To quantify the process of monetizing an economy ideally, let us examine a small closed economy (one with no imports or exports to another economy). This small closed economy has only two products and two producers. One producer grows apples and the other grows oranges. They each produce more than enough for their own consumption. They directly exchange one apple for one orange so they each may enjoy the fruits of their economy completely. These two producers desired to expand their quality of life by instituting a civil authority to establish things such as roads and police protection from criminals and instituted a civil government. They brought in an expert in the field to establish the government. The new Governor provided the desired services to the community, and, since what he provided was a service rather than a product, created currency to use to purchase apples and oranges from the producers. The value of his service was one apple and one orange per time period, the same time period in which the producers exchanged in barter their produce and received one unit of government service. The governor realized that his currency would be worthless to the economy after he had used it for the purchase and would be piling up at the producers and costly to continuously produce. So the Governor decided that his unit of currency should be used for all transactions. After he had created 2 units of currency, call them dollars, to purchase his first apple and orange he created two more to use for his next purchases at which time he would take the first two as payment for his services and created two more and gave one each to the two producers to use in their exchange of goods with each other. This provided the quantity of currency in the economy to allow one simultaneous exchange of goods and services in one time period using currency. Six dollars fully monetizes this economy.
Another producer wanted to enter the economy, a banana producer. All the existing participants had sufficient capacity to accommodate the new producer and the banana producer had sufficient capacity to supply his own needs for his product and the needs of the rest of the economy for his product. The economy welcomed the banana producer into the fold. The governor determined he would need to create six more dollars to integrate the new producer to full participation into the economy. Three dollars would be given to the banana producer to purchase an apple, an orange and a unit of government service. One dollar would be given to each of the three existing participants to purchase a banana. There are now 12 dollars in circulation which allows one simultaneous exchange of goods in the economy per time period.
Mathematically this relationship between currency and goods and services can be represented as:
MV = (GS)V
M=Money (or Currency), V=Velocity in exchanges per unit time, GS=Goods and Services
As demonstrated in the model, if velocity remains constant then quantity of goods and services exchanged in the time period must be matched exactly with the quantity of money exchanged in the time period.