The economy may be going to hell in a hand basket as bailout efforts have soured on main street and are met with ambivalence in Washington, but I'm determined to prove the cash-inventory equivalency. This relationship allows one to value the dollar (or any fiat currency) independent of comparisons with foreign currencies, and offers a precise model to explain pricing, and how it relates to monetary policy.
I see three strategies to substantiate the relationship that the total of all prices of all things for sale will self correct to be exactly equal to the money supply: 1. a mathematical proof, 2. a logical defense of the symmetry, or 3. an empirical summation of all things for sale and comparing that with the money supply. My math skills are probably insufficient for the first approach, and besides, we are dealing with diffuse and inexact values. Now, even if I were to have all the data to calculate inventory, and even if it were the same as the money supply, that might just be coincidence—although enough similarities, over a long enough time, and in enough different circumstances, might be regarded as a de facto proof.
But today I would like to consider the second approach: the logical argument, and to do so, let's start small. Let us examine the truism that purchases, at the level of an individual, cannot exceed his income. Purchases cannot exceed earnings.
Laugh, you do? Naive I am, you say? "Living in a cave, are you?" you ask, "born yesterday, perhaps?" Yes, I understand we have solvency problems from reckless credit, which only proves my point. Credit extended now consumes earnings in the future, be it your own, or the bank's in the case of default, or the taxpayer's in the case of bailouts. Repayment has to come from somewhere, it should come from the beneficiary of a loan, but if they do not pay, it will be diffused elsewhere on society. While credit allows one to leverage income over time, in a sustainable economy, purchases cannot exceed earnings.
Now let's expand "purchases cannot exceed earnings" to all of society. At the social level, I propose earnings equate with money supply. Money supply is the exact measurement of earnings across society since, excluding barter arrangements, money is the only unit of income. All paychecks taken from the money supply will go toward purchases or to savings. Purchases reflect earnings for the sellers. Earnings will pass quickly through some but settle with others; savings are still earnings, just money that is earned previously. Savings do not rest but will be lent out by banks. This consumes future earnings from the borrower as repayment, so credit balances with earnings over time. Whether money moves or stays it has been earned at some point. All earnings have to come out of the money supply. All money that enters the money supply is earned, even if it came as a lien on future earnings, or more cynically, came by virtue of having friends with a printing press. Printing money counts as "earning" it.
In a Venn diagram, with a money supply circle and earnings circle, the only part of the earnings circle that reaches outside money supply would be barter arrangements. If earned money, spent money, saved money, borrowed money, and printed money is all earned, then I see no money that does not fall within the earnings circle, other than unpaid debt to a bank that goes bankrupt and is not bailed out. The two circles are very close to being perfectly superimposed.
Let's turn to inventory. Inventory, here, is defined as the set of all goods available for purchase. The identity of inventory and actual purchases isn't quite as close. While purchases have to come from inventory, inventory can remain unsold. But the relationship of purchases to inventory is one of considerable overlap. In a sustainable economy all inventory eventually has to be sold.
So, extending the statement: "purchases cannot exceed earnings" to all society, we can almost say "inventory cannot exceed money supply." It can—if sellers overprice their items. But then sales velocity slows, and unsold inventory accumulates. Production must be slowed or prices lowered such that the item sells, otherwise producers and sellers will not be compensated and will stop producing it.
So, the cash-inventory equivalency is defended on the grounds that purchases can never exceed earnings in a sustainable economy (where purchases equate with inventory and earnings with money supply at the social level). Purchases can equal earnings though, so to maximize profits sellers will price their wares to that effect.