Stock and flow

in the past. A "flow" variable is measured over an interval of time. Therefore a flow would be measured "per unit of time".

For example, U.S. nominal gross domestic product refers to a total number of dollars spent during a specific time period, such as a year. Therefore it is a flow variable. In contrast, the U.S. nominal capital stock is the total value, in dollars, of equipment, buildings, inventories, and other real assets in the U.S. economy. The diagram illustrates how the "stock" of capital currently available is increased by the "flow" of new investment and depleted by the "flow" of depreciation.

tocks and flows in accounting

Thus, a stock refers to the value of an asset at a balance date (or point in time), while a flow refers to the total value of transactions (sales or purchases, incomes or expenditures) during an accounting period. If the flow value of an economic activity is divided by the average stock value during an accounting period, we obtain a measure of the number of turnovers (or rotations) of a stock in that accounting period. Some accounting entries are normally always represented as a flow (e.g. profit or income), while others may be represented both as a stock or as a flow (e.g. capital).

A person or country might have stocks of money, financial assets, liabilities, wealth, real means of production, capital, and human capital (or labor power). Flow magnitudes besides those shown in the diagram include income, spending, saving, debt repayment, labor, or stocks averaged over a unit of time, such as the money in circulation per year.

More general uses

Stocks and flows also have natural meanings in many contexts outside of business and its related fields. Thus stocks and flows are the basic building blocks of system dynamics models. Jay Forrester originally referred to them as "levels" (for stocks) and "rates" (for flows).

A stock (or "level variable") in this broader sense is some entity that is accumulated over time by inflows and/or depleted by outflows. Stocks can only be changed via flows. Mathematically a stock can be seen as an accumulation or integration of flows over time - with outflows subtracting from the stock. Stocks typically have a certain value at each moment of time - e.g. the number of population at a certain moment.

A flow (or "rate") changes a stock over time. Usually we can clearly distinguish inflows (adding to the stock) and outflows (subtracting from the stock). Flows typically are measured over a certain interval of time - eg. the number of births over a day or month.

Examples

Accounting, finance, etc.:

"Stock"	Possible units	"Inflow(s)"	"Outflow(s)"	Possible units
bank balance	euros	deposits interest	withdrawals	euros per month
inventory of lumber	board feet	incoming lumber	outgoing lumber	board feet per week
housing stock	dollars	housing investment	housing depreciation	dollars per year
equity shareholdings	shares (of 'stock')	purchases of shares	sales of shares	shares per month

Other contexts:

"Stock"	Possible units	"Inflow(s)"	"Outflow(s)"	Possible units
guests in a hotel	persons	guests arriving	guests leaving	persons per day
population	persons	births immigration	deaths emigration	persons per year
water in bathtub	liters	water pouring in	water draining out	liters per second
waste in disposal site	tons	dumping waste	decay of waste	tons per week
fuel tank	gallons	refueling	fuel consumption	gallons per month

Calculus interpretation

If the quantity of some "stock" variable at time $,t,$ is $,Q(t),$, then the derivative $,frac\{dQ(t)\}\{dt\},$ is the "flow" of changes in the stock. Likewise, the "stock" is the integral of the "flow".

For example, if the capital stock $,K(t),$ is increased gradually over time by a flow of gross investment $,I^g(t),$ and decreased gradually over time by a flow of depreciation $,D(t),$, then the change in the capital stock is given by

$frac\{dK(t)\}\{dt\}\; =\; I^g(t)\; -\; D(t)\; =\; I^n(t)$

Here we used the notation $,I^n(t),$ to refer to net investment, which is defined as the difference between gross investment and depreciation.

References

* George W. Harrison (1987). "Stocks and flows," "The ", v. 4, pp. 506-09.

ee also

*Stock (disambiguation)
*Flow (disambiguation)
*Systems thinking
*System dynamics