Saccal, Alessandro
(2021):
*Mechanical analyses and derivations of money velocity.*

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## Abstract

The equation of exchange is derived from a standpoint encompassing the physics and economics thereof, whereby the maximisation of a money value function, increasing in real output and decreasing in the real money supply, while accounting for time and space, subjected to a money constraint, at the macroeconomic level, gives rise to an optimal level of real output thereby, expressing the liquidity demand coefficient as the inverse quotient of space over time. The fusion of such a liquidity demand coefficient expression with the money constraint, which is the equilibrium Cambridge equation, in turn gives rise to an equation for space, being the position of money, whose differentiation is precisely instantaneous money velocity and thence the exchange equation as presented by Fisher. The present analysis also derives money position on account of non-constant instantaneous money velocity as instantiated by Fisher, advancing a framework for the macroeconomy’s general money value function and money constraint in the process. It likewise advances simulations of non-constant average and instantaneous money velocity, with a particular application to a stylised closed macroeconomy. It finally proceeds to remodel instantaneous money velocity through the use of ordinary differential equations (ODEs) for the money equations of motion, both generally, by letting the sum of the three equal a corrected exponential random walk with drift, and through a money force model, of free accumulation with financial assets resistance. This work thus remarks in sum that money velocity as customarily calculated, taught and understood is not univocal.

Item Type: | MPRA Paper |
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Original Title: | Mechanical analyses and derivations of money velocity |

English Title: | Mechanical analyses and derivations of money velocity |

Language: | English |

Keywords: | Cambridge equation; equation of exchange; liquidity; money position; money velocity; quantity theory of money. |

Subjects: | A - General Economics and Teaching > A1 - General Economics > A12 - Relation of Economics to Other Disciplines B - History of Economic Thought, Methodology, and Heterodox Approaches > B5 - Current Heterodox Approaches > B59 - Other E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E21 - Consumption ; Saving ; Wealth E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E23 - Production E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E31 - Price Level ; Inflation ; Deflation E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E41 - Demand for Money E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E43 - Interest Rates: Determination, Term Structure, and Effects E - Macroeconomics and Monetary Economics > E5 - Monetary Policy, Central Banking, and the Supply of Money and Credit > E51 - Money Supply ; Credit ; Money Multipliers Z - Other Special Topics > Z0 - General > Z00 - General |

Item ID: | 110772 |

Depositing User: | Dr. Alessandro Saccal |

Date Deposited: | 23 Nov 2021 09:27 |

Last Modified: | 23 Nov 2021 09:27 |

References: | [1] Fisher I. (1911), “The purchasing power of money: its determination and relation to credit, interest and crises.”, The McMillan company. [2] Friedman M. (1956), “Studies in the quantity theory of money", University of Chicago press. [3] Hume D. (1752), “Political discourses”, Alexander Kincaid and Alexander Donaldson. [4] Humphrey T. (2004), “Alfred Marshall and the quantity theory of money”, History of economics eJournal. [5] Hunte K. (2012), “The equation of exchange: a derivation”, The American economist. [6] Keynes J. M. (1923), “A tract on monetary reform”, The McMillan company. [7] Marx K. (1867), “Das kapital: kritik der politischen oekonomie”, Verlag von Otto Meissner. [8] Mill J. S. (1848), “Principles of political economy with some of their applications to social philosophy”, John William Parker. [9] Monge Mora M. V. (2021), “A theorem on the marginal utility of money”, EconomíaUNAM. [10] Pigou A. C. (1917), “The value of money”, Quarterly journal of economics. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/110772 |