Monetary Factors and Multiplier-Accelerator Interaction

Abstract

A common objection to trade cycle models based on the interaction of the multiplier and the accelerator is that they neglect monetary factors. In the best known of these trade cycles models, that of Hicks, monetary factors, while not entirely ignored, are not made an integral part of the model.' Tsiang has given a brief discussion of the influence of monetary factors.2 Minsky has examined the result of combining an explosive multiplier-accelerator process with a number of alternative monetary systems, assuming that all relationships are in money terms and that the process may generate changes in the price level.3 Hudson4 has considered the effect of introducing monetary factors in a model closely related to Kaldor's 1940 trade cycle model.5 The aim of the present article is to examirne the effects of making monetary factors an integral part of a multiplier-accelerator model. The multiplier-accelerator model used is the simple Hicksian one. A closed economy is assumed with no government expenditure and taxation. Price changes are ignored. No attention is paid to the ceiling and floor. There is no trend term in the autonomous components of expenditure.6 To avoid the difficulties associated with non-linear difference equations, it is assumed that all functions are linear. Denote autonomous components of expenditure, including autonomous consumption and that part of investment which would occur with zero income change and at zero rate of interest (or at the base rate of interest if the rate of interest is not measured from zero) by A, induced consumption by C, induced investment by I (all these variables being measured in real terms), the rate of interest by R, and the time-period by sub-scripts involving t. Making consumption an increasing function of income of the previous period7 gives (1) C. =CY.,, lJ. R. Hicks, A Contribution to the Theory of the Trade Cycle, 1950. Hicks nmerely adds two chapters on monetary factors at the end of his study. 2 S. C. Tsiang, Accelerator, Theory of the Firm, and the Business Cycle , Quarterly Journal of Economics, August 1951, pp. 325-41. 3 H. P. Minsky, Monetary Systems and Accelerator Models , American Economic Review, December 1957, pp. 859-83. 4H. R. Hudson, A Model of the Trade Cycle , Economic Record, December 1957, pp. 378-89. 5 N. Kaldor, A Model of the Trade Cycle-, Economic Journal, March 1940, pp. 78-92. 6 If there were a growth trend in these it would be appropriate to insert a similar trend in the liquidity preference function. 7A further complication would be to make consumption a function of the rate of interest as well. 400