This post is a follow-up on the ongoing theory line where previously I defined cash value.
The cash value equation [V=I/(P+C)] assumes no "errors of production." If the entire economy consists of 100 bags of popcorn for sale, and there are 100 dollars, each bag is worth about a dollar, or the value of the dollar is a bag of popcorn. If money supply shrinks by half, then one dollar can buy two bags of popcorn, assuming everybody with money wants them. If nobody is hungry, than those 100 bags of popcorn are worth nothing; we have an error of production. If someone puts grains of sand for sale at the beach, no reasonable person would buy what can be had for free, and again we have an error of production—except that sand is free to produce, so the only error would be the time anyone spends trying to sell it.
The price equation [$=(P+C)/I] assumes no "errors of pricing." Prices are whatever the seller decides to charge. If charges are too high, units go unsold; this is an error of pricing. If charges are too low, units are bought and resold on the market at a higher price; such would be generous but not an error. Money supply limits the prices that can be charged for all goods. If the sum of prices charged for all things exceeds the money supply, unsold inventory will start to build.
An error of pricing is to overcharge so that some units go unsold. To correct, remaining units must drop in price. If prices have to drop below the cost to make and sell the item, that would be an error of production. Both diminish the desirability of the inventory.
The core assumption in either equation is the price of the inventory of all goods is equivalent to the money supply, in terms of printed currency plus credit. In other words, the entire money supply is able to purchase all goods for sale.