Both quantity theories, Cambridge and classical, attempt to express a relationship among the amount of goods produced, the price level, amounts of money, and how money moves.
Economists associated with Cambridge University, including Alfred Marshall, A.C. Pigou, and John Maynard Keynes (before he developed his own, eponymous school of thought) contributed to a quantity theory of money that paid more attention to money demand than the supply-oriented classical version.
The Cambridge economists argued that a certain portion of the money supply will not be used for transactions; instead, it will be held for the convenience and security of having cash on hand.
is exogenous, and k is fixed in the short run, the Cambridge equation is equivalent to the equation of exchange with velocity equal to the inverse of k: Monge (2021) [1] showed that the Cambridge equation comes from a Cobb-Douglas utility function, which demonstrates that, in classical quantity theory, money has diminishing marginal utility (then, inflation is a monetary phenomenon).
[3] Marshall recognized that k would be determined in part by an individual's desire to hold liquid cash.