Stock and flow

Economics, business, accounting, and related fields often distinguish between quantities which are stocks and those which are flows. A stock variable is measured at one specific time, and represents a quantity existing at that point in time, which may have been accumulated 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.

Stocks 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.


Accounting, finance, etc.:

"Stock"Possible units"Inflow(s)""Outflow(s)"Possible units
bank balanceeurosdeposits
withdrawalseuros per month
inventory of lumberboard feetincoming lumberoutgoing lumberboard feet per week
housing stockdollarshousing investmenthousing depreciationdollars per year
equity shareholdingsshares (of 'stock')purchases of sharessales of sharesshares per month

Other contexts:

"Stock"Possible units"Inflow(s)""Outflow(s)"Possible units
guests in a hotelpersonsguests arrivingguests leavingpersons per day
persons per year
water in bathtubliterswater pouring inwater draining outliters per second
waste in disposal sitetonsdumping wastedecay of wastetons per week
fuel tankgallonsrefuelingfuel consumptiongallons 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.


See also

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