthought/profiles/keynes.htmlhttp://cruel.org/econthought/essays/capital/accelerator.htmlhttp://cruel.org/econthought/profiles/harrod.htmlhttp://cruel.org/econthought/essays/keynes/general.htmlhttp://cruel.org/econthought/profiles/keynes.htmlhttp://cruel.org/econthought/essays/multacc/oxbridge.htmlhttp://cruel.org/econthought/profiles/harrod.htmlhttp://cruel.org/econthought/essays/multacc/shocks.htmlhttp://cruel.org/econthought/essays/multacc/duespas.htmlhttp://cruel.org/econthought/essays/multacc/ratchet.htmlhttp://cruel.org/econthought/essays/multacc/hicksacc.htmlhttp://cruel.org/econthought/essays/multacc/metzinv.htmlhttp://cruel.org/econthought/essays/multacc/samacc.htmlhttp://cruel.org/econthought/essays/multacc/multacc.htmlhttp://cruel.org/econthought/essays/keynes/keynesrev.html

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nots. His associated attempt to formalize a Keynesian growth model (Harrod's, 1939, 1948) was not much muccessful: he ended up with his famous "knife-edge" instability.

Harrod's fellow Oxford economist, John Hicks (1949, 1950) picked up where Harrod left off. Hicks's (1950) tycle model sought to recast Harrod's unstable "multiplier-accelerator" dynamics into cyclical ones by havxplosive trajectories bang up against floors and ceilings. To this end, Hicks employed the formalism of dynamifference equations, that had been introduced in a similar context by PaulSamuelson (1939) in his incoxpenditure "oscillator" and by Lloyd Metzler(1941) in his inventory cycle.

Hicks's (1950) "forced non-linearity" of ceilings and floors were somewhat restrictive. The essential Hicksian mwas expanded upon by James Duesenberry(1949) and Arthur Smithies (1957) to include "ratchet effects" and btain cycles along a output growth path. Later, Duesenberry(1958) and Luigi Pasinetti(1960) considered a diffecceleratorfor the Hicksian model that would yield both growth and cycles. A bit more distinctly, Richard Goodw1951) exercise added a non-linear acceleratorto generate cycles endogenously while D.J. Smyth (1963) attemptencorporate a monetary "LM" side to the standard multiplier-accelerator model. We shall review these "sim

multiplier-accelerator models before turning to endogenous cycle theory, where "natural" non-linearities are place to generate cycles and growth.

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