Miura, Shinji (2015): Unified money circulation equation and an analogical explanation for its solvability.

PDF
MPRA_paper_67144.pdf Download (145kB)  Preview 
Abstract
The equation of exchange is wellknown as a quantitative expression of money circulation, but it has a defect in that the relation between the velocity of money and the situation of economic agents is not clear. This paper attempts to found the velocity which pays attention to movement of money. For that purpose, this paper shows a money circulation equation in which agents of the whole society are unified. If this equation has a unique solution, the velocity of money is reduced to the expenditure rate of the whole society. Thereby, the defect of the equation of exchange can be remedied. Our attempt can be interpreted as connecting the velocity of money with the multiplier analysis. Success or failure of the trial depends on its solvability. This solvability problem of the money circulation equation is closely related to the missing problems of the monetary budget constraint. This paper also attempts to explain the missing problems in the case of the budget constraint of the whole society. This paper explains that a time irreversible disposal solves those problems by using an analogy.
Item Type:  MPRA Paper 

Original Title:  Unified money circulation equation and an analogical explanation for its solvability 
Language:  English 
Keywords:  Equation of Exchange; Money Circulation; Budget Constraint 
Subjects:  C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables E  Macroeconomics and Monetary Economics > E4  Money and Interest Rates 
Item ID:  67144 
Depositing User:  Shinji Miura 
Date Deposited:  10 Oct 2015 10:51 
Last Modified:  04 Oct 2019 06:39 
References:  Ackley, G. (1951) The Multiplier Time Period: Money, Inventories, and Flexibility. The American Economic Review, 41, 350368. Anderson, C.J. (1945) The Basic Similarity of the Monetary and Investment Theories of Secondary Employment. American Journal of Economics and Sociology, 4, 203211. Archibald, G.C. (1956) Multiplier and Velocity Analysis: An Annulment. Economica, 23, 265269. Ardor, H.N. (2002) The Development of Mathematical Economics between 1711 and 1838. Ekonomik Yaklasim, 13, 139157. Augustinovics, M. (1965) A Model of MoneyCirculation. Economics of Planning, 5, 4457. Cottrell, A. (1994) Endogenous Money and the Multiplier. Journal of Post Keynesian Economics, 17, 111120. Dalziel, P. (1996) The Keynesian Multiplier, Liquidity Preference, and Endogenous Money. Journal of Post Keynesian Economics, 18, 311331. Davies, P. (2002) How to Build a Time Machine. Penguin, London. Deane, P. (1968) Petty, William. In: Sills, D.L., Ed., International Encyclopedia of the Social Science, Vol. 12, Crowell Collier and Macmillan Inc., New York. Fisher, I. (1922) The Purchasing Power of Money. New and Revised Edition, the Macmillan Company, New York. Gechert, S. (2014) On the Measurement, Theory and Estimation of Fiscal Multipliers ― A Contribution to Improve the Forecasting Precisison Regarding the Impact of Fiscal Impulses. Dr. rer. pol. Dissertation. Technische Universität Chemnitz, Chemnitz. Goodwin R.M. (1950) The Multiplier. In: Harris, S.E., Ed., The New Economics: Keynes’ Influence on Theory and Public Policy. Alfred A. Knopf, New York, 482499. Gott, J.R. (2002) Time Travel in Einstein’s Universe: The Physical Possibilities of Travel through Time, Phoenix, London. Holtrop, M.W. (1929) Theories of the Velocity of Circulation of Money in Earlier Economic Literature. Economic History, 4, 503524. Humphrey, T.M. (1984) Algebraic Quantity Equations before Fisher and Pigou. FRB Richmond Economic Review, 70, 1322. Humphrey, T.M. (1993) The Origin of Velocity Functions. FRB Richmond Economic Quarterly, 79, 117. Kahn, R. (1936) Dr. Neisser on Secondary Employment: A Note. Review of Economic Statistics, 18, 144147. Lossev, A. & Novikov, I.D. (1992) The Jinn of the Time Machine: NonTrivial SelfConsistent Solutions. Classical and Quantum Gravity, 9, 23092321. Lutz, V. (1955) Multiplier and Velocity Analysis: A Marriage. Economica, 22, 2944. Machlup, F. (1939) Period Analysis and Multiplier Theory. Quarterly Journal of Economics, 54, 127. Mayor, T. (1964) Multiplier and Velocity Analysis: An Evaluation. Journal of Political Economy, 72, 563574. Miller, W.L. (1956) The Multiplier Time Period and the Income Velocity of Active Money. Southern Economic Journal, 23, 7479. Miura, S. (2014a) Solvability of the Economic InputOutput Equation by Time Irreversibility. Advances in Linear Algebra & Matrix Theory, 4, 143155. Miura, S. (2014b) Money Circulation Equation Considering Time Irreversibility. Advances in Linear Algebra & Matrix Theory, 4, 187200. Miura, S. (2015a) Quantification of Revenue Induction and Expenditure Reflux in a Monetary Economy. Advances in Linear Algebra & Matrix Theory, 5, 2535. Miura, S. (2015b) Monetary Budget Constraint and Its Missing Problems. Open Journal of Optimization, 4, 8799. Moore, B.J. (1988) Horizontalists and Verticalists: The Macroeconomics of Credit Money. Cambridge University Press. Moore, B.J. (1994) The Demise of the Keynesian Multiplier: A Reply to Cottrell. Journal of Post Keynesian Economics, 17, 121133. Moore, B.J. (2008) The Demise of the Keynesian Multiplier Revisited. In: C. Gnos and L.P. Rochon, Eds., The Keynesian Multiplier, 120126. Neisser, H.P. (1936) Secondary Employment: Some Comments on R.F. Kahn’s Formula. Review of Economic Statistics, 18, 2430. Nemiroff, R.J. and Wilson, T. (2013) Searching the Internet for Evidence of Time Travelers. arXiv:1312.7128. Newcomb, S. (1966) Principles of Political Economy. A. M. Kelley, New York. Pigou, A.C. (1952) The Value of Money. In: a Committee of the American Economic Association Selected, Readings in Monetary Theory, G. Allen and Unwin, London. Roncaglia, A. (2008) Petty, William. In: Durlauf, S.N. and Blume, L.E., Eds., The New Palgrave Dictionary of Economics, 2nd Edition, Volume 6, Palgrave Macmillan, New York. Samuelson, P.A. (1942) Fiscal Policy and Income Determination. Quarterly Journal of Economics, 56, 575605. Theocharis, R.D. (1958) Joseph Lang and Macroeconomics, Economica, 25, 319325. Theocharis, R.D. (1983) Early Developments in Mathematical Economics. 2nd Edition, The Macmillan Press, London and Basingstoke. Tsiang, S.C. (1956) Liquidity Preference and Loanable Funds Theories, Multiplier and Velocity Analyses: A Synthesis. The American Economic Review, 46, 539564. Turvey, R. (1948) The Multiplier. Economica, 15, 259269. Uebe, G (1992) The First Flow of Funds Table: Lang’s Tableau of 1815. History of Political Economy, 24, 435453. Uebe, G. (1992) The Model of Lang―National Income Accounts in 1807. Computers & Mathematics with Applications, 24, 167179. Wang, Y, Xu, Y. and Liu, Li (2010) Keynesian Multiplier versus Velocity of Money. Physics Procedia, 3, 17071712. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/67144 