Quantification of Revenue Induction and Expenditure Reflux in a Monetary Economy

Shinji Miura^*

Independent, Gifu, Japan.

DOI: 10.4236/alamt.2015.51003                

Abstract

In a monetary economy, expenditure induces revenue for each agent. We call this the revenue induction phenomenon. Moreover, in a special case, part of the expenditure by an agent returns as their own revenue. We call this the expenditure reflux phenomenon. Although the existence of these phenomena is known from the olden days, this paper aims to achieve a more precise quantification of them. We first derive the revenue induction formula through solving the partial money circulation equation. Then, for a special case, we derive the expenditure reflux formula. Furthermore, this paper defines the revenue induction coefficient and the expenditure reflux coefficient, which are the key concepts for understanding the two formulas, and examines their range.

Keywords

Monetary Economy, Money Circulation, Revenue Induction, Expenditure Reflux

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Quesnay, F. (1972) Quesnay’s Tableau économique. Edited with New Material, Translations and Notes by Kuczynski, M. and Meek, R.L., Macmillan, London.
[2]	Kahn, R.F. (1931) The Relation of Home Investment to Unemployment. The Economic Journal, 41, 173-198. http://dx.doi.org/10.2307/2223697
[3]	Bortis, H. (2008) The Multiplier Relation as the Pure Theory of Output and Employment in a Monetary Production Economy. In: Gnos, C. and Rochon, L.P., Eds., The Keynesian Multiplier, Routledge, London, 58-84.
[4]	Taylor, L. (2014) Why Didn’t Economists Predict the Great Depression? MPRA Paper No. 54214. http://mpra.ub.uni-muenchen.de/id/eprint/54214
[5]	McGee, R.W. (2014) Keynes, Bastiat and the Multiplier. Available at SSRN 2435914. http://dx.doi.org/10.2139/ssrn.2435914
[6]	Trigg, A.B. (2006) Marxian Reproduction Schema: Money and Aggregate Demand in a Capitalist Economy. Routledge, London.
[7]	Sordi, S. and Vercelli, A. (2010) Genesis and Foundations of the Multiplier: Marx, Kalecki and Keynes. University of Siena DEPFID Working Paper, No. 07.
[8]	Hegeland, H. (1954) The Multiplier Theory. C.W.K. Gleerup, Lund.
[9]	Schneider, E. (1962) Money, Income and Employment. Translated by Klappholz, K., George Allen & Unwin Ltd., London.
[10]	Klein, L.R. (1966) The Keynesian Revolution. 2nd Edition, The Macmillan Company, New York.
[11]	Allsbrook, O.O. (1986) N. A. L. J. Johannsen: An Early Monetarist. Journal of Institutional and Theoretical Economics (JITE)/Zeitschrift für die gesamte Staatswissenschaft, 142, 431-437. http://jstor.org/stable/40750877
[12]	Hagemann, H. and Rühl, C. (1990) Nicholas Johannsen and Keynes’s “Finance Motive”. Journal of Institutional and Theoretical Economics (JITE)/Zeitschrift für die gesamte Staatswissenschaft, 146, 445-469. http://jstor.org/stable/40751327
[13]	Topp, N. (1981) A Nineteenth-Century Multiplier and Its Fate: Julius Wulff and the Multiplier Theory in Denmark, 1896-1932. History of Political Economy, 13, 824-845. http://dx.doi.org/10.1215/00182702-13-4-824
[14]	Dimand, R.W. (1988) The Origins of the Keynesian Revolution: The Development of Keynes’s Theory of Employment and Output. Edward Elgar, London.
[15]	Boserup, M. (1969) A Note on the Prehistory of the Kahn Multiplier. The Economic Journal, 79, 667-669. http://dx.doi.org/10.2307/2230427
[16]	Warming, J. (1932) International Difficulties Arising out of the Financing of Public Works during Depression. The Economic Journal, 42, 211-224. http://dx.doi.org/10.2307/2223819
[17]	Cain, N. (1979) Cambridge and Its Revolution: A Perspective on the Multiplier and Effective Demand. The Economic Record, 55, 108-117. http://dx.doi.org/10.1111/j.1475-4932.1979.tb02210.x
[18]	King, J. (1998) From Giblin to Kalecki: The Export Multiplier and the Balance of Payments Constraint on Economic Growth, 1930-1933. History of Economics Review, No. 28, 62-71. http://search.informit.com.au/documentSummary;dn=990403335;res=IELAPA
