# Stock and flow

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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 depositsinterest 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 birthsimmigration deathsemigration 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 $,Q\left(t\right),$, then the derivative $,frac\left\{dQ\left(t\right)\right\}\left\{dt\right\},$ is the "flow" of changes in the stock. Likewise, the "stock" is the integral of the "flow".

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

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

Here we used the notation $,I^n\left(t\right),$ 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

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