Editing Stock and flow (section)

==Comparing stocks and flows==
{{Further|Dimensional analysis#Commensurability}}
Stocks and flows have different units and are thus not ''[[Commensurability (philosophy of science)|commensurable]]'' – they cannot be meaningfully ''compared, equated, added, or subtracted.'' However, one may meaningfully take ''ratios'' of stocks and flows, or multiply or divide them. This is a point of some confusion for some economics students, as some confuse taking ratios (valid) with comparing (invalid).

The ratio of a stock over a flow has units of (units)/(units/time) = time. For example, the [[debt to GDP ratio]] has units of years (as GDP is measured in, for example, dollars per year whereas debt is measured in dollars), which yields the interpretation of the debt to GDP ratio as "number of years to pay off all debt, assuming all GDP devoted to debt repayment".

The ratio of a flow to a stock has units 1/time.  For example, the [[velocity of money]] is defined as [[nominal GDP]] / nominal [[money supply]]; it has units of (dollars / year) / dollars = 1/year.

In [[dynamical system (definition)|discrete time]], the change in a stock variable from one point in time to another point in time one time unit later (the [[first difference]] of the stock) is equal to the corresponding flow variable per unit of time.  For example, if a country's stock of [[physical capital]] on January 1, 2010 is 20 machines and on January 1, 2011 is 23 machines, then the flow of [[net investment]] during 2010 was 3 machines per year.  If it then has 27 machines on January 1, 2012, the flow of net investment during 2010 and 2011 averaged <math>3 \tfrac{1}{2}</math> machines per year.

In [[Dynamical system (definition)|continuous time]], the [[time derivative]] of a stock variable is a flow variable.