[19]	Sawyer, M. (2008) Kalecki and the Multiplier. In: Gnos, C. and Rochon, L.P., Eds., The Keynesian Multiplier, Routledge, London, 153-167.
[20]	Heimann, E. (1945) History of Economic Doctrines: An Introduction to Economic Theory. Oxford University Press, New York.
[21]	Wright, A.L. (1956) The Genesis of the Multiplier Theory. Oxford Economic Papers, 8, 181-193. http://jstor.org/stable/2661731
[22]	Cain, N. (1982) Hawtrey and Multiplier Theory. Australian Economic History Review, 22, 68-78.
[23]	Dimand, R.W. (1997) Hawtrey and the Multiplier. History of Political Economy, 29, 549-556. http://dx.doi.org/10.1215/00182702-29-3-549
[24]	Darity, W.A. and Young, W. (1997) Reply to “Hawtrey and the Multiplier” by Robert W. Dimand. History of Political Economy, 29, 557-559. http://dx.doi.org/10.1215/00182702-29-3-557
[25]	Ahiakpor, J.C.W. (2000) Hawtrey on the Keynesian Multiplier: A Question of Cognitive Dissonance? History of Political Economy, 32, 889-908. http://dx.doi.org/10.1215/00182702-32-4-889
[26]	Dimand, R.W. (2000) Hawtrey and the Keynesian Multiplier: A Response to Ahiakpor. History of Political Economy, 32, 909-914. http://dx.doi.org/10.1215/00182702-32-4-909
[27]	Darity, W.A. and Young, W. (2000) Reply to Ahiakpor. History of Political Economy, 32, 915-918. http://dx.doi.org/10.1215/00182702-32-4-915
[28]	Goodwin, C.D.W. (1962) Alfred De Lissa and the Birth of a Multiplier. Economic Record, 38, 74-93. http://dx.doi.org/10.1111/j.1475-4932.1962.tb01418.x
[29]	Arndt, H.W. (1966) De Lissa’s Multiplier: A Second Look. Economic Record, 42, 596-598. http://dx.doi.org/10.1111/j.1475-4932.1966.tb02990.x
[30]	Markwell, D.J. (2000) Keynes and Australia. Seminar at the Reserve Bank of Australia, 18 September 1985. http://www-dr.rba.gov.au/publications/rdp/2000/pdf/rdp2000-04.pdf
[31]	Millmow, A. (2000) Revisiting Giblin: Australia’s First Proto-Keynesian Economist? History of Economics Review, No. 31, 48-67. http://search.informit.com.au/documentSummary;dn=200102319;res=IELAPA
[32]	Coleman, W. (2004) Cambridge, England, or Cambridge, Tasmania? Some Recent Excavations of the Giblin Multiplier. History of Economics Review, No. 39, 1-14. http://search.informit.com.au/documentSummary;dn=200407273;res=IELAPA
[33]	Bishop Jr., G.W. (1965) Charles H. Dow and the Theory of the Multiplier. Financial Analysts Journal, 21, 39-41. http://dx.doi.org/10.2469/faj.v21.n1.39
[34]	Fiorito, L. (2008) John Maurice Clark’s Contribution to the Genesis of the Multiplier Analysis. In: Gnos, C. and Rochon, L.P., Eds., The Keynesian Multiplier, Routledge, London, 32-57.
[35]	Miura, S. (2014) Money Circulation Equation Considering Time Irreversibility. Advances in Linear Algebra & Matrix Theory, 4, 187-200. http://dx.doi.org/10.4236/alamt.2014.44016
[36]	Augustinovics, M. (1965) A Model of Money-Circulation. Economics of Planning, 5, 44-57. http://dx.doi.org/10.1007/BF02424905
[37]	Miura, S. (2014) Non-Singularity Conditions for Two Z-Matrix Types. Advances in Linear Algebra & Matrix Theory, 4, 109-119. http://dx.doi.org/10.4236/alamt.2014.42009
[38]	Beauwens, R. (1976) Semistrict Diagonal Dominance. SIAM Journal on Numerical Analysis, 13, 109-112. http://dx.doi.org/10.1137/0713013
[39]	Neumann, M. (1979) A Note on Generalizations of Strict Diagonal Dominance for Real Matrices. Linear Algebra and Its Applications, 26, 3-14. http://dx.doi.org/10.1016/0024-3795(79)90168-X
[40]	Varshney, K.R. (2013) Opinion Dynamics with Bounded Confidence in the Bayes Risk Error Divergence Sense. IEEE Conference on Acoustics, Speech and Signal Processing, Vancouver, 26-31 May 2013, 6600-6604.
[41]	Shang, Y.L. (2013) Deffuant Model with General Opinion Distributions: First Impression and Critical Confidence Bound. Complexity, 19, 38-49. http://dx.doi.org/10.1002/cplx.21465
[42]	Shang, Y.L. (2014) An Agent Based Model for Opinion Dynamics with Random Confidence Threshold. Communications in Nonlinear Science and Numerical Simulation, 19, 3766-3777. http://dx.doi.org/10.1016/j.cnsns.2014.03.033