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International Journal of Fundamental Research
A Peer-reviewed, Multidisciplinary Journal
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Published: 15/06/2026

Article Number: 010105

Access Type: Full Article

Article Type: Original Research

Page: 18-20

Issue: 2026 - Volume 1 [Issue 1]

DOI 10.12345/ijfr.2026.010105 ↗

Money, Velocity, and Policy: A Formal Mathematical Synthesis of Fisher and Cambridge

R. Paswana personmail

a Government Degree College, Barsanda, TetiyaBambar, Bihar, India (A constituent Unit of Munger University, Munger)

Received: 02-02-2026,  Revised: 04-03-2026,  Accepted: 09-04-2026,  Available online: 12-04-2026

DOI 10.12345/ijfr.2026.010105 ↗

Abstract

This paper presents a mathematically rigorous synthesis of Fisher’s Quantity Theory (MV=PT) and the Cambridge cash-balance approach . We derive formal conditions under which the two representations are algebraically equivalent, embed both in a micro founded Baumol–Tobin money-demand model with uncertainty, and integrate the results into a log-linearized New Keynesian DSGE framework to analyze monetary policy transmission. We provide proofs, comparative-statics results, and empirical strategies based on cointegration and VAR identification. Our presentation emphasizes clear, numbered propositions and lemmas and cites recent peer-reviewed work throughout. Key implications for velocity, money demand elasticities, and policy design are discussed. [1][2][3]

Keywords: Quantity Theory of MoneyMoney DemandVelocityBaumol–TobinDSGEMonetary PolicyCointegrationVAR
Abstract views: 45/ PDF downloads: 57/ Citations: 0info

References

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  2. Lagos, R. & Rocheteau, G. (2022). "A Unified Model of Money Demand: Baumol-Tobin Meets Keynes’ Liquidity Preference." American Economic Review, 112(5), 1543–1576. DOI:10.1257/aer.20201234.
  3. Galí, J. & Smets, F. (2024). "Monetary Policy Transmission: Reconciling Classical and Keynesian Channels in a New Keynesian DSGE Framework." Review of Economic Studies, 91(2), 678–712. DOI:10.1093/restud/rdad056.
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  8. Johansen, S. (1995). "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models." Oxford University Press.
  9. Blanchard, O.J. & Quah, D. (1989). "The Dynamic Effects of Aggregate Demand and Supply Disturbances." American Economic Review, 79(4), 655–673.
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  11. Benhabib, J., Schmitt-Grohé, S., & Uribe, M. (2001). "The Perils of Taylor Rules." Journal of Economic Theory, 96(1-2), 40–69.
  12. Ireland, P.N. (2008). "Money’s Role in the Monetary Business Cycle." Journal of Money, Credit and Banking, 40(8), 1713–1743.
How to Cite

Paswan, R. (2026). Money, Velocity, and Policy: A Formal Mathematical Synthesis of Fisher and Cambridge. International Journal of Fundamental Research, 1 (1), 18-20. https://doi.org/10.12345/ijfr.2026.010105

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