Money Circulation Equation Considering Time Irreversibility
Author(s)
Shinji Miura
ABSTRACT
The essence of money circulation is that money continues to transfer among economic agents eternally. Based on this recognition, this paper shows a money circulation equation that calculates the quantities of expenditure, revenue, and the end money from the quantity of the beginning money. The beginning money consists of the possession at term beginning, production and being transferred from the outside of the relevant society. The end money consists of the possession at term end, disappearance and transferring to the outside of the relevant society. This equation has a unique solution if and only if each part of the relevant society satisfies the space-time openness condition. Moreover, if money is transferred time irreversibly, each part of the relevant society satisfies the space-time openness condition. Hence, the solvability of the equation is guaranteed by time irreversibility. These solvability conditions are similar to those of the economic input-output equation, but the details are different. An equation resembling our money circulation equation was already shown by Mária Augustinovics, a Hungarian economist. This paper examines the commonalities and differences between our equation and hers. This paper provides the basis for some intended papers by the author.
The essence of money circulation is that money continues to transfer among economic agents eternally. Based on this recognition, this paper shows a money circulation equation that calculates the quantities of expenditure, revenue, and the end money from the quantity of the beginning money. The beginning money consists of the possession at term beginning, production and being transferred from the outside of the relevant society. The end money consists of the possession at term end, disappearance and transferring to the outside of the relevant society. This equation has a unique solution if and only if each part of the relevant society satisfies the space-time openness condition. Moreover, if money is transferred time irreversibly, each part of the relevant society satisfies the space-time openness condition. Hence, the solvability of the equation is guaranteed by time irreversibility. These solvability conditions are similar to those of the economic input-output equation, but the details are different. An equation resembling our money circulation equation was already shown by Mária Augustinovics, a Hungarian economist. This paper examines the commonalities and differences between our equation and hers. This paper provides the basis for some intended papers by the author.
Cite this paper
Miura, S. (2014) Money Circulation Equation Considering Time Irreversibility. Advances in Linear Algebra & Matrix Theory, 4, 187-200. doi: 10.4236/alamt.2014.44016.
Miura, S. (2014) Money Circulation Equation Considering Time Irreversibility. Advances in Linear Algebra & Matrix Theory, 4, 187-200. doi: 10.4236/alamt.2014.44016.
References
[1] Newcomb, S. (1966) Principles of Political Economy. A. M. Kelley, New York. [2] Fisher, I. (1922) The Purchasing Power of Money. New and Revised Edition, the Macmillan Company, New York. [3] 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. [4] 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.
http://dx.doi.org/10.1057/9780230226203.1278 [5] Theocharis, R.D. (1983) Early Developments in Mathematical Economics. 2nd Edition, The Macmillan Press, London and Basingstoke. [6] Humphrey, T.M. (1984) Algebraic Quantity Equations before Fisher and Pigou. Economic Review, 13-22.
https://www.richmondfed.org/publications/research/economic_review/1984/er700502.cfm [7] 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 [8] Beauwens, R. (1976) Semistrict Diagonal Dominance. SIAM Journal on Numerical Analysis, 13, 109-112.
http://dx.doi.org/10.1137/0713013 [9] 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 [10] 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. [11] 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 [12] 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 [13] Miura, S. (2014) Solvability of the Economic Input-Output Equation by Time Irreversibility. Advances in Linear Algebra & Matrix Theory, 4, 143-155.
http://dx.doi.org/10.4236/alamt.2014.43013 [14] Augustinovics, M. (1965) A Model of Money-Circulation. Economics of Planning, 5, 44-57.
http://dx.doi.org/10.1007/BF02424905 [15] Leontief, W. and Brody, A. (1993) Money-Flow Computations. Economic Systems Research, 5, 225-233.
http://dx.doi.org/10.1080/09535319300000019 [16] Nikaido, H. (1968) Convex Structures and Economic Theory. Academic Press, Cambridge. [17] Berman, A. and Plemmons, R.J. (1979) Nonnegative Matrices in the Mathematical Sciences. Academic Press, Cambridge. [18] Varga, R.S. (2000) Matrix Iterative Analysis. 2nd Revised and Expanded Edition, Springer, Berlin.
http://dx.doi.org/10.1007/978-3-642-05156-2 [19] Plemmons, R.J. (1977) M-Matrix Characterizations. 1—Nonsingular M-Matrices. Linear Algebra and Its Applications, 18, 175-188.
http://dx.doi.org/10.1016/0024-3795(77)90073-8
[1] Newcomb, S. (1966) Principles of Political Economy. A. M. Kelley, New York. [2] Fisher, I. (1922) The Purchasing Power of Money. New and Revised Edition, the Macmillan Company, New York. [3] 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. [4] 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.
http://dx.doi.org/10.1057/9780230226203.1278 [5] Theocharis, R.D. (1983) Early Developments in Mathematical Economics. 2nd Edition, The Macmillan Press, London and Basingstoke. [6] Humphrey, T.M. (1984) Algebraic Quantity Equations before Fisher and Pigou. Economic Review, 13-22.
https://www.richmondfed.org/publications/research/economic_review/1984/er700502.cfm [7] 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 [8] Beauwens, R. (1976) Semistrict Diagonal Dominance. SIAM Journal on Numerical Analysis, 13, 109-112.
http://dx.doi.org/10.1137/0713013 [9] 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 [10] 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. [11] 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 [12] 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 [13] Miura, S. (2014) Solvability of the Economic Input-Output Equation by Time Irreversibility. Advances in Linear Algebra & Matrix Theory, 4, 143-155.
http://dx.doi.org/10.4236/alamt.2014.43013 [14] Augustinovics, M. (1965) A Model of Money-Circulation. Economics of Planning, 5, 44-57.
http://dx.doi.org/10.1007/BF02424905 [15] Leontief, W. and Brody, A. (1993) Money-Flow Computations. Economic Systems Research, 5, 225-233.
http://dx.doi.org/10.1080/09535319300000019 [16] Nikaido, H. (1968) Convex Structures and Economic Theory. Academic Press, Cambridge. [17] Berman, A. and Plemmons, R.J. (1979) Nonnegative Matrices in the Mathematical Sciences. Academic Press, Cambridge. [18] Varga, R.S. (2000) Matrix Iterative Analysis. 2nd Revised and Expanded Edition, Springer, Berlin.
http://dx.doi.org/10.1007/978-3-642-05156-2 [19] Plemmons, R.J. (1977) M-Matrix Characterizations. 1—Nonsingular M-Matrices. Linear Algebra and Its Applications, 18, 175-188.
http://dx.doi.org/10.1016/0024-3795(77)90073-8