The place to start is the macroeconomic equation of exchange. This is a tautology which states: M*V=P*Q. In words, the money supply times the velocity of money is equal to the general price level times the quantity of goods and services produced. For a given time period, each side of this equation represents the gross domestic product for the economy being analyzed. If you state this as a difference equation, you get dM*dV=dP*dQ, or the change in the money supply times the change in the velocity of money is equal to the change in the price level times the change in production (i.e. the change in GDP.) The great macroeconomic debates tend to range around whether and how these four variables change over time, and to what degree government can and/or should try to influence specific components.
Let's define and analyze these various components a little further. The first is M, or money supply. In order to think about money supply we need to define money first. Money is a technological innovation that allows for the conversion of an individual's productivity into a highly transportable and fungible form. It is an abstraction that allows the division of labor to become much more specialized and efficient than that which a barter system would ever produce. It is generally agreed that good money satisfies three conditions: it functions as a medium of exchange (it is accepted as payment for goods, services, and debts), it serves as a unit of account, and it is a store of value. As an aside, I think that the store of value attribute of "moneyness" becomes less and less important as information and transaction costs converge to zero. This is why I find concepts such as a "gold standard" of money to be unnecessarily restrictive. What is key is the free convertibility of fiat money into any commodity such that, if you like, you can put yourself on a gold standard or an oil standard or even a "stock standard" or a "house standard" or whatever you think will protect your purchasing power better than the full faith and credit of Uncle Sam. The price of any one good, even gold, is far too vulnerable to exogenous changes in demand and supply to base a currency system on its immutable price in said currency.
Now that we've defined money, we can talk about money supply. In the U.S., the supply of money denominated in dollars is controlled by the Federal Reserve using two basic tools. The first is the creation of physical currency, and the second is the establishment of a required reserve rate for lenders. I've inserted a few money supply pictures below. The first is the monetary base, commonly referred to as M0, which is physical currency and bank reserves. This is commonly referred to as "high powered money" because it has not yet been leveraged through our fractional-reserve banking system.
Note the fairly steady rise in reserves over time (I'm sure this would be pretty linear on a logarithmic scale) and the huge spike in just the past few months. The second picture is that of various other monetary aggregates that are officially measured. You should note that the bulk of the money supply is created by the banking system through loans. The amount of lending capacity is theoretically limited by the required reserve ratio of Federal Reserve member banks, currently set at 10%. This means that every dollar of currency and reserves created by the Federal Reserve has the theoretical potential to become 10 dollars of money supply. The broadest measure of the money supply currently compiled by the Federal Reserve is known as M2, which is currency+reserves+checking accounts+travelers checks+savings accounts+CDs under $100,000. The Federal Reseve stopped compiling M3 data a few years ago because it was very expensive to do so, and they felt that it conveyed little information beyond M2. You can see that M2 tends to be roughly 7-8 times the size of the currency base, and M3 tended to be roughly 10 times the currency base, indicating that the system generally creates about as much money as is statutorily allowed.
The next component of the equation of exchange is the velocity of money. This is simply a measure of the number of times that the money supply turns over for a given period. It is computed by dividing GDP by the monetary base. In the picture below, the monetary base is M2 from the above picture, and it shows that the velocity of money has had a mean of 1.67 over the past 100 years, and has ranged from a low of 1.15 to a high of 2.12.
The third component of the equation of exchange is the price level. It isn't really useful to think of the price of the "average good produced" by an economy since goods have such wide variation in value, so in practice we try to measure the change in the price level of a representative basket of goods over time. This is complicated because consumer preferences, technology, and quality of goods produced are all constantly changing, but economists have developed some fairly sophisticated methods to correct for these things. It is extremely important for whomever is responsible for managing the money supply to have a good handle on how the general price level is changing over time.
The final component of the equation of exchange is Q, or the quantity of production. Once again, it makes very little sense to think of the units of "product" produced because goods are so variable, so we tend to think of product in terms of dollars (which brings price level into the equation by definition). GDP is typically broken down into the following: GDP = Consumption + Investment + Government Spending + Net Exports. Note that we are only trying to measure the value of final goods produced, not every intermediate step in the chain of production. When we are trying to measure how real GDP (total productivity) has changed over time, we scale our nominal GDP number by our best estimate of the change in the price level over the given time period. Below is a graph of real and nominal GDP over time.
In the next post we'll be looking at the evolution of various schools of macro-economic thought through the lens of the equation of exchange. The elasticities of the four inputs to the equation will be key to the deflation discussion, along with increasing financial intermediation in directing productive activity, inter-temporal effects, the role of expectations in decision making, the danger of aggregating individual choices into something we call "demand" and a particular focus on the role of money as a unit of account.